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Jan 2005

Volume 17, Issue 1, Articles (01xxxx)

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Can turbophoresis be predicted by large-eddy simulation?

J. G. M. Kuerten and A. W. Vreman

Phys. Fluids 17, 011701 (2005); http://dx.doi.org/10.1063/1.1824151 (4 pages) | Cited 23 times

Online Publication Date: 23 November 2004

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Direct numerical simulation (DNS) and large-eddy simulation (LES) of particle-laden turbulent channel flow, in which the particles experience a drag force, are performed. In this flow turbophoresis leads to an accumulation of particles near the walls. It is shown that the turbophoresis in LES is reduced, in case the subgrid effects in the particle equations of motion are ignored. To alleviate this problem an inverse filtering model is proposed and incorporated into the particle equations. The model is shown to enhance the turbophoresis in actual LES, such that a good agreement with the DNS prediction is obtained.
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47.27.E- Turbulence simulation and modeling
47.11.-j Computational methods in fluid dynamics
47.27.tb Turbulent diffusion
47.55.Kf Particle-laden flows
47.60.-i Flow phenomena in quasi-one-dimensional systems

Friction drag reduction achievable by near-wall turbulence manipulation at high Reynolds numbers

Kaoru Iwamoto, Koji Fukagata, Nobuhide Kasagi, and Yuji Suzuki

Phys. Fluids 17, 011702 (2005); http://dx.doi.org/10.1063/1.1827276 (4 pages) | Cited 12 times

Online Publication Date: 23 November 2004

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The Reynolds-number dependence of the drag reduction achievable by diminishing to zero the near-wall turbulent velocity fluctuations is clarified. This reduction could be obtained by a virtual active feedback control system. The formula derived suggests that large drag reduction can be attained even at high Reynolds numbers if turbulence fluctuations adjacent to the wall are completely damped. For example, 35% drag reduction rate can be obtained at Reτ = 105 if the turbulence only below y+ = 10 vanishes. Thus, the active feedback control strategy, which has been studied mostly at low Reynolds numbers, would be much promising even in high Reynolds number flows of real applications. Results from the direct numerical simulation of turbulent channel flow at a Reynolds number of Reτ = 642 are also presented to clarify the phenomena in the controlled flow.
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47.27.E- Turbulence simulation and modeling
47.27.Jv High-Reynolds-number turbulence
47.27.nb Boundary layer turbulence
47.27.Rc Turbulence control
47.85.L- Flow control
47.11.-j Computational methods in fluid dynamics
47.20.-k Flow instabilities
47.60.-i Flow phenomena in quasi-one-dimensional systems

Vortex synchronization regions in shedding from an oscillating cylinder

Fernando L. Ponta and Hassan Aref

Phys. Fluids 17, 011703 (2005); http://dx.doi.org/10.1063/1.1827275 (4 pages) | Cited 5 times

Online Publication Date: 23 November 2004

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A classification of the vortex patterns in the wake of a normally oscillating cylinder was given by Williamson and Roshko who also studied when the various vortex patterns would occur. Using a symbolic code of letters and numbers that describes the combination of pairs and single vortices shed during each cycle of the forced oscillation of the cylinder, they gave a “map” of vortex-synchronization regions with the wavelength and amplitude of the oscillation as coordinates. In this study, we provide a theoretical basis for the experimental Williamson–Roshko map of vortex synchronization. We show that the region boundaries consist of two families of curves given by specific relations between the values of two nondimensional parameters defining the map. We construct a synthetic map that compares favorably with the experimental data.
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47.10.-g General theory in fluid dynamics
47.32.C- Vortex dynamics
47.27.wb Turbulent wakes
47.54.-r Pattern selection; pattern formation
47.60.-i Flow phenomena in quasi-one-dimensional systems

Continuous or catastrophic solid–liquid transition in jammed systems

P. Coussot, N. Roussel, S. Jarny, and H. Chanson

Phys. Fluids 17, 011704 (2005); http://dx.doi.org/10.1063/1.1823531 (4 pages) | Cited 10 times

Online Publication Date: 7 December 2004

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Pasty materials encountered in industry and in earth science are intermediate between solids and liquids either in terms of their internal structure (disordered but jammed) or from a mechanical point of view. Our results indicate that the apparent behavior of a particulate system (soils, suspensions, clays, etc.) can range from liquid-like to soil or solid-like depending on the relative importance of the energy supplied to it and its “state of jamming” which evolves in time, and the transition from one state to another may appear either continuous or catastrophic.
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47.55.Kf Particle-laden flows
83.10.Tv Structural and phase changes
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
64.70.D- Solid-liquid transitions
83.80.Nb Geological materials: Earth, magma, ice, rocks, etc.

