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Jun 2003

Volume 15, Issue 6, pp. L41-L48, 1357-1817

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Spectra of the very large anisotropic scales in turbulent channels

Juan C. del Álamo and Javier Jiménez

Phys. Fluids 15, L41 (2003); http://dx.doi.org/10.1063/1.1570830 (4 pages) | Cited 69 times

Online Publication Date: 23 April 2003

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The spectra of numerically simulated channels at Reτ = 180 and Reτ = 550 in very large boxes are described and analyzed. They support a model in which the u-structures can be decomposed in two components. The first one is formed by structures of size λx≳5 h, λz ≈ 2 h, which span most of the channel height, and penetrate into the buffer layer. The second one has maximum intensity in the near-wall region, where it is highly anisotropic and scales in inner units. It widens, lengthens, and becomes more isotropic in the outer layer, where it scales with h. The cospectrum exhibits an analogous quasi-isotropic range, whose width grows linearly with wall distance. At the present Reynolds numbers, nothing can be said about a possible streamwise similarity, due to limited scale separation. An extensive set of statistics from the simulations is downloadable from ftp://torroja.dmt.upm.es/channels. © 2003 American Institute of Physics.
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47.27.-i Turbulent flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics

Flow induced patterning at the air–water interface

R. Miraghaie, J. M. Lopez, and A. H. Hirsa

Phys. Fluids 15, L45 (2003); http://dx.doi.org/10.1063/1.1572163 (4 pages) | Cited 8 times

Online Publication Date: 6 May 2003

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Patterns on the air–water interface of a swirling cylinder flow are produced via hydrodynamic symmetry-breaking instability of the bulk flow. The patterns are rotating waves breaking the axisymmetry of the system and are longitudinal at the free surface (i.e., not surface deforming). Qualitative observations and quantitative measurements of velocity and vorticity are provided. Three-dimensional Navier–Stokes computations identify the symmetry-breaking mode responsible for the waves. These waves are then used to pattern Langmuir monolayers at concentrations sufficiently below saturation. © 2003 American Institute of Physics.
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47.32.-y Vortex dynamics; rotating fluids
47.10.-g General theory in fluid dynamics
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A molecular dynamics study of drop spreading on a solid surface

Xuhong Wu, Nhan Phan-Thien, Xi-Jun Fan, and Teng Yong Ng

Phys. Fluids 15, 1357 (2003); http://dx.doi.org/10.1063/1.1566751 (6 pages) | Cited 3 times

Online Publication Date: 17 April 2003

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In this paper, the effects of size of the chains composed of the drop and initial velocity of the drop on the drop terraced spreading are studied. The chain size effects on the base radius of drop are studied at zero initial velocity. A logarithm dependence of the drop base radius on the time is found for 2-atom to 16-atom flexible chain systems with large lattice dimension of solid and a power law t1/2 for small lattice dimension of solid. The longer the chain, the slower is the spreading. With a nonzero initial velocity, the drop base radius increases with increasing initial velocity before the drop splits into smaller separated drops. As the initial velocity increases, the transition from a logarithm to a power law t1/2 relation for the time dependence of the drop base radius is first noted here. © 2003 American Institute of Physics.
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68.08.Bc Wetting
71.15.Pd Molecular dynamics calculations (Car-Parrinello) and other numerical simulations

Contact line instability and pattern selection in thermally driven liquid films

Roman O. Grigoriev

Phys. Fluids 15, 1363 (2003); http://dx.doi.org/10.1063/1.1566958 (12 pages) | Cited 11 times

Online Publication Date: 17 April 2003

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Liquids spreading over a solid substrate under the action of various forces are known to exhibit a long wavelength contact line instability. We use an example of thermally driven spreading on a horizontal surface to study how the stability of the flow can be altered, or patterns selected, using feedback control. We show that thermal perturbations of certain spatial structure imposed behind the contact line and proportional to the deviation of the contact line from its mean position can completely suppress the instability. Due to the presence of mean flow and a spatially nonuniform nature of spreading liquid films the dynamics of disturbances is governed by a non-normal evolution operator, opening up a possibility of transient amplification and nonlinear instabilities. We show that in the case of thermal driving the non-normality can be significant, especially for small wavenumber disturbances, and trace the origin of transient amplification to a close alignment of a large group of eigenfunctions of the evolution operator. However, for values of noise likely to occur in experiments we find that the transient amplification is not sufficiently strong to either change the predictions of the linear stability analysis or invalidate the proposed control approach. © 2003 American Institute of Physics.
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68.08.Bc Wetting
68.15.+e Liquid thin films
47.54.-r Pattern selection; pattern formation
47.20.-k Flow instabilities
02.10.Ud Linear algebra
47.85.L- Flow control
47.45.Gx Slip flows and accommodation