Direct numerical simulation of polymer-induced drag reduction in turbulent boundary layer flow

Costas D. Dimitropoulos, Yves Dubief, Eric S. G. Shaqfeh, Parviz Moin, and Sanjiva K. Lele

Phys. Fluids 17, 011705 (2005); http://dx.doi.org/10.1063/1.1829751 (4 pages) | Cited 29 times

Online Publication Date: 7 December 2004

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We describe a method for direct numerical simulation of polymer-induced friction drag reduction in turbulent boundary layers. The effect of the polymer additives that induce spatial variations of skin-friction drag is included in the momentum equation through a continuum constitutive model for the viscoelastic stress, which is based on the evolution of a parameter describing the fluid microstructure. We demonstrate that the turbulence structure and polymer microstructure evolve asynchronously as one moves in the streamwise direction. We observe an initial development length, which is followed by a quasisteady region where variations in drag reduction are weak. High drag reduction behavior can be present at short downstream distances from the inflow plane.
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47.27.E- Turbulence simulation and modeling
47.27.nb Boundary layer turbulence
47.50.-d Non-Newtonian fluid flows
47.11.-j Computational methods in fluid dynamics

A friction factor bound for transitional pipe flow

S. C. Plasting and R. R. Kerswell

Phys. Fluids 17, 011706 (2005); http://dx.doi.org/10.1063/1.1828103 (4 pages) | Cited 2 times

Online Publication Date: 7 December 2004

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An upper bound λmax on the friction factor λ is found for transitional pipe flow up to Reynolds numbers of Re = 4000. This bound corresponds to the laminar Hagen–Poiseuille value until the energy stability point of Re = 81.52 (where λmax = 0.7851) after which it decreases monotonically to approach a viscosity-independent asymptote of 0.27±0.01 as Re→∞. Comparison is made with the friction factors associated with recently discovered, finite-amplitude traveling waves in rotating and nonrotating pipe flow as well as experimental data.
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47.10.-g General theory in fluid dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.15.Fe Stability of laminar flows
47.20.Gv Viscous and viscoelastic instabilities
47.32.-y Vortex dynamics; rotating fluids
47.35.-i Hydrodynamic waves
47.15.G- Low-Reynolds-number (creeping) flows
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back to top Interfacial Flows

A note on the small oscillation regimes of rotating liquid bridges: Transition from surface to internal wave modes

A. M. Gañán-Calvo and J. M. Montanero

Phys. Fluids 17, 012101 (2005); http://dx.doi.org/10.1063/1.1819471 (6 pages) | Cited 2 times

Online Publication Date: 23 November 2004

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An analysis of the small oscillation modes of rotating liquid bridges is carried out. The study is performed in the particular conditions when both surface and internal wave mode frequencies almost coincide for a certain meridional and azimuthal wave number. The critical values of the rotation speed and the natural frequencies for which this transitional condition takes place are obtained numerically as a function of the parameters characterizing the fluid configuration. The influence of both the outer bath and the liquid bridge equilibrium shape on the transition is analyzed. Analytical expressions providing the critical values of the rotation speed and the natural frequencies are obtained for cylindrical liquid bridges.
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47.10.-g General theory in fluid dynamics
47.35.-i Hydrodynamic waves
47.32.-y Vortex dynamics; rotating fluids
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.55.Kf Particle-laden flows
47.20.-k Flow instabilities

Mean field kinetic theory description of evaporation of a fluid into vacuum

Aldo Frezzotti, Livio Gibelli, and Silvia Lorenzani

Phys. Fluids 17, 012102 (2005); http://dx.doi.org/10.1063/1.1824111 (12 pages) | Cited 13 times

Online Publication Date: 9 December 2004

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The evaporation of a liquid slab into vacuum is studied by numerical solutions of the Enskog–Vlasov equation for a fluid of spherical molecules interacting by Sutherland potential. The equation provides a simplified description of the microscopic behavior of the fluid but it has the capability of handling both the liquid and vapor phase, thus eliminating the necessity of postulating ad hoc models for boundary conditions at the vapor-liquid interface. This work focuses on obtaining the structure of the vapor-liquid interface in nonequilibrium conditions as well as the distribution function of evaporating molecules. The results show that the molecules crossing a properly defined vapor-liquid boundary have an almost Maxwellian distribution function and that the vapor phase is reasonably well described by the Boltzmann equation with diffusive boundary condition.
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47.10.-g General theory in fluid dynamics
47.55.Kf Particle-laden flows
68.03.Fg Evaporation and condensation of liquids
47.45.Dt Free molecular flows
05.20.Dd Kinetic theory