A model for the mixing time scale of a turbulent reacting scalar

Chong M. Cha and Philippe Trouillet

Phys. Fluids 15, 1375 (2003); http://dx.doi.org/10.1063/1.1565333 (6 pages) | Cited 13 times

Online Publication Date: 17 April 2003

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Current micromixing models in transported PDF (probability density function equation) modeling of initially nonpremixed, turbulent reacting flows ignore the direct influence of chemistry on the dissipation rate of reacting scalar fluctuations. Following mapping closure, a model for the time scale of reactive scalar mixing in the flamelet regime is developed and comparisons made with direct numerical simulations of a turbulent reacting jet. The modeling results show a significant improvement over the generally used estimate of substituting the time scale of the reacting scalar by that of a conserved scalar in traditional transported PDF approaches. The model can readily be applied to many existing mixing submodels used in transported PDF modeling when the time scales of the reacting scalars appear explicitly in the formulation. The submodels allow the transported PDF approach to now encompass the fast as well as slow chemistry regimes. © 2003 American Institute of Physics.
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47.27.-i Turbulent flows
47.70.Fw Chemically reactive flows
47.11.-j Computational methods in fluid dynamics
47.27.wg Turbulent jets

Shape-preserving solutions for quantum vortex motion under localized induction approximation

Tomasz Lipniacki

Phys. Fluids 15, 1381 (2003); http://dx.doi.org/10.1063/1.1566756 (15 pages) | Cited 3 times

Online Publication Date: 17 April 2003

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The motion of a quantum vortex in superfluid helium is considered in the localized induction approximation. In this approximation the instantaneous velocity of quantum vortex is proportional to the local curvature and is parallel to the vector, which is a linear combination of the local binormal and the principal normal to the vortex line. The motion in the direction of the principal normal is specific for a quantum vortex and implies that the vortex shrinks, in contrast to the classical vortex in an ideal fluid. In the present work we deal with two four-parameter classes of shape-preserving solutions (one with increasing and one with decreasing spatial scale) resulting from equations governing the curvature and the torsion. The solutions describe vortex lines whose motion is equivalent to a transformation being a superposition of a homothety and a rotation. In a particular case when the transformation is a pure homothety, we find analytic solutions for the curvature and the torsion. In the general case, when the transformation is a superposition of a nontrivial rotation and a homothety, the asymptotics of the solutions of the first class are given explicitly and are related to the parameters characterizing the transformation. It is found that the solutions of the second class (with decreasing scale) either have asymptotes or are periodic (when the transformation is a pure homothety) or else exhibit chaotic behavior. © 2003 American Institute of Physics.
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67.25.dk Vortices and turbulence
47.32.C- Vortex dynamics
47.52.+j Chaos in fluid dynamics

Power laws for rough wall turbulent boundary layers

N. A. Kotey, D. J. Bergstrom, and M. F. Tachie

Phys. Fluids 15, 1396 (2003); http://dx.doi.org/10.1063/1.1565334 (9 pages) | Cited 8 times

Online Publication Date: 29 April 2003

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An assessment of the ability of power laws to describe the mean velocity profile in the overlap region of a zero pressure gradient turbulent boundary layer is reported. The experiments were performed in a wind tunnel on smooth and four different types of rough surfaces at moderate Reynolds numbers. A novel modification to the power law velocity profile is proposed to account for the effect of surface roughness in the overlap region. This modification is analogous to the use of a roughness function to produce a downward shift in the logarithmic velocity profile. The roughness parameters in the proposed equation more accurately follow the effect of roughness on skin friction than does the roughness shift ΔU+. The present study shows that power laws can be used to effectively describe the mean velocity profile over a wider range than a log law for both smooth and rough surfaces. © 2003 American Institute of Physics.
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47.27.nb Boundary layer turbulence
68.08.-p Liquid-solid interfaces
47.11.-j Computational methods in fluid dynamics
47.20.Dr Surface-tension-driven instability