Effect of surfactant on the long-wave instability of a shear-imposed liquid flow down an inclined plane

Hsien-Hung Wei

Phys. Fluids 17, 012103 (2005); http://dx.doi.org/10.1063/1.1823171 (5 pages) | Cited 10 times

Online Publication Date: 14 December 2004

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The effect of an insoluble surfactant on the linear stability of a shear-imposed flow down an inclined plane is examined in the long-wavelength limit. It has been known that a free falling film flow with surfactant is stable to long-wavelength disturbances at sufficiently small Reynolds numbers. Imposing an additional interfacial shear, however, could cause instability due to the shear-induced Marangoni effect. Two modes of the stability are identified and the corresponding growth rates are derived. The underlying mechanisms of the stability are also elucidated in detail.
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47.10.-g General theory in fluid dynamics
47.20.Ft Instability of shear flows (e.g., Kelvin-Helmholtz)
47.35.-i Hydrodynamic waves
47.20.Dr Surface-tension-driven instability
47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
68.15.+e Liquid thin films
back to top Viscous and Non-Newtonian Flows

Radial mixing of granular materials in a rotating cylinder: Experimental determination of particle self-diffusivity

Suman K. Hajra and D. V. Khakhar

Phys. Fluids 17, 013101 (2005); http://dx.doi.org/10.1063/1.1825331 (11 pages) | Cited 9 times

Online Publication Date: 1 December 2004

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Particle self-diffusion has a significant effect on mixing and thus on performance of rotating cylinder systems such as rotary kilns and drum mixers. We study experimentally the radial mixing of monodisperse beads of different colors in a quasi-two-dimensional cylinder rotated in the continuous flow regime. In this regime a shallow surface layer of particles flows steadily while the rest of the material rotates as a solid body. The initial distribution of tracer particles is taken to be radially symmetric and cylinder is taken to be half full. Both facilitate estimation of the particle self-diffusivity since the evolving concentration distribution during mixing in this case is radial for most part and the mixing in these conditions is shown to be dominated by diffusion of particles. A qualitative study of the mixing is carried out using digital photography. Radial number fraction profiles of the tracer particles are obtained by bulk sampling. Since mixing occurs only in the flowing layer, mixing is considered in terms of “passes” defined as the number of times the material in the bed entirely flows through the layer. Experimental results indicate that the mixing per pass decreases with increasing rotational speed, increases with increasing particle size, and is nearly independent of cylinder size. The mixed state captured by digital photography and the measured radial concentration profiles are well described by a convective diffusion model, using diffusivity as a fitting parameter. The diffusivity obtained from the model follows the scaling proposed by Savage [ “Disorder, diffusion, and structure formation in granular flow,” Disorder and Granular Media, edited by A. Hansen and D. Bideau (Elsevier, Amsterdam, 1993), pp. 255–285 ] and a simple expression for the diffusivity is obtained in terms of the particle diameter and the static and dynamic angles of repose.
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47.32.-y Vortex dynamics; rotating fluids
47.55.Kf Particle-laden flows
47.11.-j Computational methods in fluid dynamics
47.10.-g General theory in fluid dynamics
66.10.C- Diffusion and thermal diffusion

Exact solutions for two-dimensional steady flows of a power-law liquid on an incline

Carlos Alberto Perazzo and Julio Gratton

Phys. Fluids 17, 013102 (2005); http://dx.doi.org/10.1063/1.1829625 (8 pages) | Cited 2 times