Bifurcation of and ghost effect on the temperature field in the Bénard problem of a gas in the continuum limit

Yoshio Sone and Toshiyuki Doi

Phys. Fluids 15, 1405 (2003); http://dx.doi.org/10.1063/1.1567718 (19 pages) | Cited 8 times

Online Publication Date: 2 May 2003

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See Also: Erratum

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A gas in a time-independent state under a uniform weak gravity in a general domain is considered. The asymptotic behavior of the gas in the limit that the Knudsen number of the system tends to zero (or in the continuum limit) is investigated on the basis of the Boltzmann system for the case where the flow velocity vanishes in this limit, and the fluid-dynamic-type equations and their associated boundary conditions describing the behavior of the gas in the continuum limit are derived. The equations, different from the Navier–Stokes ones, contain thermal stress and infinitesimal velocity amplified by the inverse of the Knudsen number. The system is applied to analysis of the behavior of a gas between two parallel plane walls heated from below (Bénard problem), and a bifurcated strongly distorted temperature field is found in infinitesimal velocity and gravity. This is an example showing that the Navier–Stokes system fails to describe the correct behavior of a gas in the continuum limit. © 2003 American Institute of Physics.
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51.10.+y Kinetic and transport theory of gases
47.27.T- Turbulent transport processes
47.40.-x Compressible flows; shock waves
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
44.15.+a Channel and internal heat flow
47.11.-j Computational methods in fluid dynamics

Control of aeolian tones radiated from a circular cylinder in a uniform flow

Osamu Inoue, Masaaki Mori, and Nozomu Hatakeyama

Phys. Fluids 15, 1424 (2003); http://dx.doi.org/10.1063/1.1571546 (18 pages) | Cited 4 times

Online Publication Date: 2 May 2003

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Effects of artificial forcing on the generation and propagation mechanisms of the sound generated by a circular cylinder in a uniform flow are investigated by direct solution of the two-dimensional, unsteady, compressible Navier–Stokes equations. Two types of forcing are considered: rotation of the cylinder at a constant angular velocity and periodic blowing/suction from the (nonrotating) cylinder surface. For the case of a rotating cylinder, results show that the sound generation can be controlled by controlling the periodic shedding of (Kármán) vortices from the cylinder surface into its wake. On the other hand, results for the case of periodic blowing/suction show that the generation and propagation of the sound can be effectively controlled without drastic changes of the vortex shedding. It is found in this case that the interactions among the lift dipole (which is generated by the vortex shedding), the drag dipole and the monopole (both of which are generated by the periodic blowing/suction) play a principal role in the control process of the generation and propagation of the sound. © 2003 American Institute of Physics.
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47.27.Sd Turbulence generated noise
47.40.-x Compressible flows; shock waves
47.32.C- Vortex dynamics
47.27.wb Turbulent wakes

Stochastic simulations of buoyancy-reversal experiments

Scott Wunsch

Phys. Fluids 15, 1442 (2003); http://dx.doi.org/10.1063/1.1572160 (15 pages) | Cited 5 times

Online Publication Date: 2 May 2003

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Buoyancy reversal occurs when the mixing of two fluids, initially stably stratified, produces a mixture which is more dense than either pure fluid. The resulting instability generates turbulent mixing, and may play an important role in geophysical and astrophysical flows. In this work, a stochastic one-dimensional model is used to simulate these systems. Model validation is accomplished using experimental comparisons. Scalings inferred from the model simulations are used to suggest extrapolations from experimental results to natural systems. © 2003 American Institute of Physics.
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47.27.-i Turbulent flows
47.11.-j Computational methods in fluid dynamics

Cavitation luminescence in a water hammer: Upscaling sonoluminescence

C.-K. Su, C. Camara, B. Kappus, and S. J. Putterman

Phys. Fluids 15, 1457 (2003); http://dx.doi.org/10.1063/1.1572493 (5 pages) | Cited 14 times

Online Publication Date: 2 May 2003

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Oscillatory acceleration and deceleration of a column of water leads to a pipe hammer as well as cavitation. With a small amount of xenon gas dissolved in the water, we can detect a stream of predominantly ultraviolet subnanosecond flashes of light which are attributed to collapsing bubbles. The observed emission can exceed 108 photons for a single collapse and has a peak power over 0.4 W. © 2003 American Institute of Physics.
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47.55.dp Cavitation and boiling
43.35.Hl Sonoluminescence
47.55.D- Drops and bubbles
78.60.Mq Sonoluminescence, triboluminescence