Online Publication Date: 10 December 2004

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Under assumptions that are not too restrictive it is possible to reduce the equations that describe steady viscous gravity flows of a power-law liquid on an inclined plane to an equivalent problem consisting of an unsteady one-dimensional nonlinear diffusion process. In a paper dealing with the steady spreading flow of a Herschel–Buckley liquid, Wilson and Burgess [“The steady, spreading flow of a rivulet of mud,” J. Non-Newtonian Fluid Mech. 79, 77 (1998) ] noticed a formal analogy between the steady, two-dimensional viscous gravity flows of a power-law liquid on an incline and a one-dimensional time-dependent nonlinear diffusion phenomena; however, they did not pursue the matter further. Here we develop the analogy and show how it can be used to find a large number of exact solutions representing steady two-dimensional flows of power-law liquids, based on the available knowledge concerning nonlinear diffusion. We describe flows whose widths stay constant until a certain distance from the source, which are analogous to the well-known waiting-time solutions of nonlinear diffusion. We then introduce a phase-plane formalism that allows us to find self-similar solutions and we give as examples three different currents limited laterally by a wall that ends abruptly and currents on an inclined stripe. Finally we describe the two-dimensional currents that are analogous to the traveling wave solutions of the nonlinear diffusion equation. The approximations involved in the analogy are essentially equivalent to those of the lubrication theory, so that they do not impose restrictions more severe than those usually present in problems of this type. The present theory does not include surface tension effects, which implies that the appropriate Bond number must be large.
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47.10.-g General theory in fluid dynamics
47.50.-d Non-Newtonian fluid flows
47.53.+n Fractals in fluid dynamics
back to top Laminar Flows

Cavitation in flow through a micro-orifice inside a silicon microchannel

Chandan Mishra and Yoav Peles

Phys. Fluids 17, 013601 (2005); http://dx.doi.org/10.1063/1.1827602 (15 pages) | Cited 19 times

Online Publication Date: 14 December 2004

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Hydrodynamic cavitation in flows through a micro-orifice entrenched in a microchannel has been detected and experimentally investigated. Microfabrication techniques have been employed to design and develop a microfluidic device containing an 11.5 μm wide micro-orifice inside a 100.2 μm wide and 101.3 μm deep microchannel. The flow of de-ionized water through the micro-orifice reveals the presence of multifarious cavitating flow regimes. This investigation divulges both similarities and differences between cavitation in micro-orifices and cavitation in their macroscale counterparts. The low incipient cavitation number obtained from the current experiments suggests a dominant size scale effect. Choking cavitation is observed to be independent of any pressure or velocity scale effects. However, choking is significantly influenced by the small stream nuclei residence time at such scales. Flow rate choking leads to the establishment of a stationary cavity. Large flow and cavitation hysteresis have been detected at the microscale leading to very high desinent cavitation numbers. The rapid transition from incipient bubbles to choking cavitation and subsequent supercavitation suggests the presence of radically different flow patterns at the microscale. Supercavitation results in a thick cavity, which extends throughout the microchannel, and is encompassed by the liquid. Cavitation at the microscale is expected to considerably influence the design of innovative high-speed microfluidic systems.
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47.85.Np Fluidics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.55.dp Cavitation and boiling
back to top Instability and Transition

The dominant wave mode within a trailing line vortex

James P. Denier and Jillian A. K. Stott

Phys. Fluids 17, 014101 (2005); http://dx.doi.org/10.1063/1.1814583 (9 pages) | Cited 2 times

Online Publication Date: 23 November 2004

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We identify the dominant, or most unstable, wave mode for the flow in a trailing line vortex. This dominant mode is found to reside in a wavenumber regime between that of inviscid wave modes and the viscous upper branch neutral wave modes. A reevaluation of the growth rate in the vicinity of the upper branch of the curve of neutral stability allows us to predict the neutral value of the azimuthal and axial wavenumber as a function of the imposed swirl within the trailing line vortex.
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47.10.-g General theory in fluid dynamics
47.32.C- Vortex dynamics
47.35.-i Hydrodynamic waves
47.20.Cq Inviscid instability
47.20.Gv Viscous and viscoelastic instabilities

Nonlinear evolution of Mack modes in a hypersonic boundary layer

Ndaona Chokani

Phys. Fluids 17, 014102 (2005); http://dx.doi.org/10.1063/1.1825471 (13 pages) | Cited 4 times

Online Publication Date: 1 December 2004

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In hypersonic boundary layer flows the nonlinear disturbance evolution occurs relatively slowly over a very long length scale and has a profound effect on boundary layer transition. In the case of low-level freestream disturbances and negligible surface roughness, the transition is due to the modal growth of exponentially growing Mack modes that are destabilized by wall cooling. Cross-bicoherence measurements, derived from hot-wire data acquired in a quiet hypersonic tunnel, are used to identify and quantify phase-locked, quadratic sum and difference interactions involving the Mack modes. In the early stages of the nonlinear disturbance evolution, cross-bicoherence measurements indicate that the energy exchange between the Mack mode and the mean flow first occurs to broaden the sidebands; this is immediately followed by a sum interaction of the Mack mode to generate the first harmonic. In the next stages of the nonlinear disturbance evolution, there is a difference interaction of the first harmonic, which is also thought to contribute to the mean flow distortion. This difference interaction, in the latter stages, is also accompanied by a difference interaction between Mack mode and first harmonic, and a sum interaction, which forces the second harmonic. Analysis using the digital complex demodulation technique, shows that the low-frequency, phase-locked interaction that is identified in the cross bicoherence when the Mack mode and first harmonic have large amplitudes, arises due to the amplitude modulation of Mack mode and first harmonic.
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47.40.Ki Supersonic and hypersonic flows
47.27.nb Boundary layer turbulence
47.15.Fe Stability of laminar flows
47.27.Cn Transition to turbulence

Amplification of boundary layer instability by hot wall thermal oscillation in a side heated cavity

Sung Ki Kim, Seo Young Kim, and Young Don Choi

Phys. Fluids 17, 014103 (2005); http://dx.doi.org/10.1063/1.1828122 (12 pages) | Cited 2 times

Online Publication Date: 7 December 2004

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A numerical study has been conducted to investigate the amplification of boundary layer instability in a side-heated enclosure with a thermal oscillation of vertical hot wall. The impetus of the present study is to elucidate the influence of wall thermal oscillation, in which the imposing frequency is one order of magnitude higher than that of the internal gravity wave on the fluctuation characteristics of boundary layer flow and internal flow in an enclosure. The numerical results show that the intensity of fluctuation of boundary layer flow is augmented and the internal flow in the cavity core is substantially influenced when the wall thermal oscillation is in tune with the characteristic frequency of boundary layer instability. For the wall thermal oscillation with a specific frequency, the modulated frequency fluctuation appears in the corner region due to the flow interaction between the vertical boundary layer flow and the wall jet along the horizontal walls. The amplified fluctuation of boundary layer flow affects the time-averaged heat transfer. The maximum enhancement of Nusselt number is obtained for the wall thermal oscillation in tune with the boundary layer instability frequency. The effect of wall thermal oscillation on heat transfer is more pronounced when the forcing amplitude is the average value of nondimensional temperature difference between the hot and cold walls.
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47.27.nb Boundary layer turbulence
47.20.-k Flow instabilities
47.27.T- Turbulent transport processes
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.10.-g General theory in fluid dynamics
47.35.-i Hydrodynamic waves
47.27.wg Turbulent jets

Nonlinear waves in the pressure driven flow in a finite rotating pipe

E. Sanmiguel-Rojas and R. Fernandez-Feria

Phys. Fluids 17, 014104 (2005); http://dx.doi.org/10.1063/1.1828124 (12 pages) | Cited 4 times

Online Publication Date: 9 December 2004

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To investigate the nature of nonlinear waves appearing in an axially rotating pipe, we have performed a series of time-depending, three-dimensional numerical simulations of the incompressible Navier–Stokes equations in a rotating long pipe. As a difference with some previous works on the subject, which look for several given types of traveling wave solutions in pipes of infinite length, we leave the flow to evolve freely after a pressure difference is set between two points, one on each end of the finite rotating pipe. We use a recently developed numerical method that allows us to simulate numerically the three-dimensional flow produced in a pipe when Dirichlet boundary condition for the pressure is given on part of the inlet and outlet sections of the pipe. This technique is further improved here so that the pressure is only fixed at just one point on each one of the open boundaries of the pipe. Thus, no restrictions on the flow properties are given in these sections, allowing the free entrance and exit of possible waves through the pipe. We find that packets of traveling spiral waves are formed for values of the Reynolds numbers based on both the axial and the azimuthal velocities just above the critical ones given by the linear stability theory. These traveling waves have the same characteristics predicted by the linear stability theory and produce no significant mean flux defect. As the values of these parameters are increased above their critical values, the spiral waves become more involved and their amplitude increase, giving rise to a significant axial mean flow defect. For sufficiently high Reynolds numbers, we detect the apparition of spiral waves traveling also upstream, in agreement with the stability analysis for absolute instabilities. At the end, these traveling waves appearing above the onset for absolute instabilities transform into a standing spiral wave superimposed to the rotating Hagen–Poiseuille flow.
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47.35.-i Hydrodynamic waves
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.11.-j Computational methods in fluid dynamics
47.10.-g General theory in fluid dynamics
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.32.-y Vortex dynamics; rotating fluids