Direct numerical simulation of stagnation region flow and heat transfer with free-stream turbulence

Sungwon Bae, Sanjiva K. Lele, and Hyung Jin Sung

Phys. Fluids 15, 1462 (2003); http://dx.doi.org/10.1063/1.1565332 (23 pages) | Cited 4 times

Online Publication Date: 2 May 2003

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A direct numerical simulation is performed for stagnation-region flow with free-stream turbulence. A fully implicit second-order time-advancement scheme with fourth-order finite differences and an optimized scheme are employed. The optimized scheme is developed to save computational cost. The free-stream turbulence is a precomputed field of isotropic turbulence. The present DNS results in the “damping” and “attached amplifying” regimes are found to be similar to those of the organized inflow disturbances. Emphasis is placed on the flow and temperature fields in the “detached amplifying” regime. The contours of instantaneous flow field illustrate that streamwise vortices are stretched in the streamwise direction by mean strain rate. The temperature field is also stretched in the streamwise direction near the wall. The surface contours reveal that the temperature field is influenced significantly by streamwise vorticity. Due to the dominance of the mean strain, the log-law region is not observed for ū and math, the inner scaling fails, but the outer scaling works. The single-point turbulence statistics and the turbulent statistics budgets are obtained. The flow statistics reflect the typical characteristics of stagnation-region flow which are generically different from those of other canonical shear flows. One of the typical features of the budgets is that the velocity pressure correlation and the turbulent transport play significant roles in the stagnation-region flow. Finally, the present simulation data are compared with experimental results. It is found that the effect of large-scale eddies on the enhancement of wall heat transfer is substantial in the turbulent stagnation-region heat transfer. © 2003 American Institute of Physics.
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47.11.-j Computational methods in fluid dynamics
47.27.-i Turbulent flows
47.32.C- Vortex dynamics
47.27.T- Turbulent transport processes
02.70.Bf Finite-difference methods

Exact self-similarity solution of the Navier–Stokes equations for a porous channel with orthogonally moving walls

Eric C. Dauenhauer and Joseph Majdalani

Phys. Fluids 15, 1485 (2003); http://dx.doi.org/10.1063/1.1567719 (11 pages) | Cited 23 times

Online Publication Date: 2 May 2003

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This article describes a self-similarity solution of the Navier–Stokes equations for a laminar, incompressible, and time-dependent flow that develops within a channel possessing permeable, moving walls. The case considered here pertains to a channel that exhibits either injection or suction across two opposing porous walls while undergoing uniform expansion or contraction. Instances of direct application include the modeling of pulsating diaphragms, sweat cooling or heating, isotope separation, filtration, paper manufacturing, irrigation, and the grain regression during solid propellant combustion. To start, the stream function and the vorticity equation are used in concert to yield a partial differential equation that lends itself to a similarity transformation. Following this similarity transformation, the original problem is reduced to solving a fourth-order differential equation in one similarity variable η that combines both space and time dimensions. Since two of the four auxiliary conditions are of the boundary value type, a numerical solution becomes dependent upon two initial guesses. In order to achieve convergence, the governing equation is first transformed into a function of three variables: The two guesses and η. At the outset, a suitable numerical algorithm is applied by solving the resulting set of twelve first-order ordinary differential equations with two unspecified start-up conditions. In seeking the two unknown initial guesses, the rapidly converging inverse Jacobian method is applied in an iterative fashion. Numerical results are later used to ascertain a deeper understanding of the flow character. The numerical scheme enables us to extend the solution range to physical settings not considered in previous studies. Moreover, the numerical approach broadens the scope to cover both suction and injection cases occurring with simultaneous wall motion. © 2003 American Institute of Physics.
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47.15.-x Laminar flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.10.-g General theory in fluid dynamics
47.56.+r Flows through porous media

A subgrid-scale mixing model for large-eddy simulations of turbulent reacting flows using the filtered density function

Chong M. Cha and Philippe Trouillet

Phys. Fluids 15, 1496 (2003); http://dx.doi.org/10.1063/1.1569920 (9 pages) | Cited 17 times