Nonmodal growth of three-dimensional disturbances on plane Couette–Poiseuille flows

Lars B. Bergström

Phys. Fluids 17, 014105 (2005); http://dx.doi.org/10.1063/1.1830511 (10 pages) | Cited 5 times

Online Publication Date: 14 December 2004

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The time development of three-dimensional disturbances superimposed on a variety of mean flow profiles representing plane Couette–Poiseuille flow is investigated numerically. Specifically, with y representing the wall normal coordinate, the mean flow profiles U(y) are represented by U(y) = A(1−y2)+By, where B = 1 when 0 ⩽ A ⩽ 1/2 and B = 2math when 1/2 ⩽ A ⩽ 1. For streamwise independent disturbances, which are the most amplified ones, there is an increase of the disturbance peak amplification when the parameter A increases in the interval 1/10 ⩽ A ⩽ 1/2. In the interval 1/2 ⩽ A ⩽ 9/10, and especially for 9/10 ⩽ A ⩽ 1, the disturbance peak amplification decreases rapidly when A is increased. For A close to 1, a slight reduction of A will therefore cause a strong increase of the disturbance amplification.
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47.15.Fe Stability of laminar flows
47.27.Cn Transition to turbulence
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.10.-g General theory in fluid dynamics
47.20.-k Flow instabilities

Vortex dynamics in starting square water jets

Jiao Jian Ai, S. C. M. Yu, Adrian Wing-Keung Law, and L. P. Chua

Phys. Fluids 17, 014106 (2005); http://dx.doi.org/10.1063/1.1823532 (12 pages) | Cited 1 time

Online Publication Date: 15 December 2004

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This paper presents the results of an experimental study on starting square jets at three Reynolds numbers (Re = U0De/υ = 2358,3528,4716) utilizing planar laser induced fluorescence. Starting circular jets under the same initial Re were also investigated as a basis for comparison. Observations showed that for both circular and square jets, the rate of penetration is almost constant within the first four diameters from the exit plane. Beyond that, the rate reaches an asymptotic behavior that is inversely proportional to the square root of time (t1/2). It was also found that the jet front travels slower in square jets. The interaction and deformation between the spanwise and streamwise vortices in square jets lead to an enhanced entrainment. The phenomena of axis switching, vortex pinch-off, vortices leapfrogging and coalescence were all observed in the experiments and their formation mechanisms are discussed in detail. The normalized value for the pinch-off time obtained is found to be about 7 and the expansion rate of the head vortex core is proportional to t1.5.
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47.32.C- Vortex dynamics
47.27.wg Turbulent jets

Crystal shapes and crystallization in continuum modeling

Markus Hütter, Gregory C. Rutledge, and Robert C. Armstrong

Phys. Fluids 17, 014107 (2005); http://dx.doi.org/10.1063/1.1830512 (13 pages) | Cited 6 times

Online Publication Date: 15 December 2004

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A crystallization model appropriate for application in continuum modeling of complex processes is presented. As an extension to the previously developed Schneider equations [ W. Schneider, A. Köppel, and J. Berger, “Non-isothermal crystallization of polymers,” Int. Polym. Proc. 2, 151 (1988) ], the model presented here allows one to account for the growth of crystals of various shapes and to distinguish between one-, two-, and three-dimensional growth, e.g., between rod-like, plate-like, and sphere-like growth. It is explained how a priori knowledge of the shape and growth processes is to be built into the model in a compact form and how experimental data can be used in conjunction with the dynamic model to determine its growth parameters. The model is capable of treating transient processing conditions and permits their straightforward implementation. By using thermodynamic methods, the intimate relation between the crystal shape and the driving forces for phase change is highlighted. All these capabilities and the versatility of the method are made possible by the consistent use of four structural variables to describe the crystal shape and number density, irrespective of the growth dimensionality.
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81.05.Lg Polymers and plastics; rubber; synthetic and natural fibers; organometallic and organic materials
61.41.+e Polymers, elastomers, and plastics
81.10.Aj Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation
81.10.Dn Growth from solutions
64.70.D- Solid-liquid transitions
back to top Turbulent Flows

Quantized energy cascade statistics model of fully developed turbulence

Jie Guo and Ning Zheng

Phys. Fluids 17, 015101 (2005); http://dx.doi.org/10.1063/1.1819941 (8 pages)