Online Publication Date: 2 May 2003

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The filtered density function approach [Colucci et al., Phys. Fluids 10, 499 (1999); Jaberi et al., J. Fluid Mech. 401, 85 (1999)] for large-eddy simulations of initially nonpremixed turbulent reacting flows is extended to encompass the flamelet regime. This is done by developing a model which describes the effect of realistic, Arrhenius chemical kinetics on the subgrid mixing time scale for reactive scalars. The model is based on mapping closure and flamelet modeling and can readily be applied to many existing micro-mixing models where the time scales of the reacting scalars appear explicitly in the formulation. Testing of the model using spatially filtered direct numerical simulation data of a turbulent reacting jet [Boersma, Center for Turbulence Research Annual Research Briefs (Stanford University/NASA Ames, 1999), pp. 59–72] show a significant improvement over the generally used estimate of substituting the time scale of the reacting scalars by that of a conserved scalar. The impact of internal intermittency on the performance of the new model is discussed. © 2003 American Institute of Physics.
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47.70.Fw Chemically reactive flows
47.27.E- Turbulence simulation and modeling
47.11.-j Computational methods in fluid dynamics
47.27.Gs Isotropic turbulence; homogeneous turbulence
47.27.wg Turbulent jets
82.40.-g Chemical kinetics and reactions: special regimes and techniques

On the optimization of mixing protocol in a certain class of three-dimensional Stokes flows

A. J. S. Rodrigo, J. P. B. Mota, A. Lefèvre, and E. Saatdjian

Phys. Fluids 15, 1505 (2003); http://dx.doi.org/10.1063/1.1572492 (12 pages) | Cited 10 times

Online Publication Date: 2 May 2003

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Mixing in a special class of three-dimensional, non-inertial periodic flows is studied numerically. In the type of flow considered here, the cross-sectional velocity components are independent of the axial flow and the axial flow is independent of the axial coordinate. Using the eccentric helical annular mixer as a prototype, we consider the counter-rotating case with steady rotation of the outer cylinder and sinusoidal modulation of the inner one. Apart from the mixer geometry, the behavior of the system is governed by two dimensionless parameters obtained by scaling the cross-sectional stirring protocol with respect to the characteristic residence time of the fluid in the mixer. The first parameter is related to the average number of turns of the outer cylinder and the second one is related to the average number of modulation periods of the inner cylinder. The convection-diffusion equation is solved numerically, with temperature as a passive scalar, at high Péclet number. For a given three-dimensional mixer geometry and axial flow rate we show that there is an optimum modulation frequency for which the exit standard deviation of the temperature field is a minimum. Lagrangian simulations at infinite Péclet number and the use of other tools to study mixing, such as stretching calculations and tracer tracking methods, confirm that the optimized protocol does result in very effective mixing. © 2003 American Institute of Physics.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
64.75.-g Phase equilibria
05.60.-k Transport processes
66.10.C- Diffusion and thermal diffusion

Homotopy of exact coherent structures in plane shear flows

Fabian Waleffe

Phys. Fluids 15, 1517 (2003); http://dx.doi.org/10.1063/1.1566753 (18 pages) | Cited 68 times

Online Publication Date: 2 May 2003

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Three-dimensional steady states and traveling wave solutions of the Navier–Stokes equations are computed in plane Couette and Poiseuille flows with both free-slip and no-slip boundary conditions. They are calculated using Newton’s method by continuation of solutions that bifurcate from a two-dimensional streaky flow then by smooth transformation (homotopy) from Couette to Poiseuille flow and from free-slip to no-slip boundary conditions. The structural and statistical connections between these solutions and turbulent flows are illustrated. Parametric studies are performed and the parameters leading to the lowest onset Reynolds numbers are determined. In all cases, the lowest onset Reynolds number corresponds to spanwise periods of about 100 wall units. In particular, the rigid-free plane Poiseuille flow traveling wave arises at Reτ = 44.2 for Lx+ = 273.7 and Lz+ = 105.5, in excellent agreement with observations of the streak spacing. A simple one-dimensional map is proposed to illustrate the possible nature of the “hard” transition to shear turbulence and connections with the unstable exact coherent structures. © 2003 American Institute of Physics.
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47.27.nb Boundary layer turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.10.-g General theory in fluid dynamics
47.45.Gx Slip flows and accommodation

Two-way coupling simulations of instabilities in a plane bubble plume

Ophélie Caballina, Eric Climent, and Jan Dušek

Phys. Fluids 15, 1535 (2003); http://dx.doi.org/10.1063/1.1566754 (10 pages) | Cited 5 times

Online Publication Date: 2 May 2003

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In the present study we aim at investigating the instabilities in a plane bubble plume by means of two-way coupling simulations. The continuous phase motion is obtained by direct numerical solution of the Navier–Stokes equations forced by the presence of the bubbles. The collective effects induced by the presence of the bubbles are modeled by a spatiotemporal distribution of momentum. Time evolution of the dispersed phase is solved by Lagrangian tracking of all the bubbles. In the present study, the motion of the carrying fluid is initiated and driven by the induced buoyancy of bubbles released from a source located in an initially quiescent fluid layer. A quantitative analysis of the flow transition is thus investigated for several plume widths and for various fluid viscosities over a range of Grashof numbers based on the injection conditions. An analogy is drawn with buoyant single-phase flows for the steady laminar region. Following the similarity formulation of Fujii [Int. J. Heat Mass Transfer 6, 597 (1963)] under boundary layer approximations for free thermal plumes, the velocity profiles can be collapsed to a single self-similar plot. Nevertheless, this analogy with single-phase flow shows some discrepancies in the description of the transition. Numerical data emphasize that the key parameter controlling the height of transition is the Grashof number, which is based on injection conditions of the dispersed phase. Our results concur with the recent experiments of Alam and Arakeri [J. Fluid Mech. 254, 363 (1993)]. Although the Grashof number also determines the transition in thermal plumes [Wakitani and Yosinobu, Fluid Dyn. Res. 2, 363 (1988)], the two-phase configuration is more unstable. These new results underline the important role played by the slip velocity of the bubbles in plume stability. Indeed, it tends to delay the plume transition when the slip velocity increases and approaches the buoyancy-induced velocity. This feature should also be related to the lack of diffusion by the bubble cloud in the Lagrangian transport of the density gradient. © 2003 American Institute of Physics.
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47.55.D- Drops and bubbles
47.55.Kf Particle-laden flows
47.27.Cn Transition to turbulence
47.45.Gx Slip flows and accommodation
47.15.Fe Stability of laminar flows
47.11.-j Computational methods in fluid dynamics
47.27.nb Boundary layer turbulence
47.10.-g General theory in fluid dynamics

Capillary rise in nesting cylinders

Victor Brady, Paul Concus, and Robert Finn

Phys. Fluids 15, 1545 (2003); http://dx.doi.org/10.1063/1.1566449 (7 pages) | Cited 1 time

Online Publication Date: 5 May 2003

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We investigate computationally recent results concerning the question of whether liquid necessarily rises higher in a capillary tube of smaller section, when tubes are placed vertically in an infinite reservoir. The numerical results corroborate for a particular example a striking discontinuous behavior that was predicted mathematically. © 2003 American Institute of Physics.
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68.03.Kn Dynamics (capillary waves)
47.60.-i Flow phenomena in quasi-one-dimensional systems

An extension of generalized Taylor dispersion in unbounded homogeneous shear flows to run-and-tumble chemotactic bacteria

R. N. Bearon

Phys. Fluids 15, 1552 (2003); http://dx.doi.org/10.1063/1.1569482 (12 pages) | Cited 9 times

Online Publication Date: 5 May 2003

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In the absence of flow, the biased random walk of bacteria such as Escherichia coli is modeled by straight runs punctuated by random changes in direction, tumbles. We model chemotaxis by allowing the tumble rate of a run to depend on the component of swimming velocity in the direction of the chemoattractant gradient. In the well-studied situation of weak bias in tumble rate, bacteria disperse over a diffusive time scale, and the evolution of density satisfies the classic Keller–Segel advection-diffusion equation. In this paper, we model swimming bacteria being advected and rotated by an unbounded homogeneous shear flow. The flow field alters the trajectories of individuals and thus affects the macroscopic dispersion of a population. We adapt the formal framework of generalized Taylor dispersion theory to make it applicable for run-and-tumble bacteria with an arbitrary bias in tumble rate. This enables us to obtain a macroscopic description of the dispersion of bacteria. For the particular case of simple shear flow, we calculate explicitly the effect of flow on the diffusion tensor and mean swimming velocity. © 2003 American Institute of Physics.
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87.15.Vv Diffusion
87.10.-e General theory and mathematical aspects
47.27.nb Boundary layer turbulence
47.27.T- Turbulent transport processes
05.40.Fb Random walks and Levy flights