Online Publication Date: 23 November 2004

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In this paper, it is proposed that the modeling of the inertial ranges up to the integral scale of fully developed turbulence can be described by eddies system that is characterized by a continuous energy flux cascade which obeys Fermi–Dirac statistics distribution. Both ways of introducing the Fermi–Dirac distribution characteristic into modeling of fully developed turbulence energy cascade are suggested. One is based on β model. The key viewpoint is that the turbulent fluctuations reach a statistically quasiequilibrium state which is characterized by a continuous energy flux cascade from large to small scales, a fraction β of the total space obeys Fermi–Dirac distribution. Another one is based on a hierarchy of fluctuation structures. The main feature of the model predictions is the term of the denominator characteristic of the Fermi–Dirac distribution, where an effective temperature is defined with the turbulent fluctuation energy. The main argument which is in favor of this model is to agree with experimental data up to the integral scale that generally departs from homogeneous scaling. The predictions of the quantized energy cascade statistics model for second-order as well as higher-order structure functions and energy spectrum are in agreement with experimental data. The model predictions extend over a much wider range of scales with respect to the inertial range, satisfy strictly generalized extended self-similarity, and obey extended self-similarity at the precision of experiment. So, this model may explain some departure from homogeneous scaling around the inertial ranges up to the integral scale.
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47.27.E- Turbulence simulation and modeling
47.10.-g General theory in fluid dynamics
47.53.+n Fractals in fluid dynamics

Statistical analysis of the velocity field in a mechanical precessing jet flow

J. Mi and G. J. Nathan

Phys. Fluids 17, 015102 (2005); http://dx.doi.org/10.1063/1.1824138 (17 pages) | Cited 1 time

Online Publication Date: 1 December 2004

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An experimental investigation of a precessing jet issuing from a mechanically rotating nozzle directed at an angle of α = 45° relative to the axis of rotation is reported. Both conventional and conditional statistics of the velocity field of the jet were measured using a combined hot-wire and cold-wire (to identify any reverse flow) probe. Three distinct values ( ≈ 0.005, 0.01, and 0.02) of the precession Strouhal number Stp (≡ rotation frequency × nozzle diameter / jet exit bulk velocity) were used to assess the effect of varying Stp. The measurements reveal that the Strouhal number in general has significant influence on the entire mixing field generated by a precessing jet. The occurrence of precession at all the Strouhal numbers of investigation produces a central recirculation zone at x ⩽ 7d, where x is a distance measured from the rotating nozzle exit. A critical Strouhal number, i.e., Stp,cr ≈ 0.008 for the present case, is identified: at Stp ≥ Stp,cr the core jet converges to the axis of rotation while at Stp ≥ Stp,cr it does not. The characteristics of the turbulent flow in the near and intermediate regions are quite different and depend upon the magnitude of Stp. The near-field region, x/d ⩽ 10–15, is dominated by a regime of global precession of the entire jet. As a result, the large-scale entrainment of the ambient fluid is substantially enhanced while the fine-scale turbulent mixing is suppressed. Under the supercritical regime (i.e., Stp ≥ Stp,cr), the jet in the far field resembles some features of the nonprecessing counterpart. Nevertheless, significant differences still retain in the statistical properties.
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47.10.-g General theory in fluid dynamics
47.27.wg Turbulent jets
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.32.-y Vortex dynamics; rotating fluids
02.50.-r Probability theory, stochastic processes, and statistics

Toward improved consistency of a priori tests with a posteriori tests in large eddy simulation

Noma Park, Jung Yul Yoo, and Haecheon Choi

Phys. Fluids 17, 015103 (2005); http://dx.doi.org/10.1063/1.1823511 (20 pages)

Online Publication Date: 7 December 2004

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It is well known that conventional a priori tests based on the instantaneous true subgrid scale (SGS) stress do not provide a useful diagnostic information on deterministic SGS models due to the stochastic nature of unresolved scales. In this study, the possibility of an alternative diagnostics based on the “best deterministic” model is investigated. The optimal SGS model [ J. A. Langford and R. D. Moser, “Optimal LES formulation for isotropic turbulence,” J. Fluid Mech. 398, 321 (1999) ] is considered as one of nearly best deterministic models. The validity of the optimal model is confirmed by a posteriori test, showing that the field from the optimal large eddy simulation can be regarded as one of the representative fields among all the possible realizations of filtered direct numerical simulation. Then, a priori and a posteriori tests for several SGS models are performed on the forced isotropic turbulence with a sharp cutoff filter. It is shown that a priori tests based on the optimal model are highly consistent with a posteriori tests. Also, dynamic eddy viscosity models are very close to the optimal model both in a priori and a posteriori senses, which implies that the accurate prediction of backward dissipation is not necessarily required for the deterministic model to predict accurate flow statistics at least for the isotropic turbulence. Therefore, the direct application of scale-invariance concept to the resolved field is shown to be unsuccessful for the spectral cutoff filter. The present study strongly suggests that this concept should be realized in terms of the dynamic constant(s) of dissipative models.
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47.11.-j Computational methods in fluid dynamics
47.27.Gs Isotropic turbulence; homogeneous turbulence
47.27.E- Turbulence simulation and modeling
02.50.Fz Stochastic analysis