Laminar flamelet decomposition for conditional source-term estimation

W. Kendal Bushe and Helfried Steiner

Phys. Fluids 15, 1564 (2003); http://dx.doi.org/10.1063/1.1569483 (12 pages) | Cited 8 times

Online Publication Date: 5 May 2003

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A new decomposition approach to conditional source-term estimation (CSE) is proposed and discussed. The new approach is tested in the a priori sense using direct numerical simulations (DNS). It is found that—where CSE had previously been found to provide closure for chemical source-terms with arbitrary chemistry in the large eddy simulation paradigm—it can provide this closure in the Reynolds averaged Navier–Stokes paradigm as well. Using the proposed decomposition improves the predictions of CSE considerably. Only the assumptions that gradients in conditional averages are small and that the probability density function of mixture fraction can be adequately approximated using a presumed functional form are needed. The computational cost of the new laminar flamelet decomposition approach to CSE is also substantially lower than that of the original approach. © 2003 American Institute of Physics.
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82.33.Vx Reactions in flames, combustion, and explosions
47.70.Fw Chemically reactive flows
47.15.Fe Stability of laminar flows
47.55.Kf Particle-laden flows
47.10.-g General theory in fluid dynamics
47.11.-j Computational methods in fluid dynamics

Transient and steady-state amplitudes of forced waves in rectangular basins

D. F. Hill

Phys. Fluids 15, 1576 (2003); http://dx.doi.org/10.1063/1.1569917 (12 pages) | Cited 14 times

Online Publication Date: 5 May 2003

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A weakly-nonlinear analysis of the transient evolution of two-dimensional, standing waves in a rectangular basin is presented. The waves are resonated by periodic oscillation along an axis aligned with the wavenumber vector. The amplitude of oscillation is assumed to be small with respect to the basin dimensions. The effects of detuning, viscous damping, and cubic nonlinearity are all simultaneously considered. Moreover, the analysis is formulated in water of general depth. Multiple-scales analysis is used in order to derive an evolution equation for the complex amplitude of the resonated wave. From this equation, the maximum transient and steady-state amplitudes of the wave are determined. It is shown that steady-state analysis will underestimate the maximum response of a basin set into motion from rest. Amplitude response diagrams demonstrate good agreement with previous experimental investigations. The analysis is invalid in the vicinity of the “critical depth” and in the shallow-water limit. A separate analysis, which incorporates weak dispersion, is presented in order to provide satisfactory results in shallow water. © 2003 American Institute of Physics.
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47.35.-i Hydrodynamic waves
47.60.-i Flow phenomena in quasi-one-dimensional systems

On the measurement of “tack” for adhesives

Mahesh Tirumkudulu, William B. Russel, and T. J. Huang

Phys. Fluids 15, 1588 (2003); http://dx.doi.org/10.1063/1.1571058 (18 pages) | Cited 25 times

Online Publication Date: 5 May 2003

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One of the tests for determining the bond strength of adhesives involves measuring the force or the work required to pull apart two surfaces separated by a thin film of adhesive. The pull-off force is measured via the bending of a cantilever that connects one of the surfaces to a motor controlled vertical traverse. Although such tests are routinely performed, little attention has been paid to the understanding of force measurements and their relation to the dynamics of the instrument. Specifically, the measured force versus gap profile for the pull-off process is different from that measured when the same adhesive is compressed between two approaching surfaces. Through experiments on Newtonian liquids and a simple analysis involving lubrication analysis of thin liquid films, we show that the hysteresis in measurements results from a combination of an instrument-related instability and the nucleation and collapse of cavitation bubbles in the flow field. © 2003 American Institute of Physics.
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46.55.+d Tribology and mechanical contacts
81.40.Pq Friction, lubrication, and wear
47.55.dp Cavitation and boiling
47.55.D- Drops and bubbles

Ponomarenko dynamo with time-periodic flow

Christiane Normand

Phys. Fluids 15, 1606 (2003); http://dx.doi.org/10.1063/1.1571547 (6 pages) | Cited 11 times

Online Publication Date: 5 May 2003

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The Ponomarenko dynamo theory is revisited to take into account time-dependent flows. Our purpose is to investigate how a small departure from a steady flow can modify the onset of dynamo action. We consider a typical helical flow when the velocity components are modulated in time at the same frequency and with a small modulation amplitude of the order ε. Using ε as an expansion parameter we calculated the shift in the critical magnetic Reynolds number and the shift in frequency at dynamo onset. We found that modulation can either lower or enhance the threshold of dynamo action depending on ε1, the relative amplitude of modulation of the azimuthal and axial velocity components. More specifically, in-phase modulation with 0.7 ⩽ ε1 ⩽ 1 delays the onset of dynamo action, while in a larger range including out-of-phase modulation, −1 ⩽ ε1<0.7, low-frequency forcing promotes dynamo action. © 2003 American Institute of Physics.
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84.50.+d Electric motors

Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state

Cyrus K. Aidun and E-Jiang Ding

Phys. Fluids 15, 1612 (2003); http://dx.doi.org/10.1063/1.1571825 (10 pages) | Cited 7 times

Online Publication Date: 5 May 2003

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The dynamics and interaction of two circular cylinders settling in an infinitely long narrow channel (width equal to four times the cylinder diameter) is explained by direct computational analysis. The results show that at relatively low Reynolds numbers (based on the average particle velocity and diameter), the particles undergo complex transitions to reach a low-dimensional chaotic state represented by a strange attractor. As the Reynolds number increases, the initial periodic state goes through a turning point and a subcritical transition to another periodic branch. Further increase in the Reynolds number results in a cascade of period-doubling bifurcations to a chaotic state represented by a low dimensional chaotic attractor. The entire sequence of transitions takes place in a relatively narrow range of Reynolds number between 2 and 6. The physical reason for the period-doubling transitions is explained based on the interaction of the particles with each other and the channel walls. The particles undergo near contact interactions as settling in the channel. To accurately capture the dynamics, the computational method requires accurate resolution of the particle interactions. The computational results are obtained with our lattice-Boltzmann method developed for suspended particles near contact. The results show that even in the most simple and ideal multiparticle sedimentation, the system undergoes transition to complex dynamics at relatively low Reynolds number. © 2003 American Institute of Physics.
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82.70.-y Disperse systems; complex fluids
47.55.Kf Particle-laden flows
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics
47.52.+j Chaos in fluid dynamics

Dense granular flow around an immersed cylinder

D. Chehata, R. Zenit, and C. R. Wassgren

Phys. Fluids 15, 1622 (2003); http://dx.doi.org/10.1063/1.1571826 (10 pages) | Cited 27 times

Online Publication Date: 5 May 2003

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The flow around a fixed cylinder immersed in a uniform granular flow is studied experimentally. Experiments are performed in a tall vertical chute producing a quasi two-dimensional granular flow. A storage bin at the top of the chute feeds glass particles into the channel while the mean velocity of the flow is controlled by varying the exit width of a hopper located at the channel bottom. Measurements of the drag force acting on a fixed cylinder are made using a strain gauge force measurement system. The flow velocity field is measured through a transparent wall using a particle image velocimetry analysis of high speed video recordings of the flow. Experiments are performed for a range of upstream particle velocities, cylinder diameters, and two sizes of glass particles. For the range of velocities studied, the mean drag force acting on the cylinder is independent of the mean flow velocity, contrary to what is expected from any ordinary fluid. The drag force increases with cylinder diameter and decreases with particle diameter. The drag force scales with the asymptotic static stress state in a tall granular bed. The drag coefficient, defined in terms of a dynamic pressure and an effective cylinder diameter, scales with the flow Froude number based on the hydraulic diameter of the channel. This analysis indicates that the drag acting on the cylinder is strongly affected by the surrounding channel geometry. Although the drag force on the cylinder does not change with the upstream flow velocity, the flow streamlines do change with velocity. A large stagnation zone forms at the leading edge of the cylinder while at the trailing edge an empty wake is observed. The wake size increases with flow velocity. Measurements of the flow vorticity and granular temperature are also presented and discussed. © 2003 American Institute of Physics.
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47.55.Kf Particle-laden flows
47.27.-i Turbulent flows
47.32.C- Vortex dynamics
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