Vortical structures over rectangular cavities at low speed

Graham Ashcroft and Xin Zhang

Phys. Fluids 17, 015104 (2005); http://dx.doi.org/10.1063/1.1833412 (8 pages) | Cited 11 times

Online Publication Date: 14 December 2004

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Experiments have been performed to acquire qualitative and quantitative flow-field data for an open cavity flow using the particle image velocimetry technique. The study focuses on the time-mean and instantaneous development of the turbulent flow structures in the cavity shear layer. The effects of geometry (length-to-depth ratio) and flow speed on these structures are investigated. The shear layers are found to be characterized by coherent vortical structures whose size and rate of growth vary with geometry. The smaller scales of the flow are investigated using a large-eddy decomposition method. Results show these stochastic structures to predominate primarily in the shear layer and aft wall regions.
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47.27.nb Boundary layer turbulence
47.32.C- Vortex dynamics

Characterization of near-wall turbulence in terms of equilibrium and “bursting” solutions

Javier Jiménez, Genta Kawahara, Mark P. Simens, Masato Nagata, and Makoto Shiba

Phys. Fluids 17, 015105 (2005); http://dx.doi.org/10.1063/1.1825451 (16 pages) | Cited 19 times

Online Publication Date: 15 December 2004

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Near-wall turbulence in the buffer region of Couette and Poiseuille flows is characterized in terms of recently-found nonlinear three-dimensional solutions to the incompressible Navier–Stokes equations for wall-bounded shear flows. The data suggest that those solutions can be classified into two families, of which one is dominated by streamwise vortices, and the other one by streaks. They can be associated with the upper and lower branches of the equilibrium solutions for Couette flow found by Nagata [“Three-dimensional finite-amplitude solutions in plane Couette flow: Bifurcation from infinity,” J. Fluid Mech. 217, 519 (1990 )]. The quiescent structures of near-wall turbulence are shown to correspond to the vortex-dominated family, but evidence is presented that they burst intermittently both in minimal and in fully turbulent flows. The intensity and period of the bursts are Reynolds-number dependent, but they saturate at high enough Reynolds numbers. The time-periodic exact solution found for Couette flow by Kawahara and Kida [“Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst,” J. Fluid Mech. 449, 291 (2001 )] can be used as a simplified model for the bursting process.
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47.27.nb Boundary layer turbulence
47.27.E- Turbulence simulation and modeling
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.15.-x Laminar flows
47.32.C- Vortex dynamics
47.10.-g General theory in fluid dynamics
47.11.-j Computational methods in fluid dynamics
47.27.N- Wall-bounded shear flow turbulence

Direct numerical simulation of homogeneous turbulence with hyperviscosity

A. G. Lamorgese, D. A. Caughey, and S. B. Pope

Phys. Fluids 17, 015106 (2005); http://dx.doi.org/10.1063/1.1833415 (10 pages) | Cited 11 times

Online Publication Date: 15 December 2004

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We perform direct numerical simulations (DNS) of the hyperviscous Navier–Stokes equations in a periodic box. We consider values of the hyperviscosity index h = 1, 2, 8, and vary the hyperviscosity to obtain the largest range of lengthscale ratios possible for well-resolved pseudo-spectral DNS. It is found that the spectral bump, or bottleneck, in the energy spectrum observed at the start of the dissipation range becomes more pronounced as the hyperviscosity index is increased. The calculated energy spectra are used to develop an empirical model for the dissipation range which accurately represents the bottleneck. This model is used to predict the approach of the turbulent kinetic energy k to its asymptotic value, k, as the hyperviscosity tends to zero.
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47.27.E- Turbulence simulation and modeling
47.27.Gs Isotropic turbulence; homogeneous turbulence
47.11.-j Computational methods in fluid dynamics
47.10.-g General theory in fluid dynamics
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