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Dec 2002

Volume 14, Issue 12, pp. L85-L89, 4105-4459

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Splashing impact of a spray onto a liquid film

D. Sivakumar and C. Tropea

Phys. Fluids 14, L85 (2002); http://dx.doi.org/10.1063/1.1521418 (4 pages) | Cited 16 times

Online Publication Date: 30 October 2002

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The impact of single droplets within a spray onto a thin liquid film produced by this spray has been studied using direct visualization and the phase Doppler technique. The temporal evolution of the crown radius and its height has been compared with results corresponding to the impact of an isolated drop onto an undisturbed liquid film. Significant differences in crown formation indicate to what extent interactions between neighboring drop impacts can affect the resulting secondary spray. The results of this study have significance for future modeling of spray impact. © 2002 American Institute of Physics.
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47.55.Kf Particle-laden flows
68.15.+e Liquid thin films
47.80.-v Instrumentation and measurement methods in fluid dynamics

Power laws for turbulent boundary layer flow

Joseph B. Keller

Phys. Fluids 14, L89 (2002); http://dx.doi.org/10.1063/1.1524615 (1 page)

Online Publication Date: 6 November 2002

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A differential equation for the mean velocity u(y) at distance y from the wall in a turbulent boundary layer flow is proposed and solved. It leads to a power law for u(y), followed by a rapid transition to a different power law, in agreement with the results of Barenblatt, Chorin and Prostokishin [Phys. Fluids 12, 2159 (2000)]. © 2002 American Institute of Physics.
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47.27.nb Boundary layer turbulence
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A linear approach for the evolution of coherent structures in shallow mixing layers

Bram C. van Prooijen and Wim S. J. Uijttewaal

Phys. Fluids 14, 4105 (2002); http://dx.doi.org/10.1063/1.1514660 (10 pages) | Cited 19 times

Online Publication Date: 18 October 2002

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The development of large coherent structures in a shallow mixing layer is analyzed. The results are validated with experimental data obtained from particle tracking velocimetry. The mean flow field is modeled using the self-similarity of the velocity profiles. The characteristic features of the down-stream development of a shallow mixing layer flow, like the decrease of the velocity difference over the mixing layer, the decreasing growth of the mixing layer width, and the transverse shift of the center of the mixing layer layer are fairly well represented. It turned out that the entrainment coefficient could be taken constant, equal to a value obtained for unbounded mixing layers: α = 0.085. Linearization of the shallow water equations leads to a modified Orr–Sommerfeld equation, with turbulence viscosity and bottom friction as dissipative terms. Growth rates are obtained for each position downstream, using the model for the mean flow field. For a given energy density spectrum at the inflow boundary, integration of the growth rates along the downstream direction yields the spectra at various downstream positions. These spectra provide a measure for the intensity and the length scale of the coherent structures (the dominant mode). The length scales found are in good agreement with the measured ones. The length scale of the most unstable mode appears much larger than the length scale of the dominant mode. Obviously, the longevity of the coherent structures plays a significant role. Three growth regimes can be distinguished: in the first regime the dominant mode is growing, in the second regime the dominant mode is dissipating, but other modes are still growing, and in the third regime all modes are dissipating. It is concluded that the development of the coherent structures in a shallow mixing layer can fairly well be described and interpreted by the proposed linear analysis. © 2002 American Institute of Physics.
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47.53.+n Fractals in fluid dynamics
92.40.Qk Surface water, water resources
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.-k Flow instabilities

Viscous modes in two-phase mixing layers

Philip Yecko, Stéphane Zaleski, and Jose-Maria Fullana

Phys. Fluids 14, 4115 (2002); http://dx.doi.org/10.1063/1.1513987 (8 pages) | Cited 18 times

Online Publication Date: 18 October 2002

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The temporal instability of parallel viscous two-phase mixing layers is studied by adopting a composite error function flow profile such that boundary layers in each fluid sandwich the interface. Linear spectra and neutral stability curves are calculated numerically and the effects of varying the density ratio, viscosity ratio and Weber number are presented. In addition to the interfacial mode two Tollmien–Schlichting type modes are found and attributed to the presence of the two viscous boundary layers. This is important because it is shown that any of these three modes may be the most unstable, depending on parameter values. Mode multiplicity and competition has not yet been thoroughly explored for this problem even though it is essential to the analysis of experiments and to further stability study of flows relevant to breaking up of interfaces. © 2002 American Institute of Physics.
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47.55.Kf Particle-laden flows
47.15.Cb Laminar boundary layers
47.15.Fe Stability of laminar flows
47.11.-j Computational methods in fluid dynamics

Model equations in rarefied gas dynamics: Viscous-slip and thermal-slip coefficients

C. E. Siewert and Felix Sharipov

Phys. Fluids 14, 4123 (2002); http://dx.doi.org/10.1063/1.1514973 (7 pages) | Cited 22 times

Online Publication Date: 18 October 2002

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Various model equations are used to define the viscous-slip and the thermal-slip coefficients in rarefied gas dynamics. More specifically, the BGK model, the S model, the variable collision model and the CES model are used to establish the slip coefficients basic to Kramers’ problem and the half-space problem of thermal creep. While the most general results are developed from use of the Maxwell boundary condition, results for the BGK model and the S model as defined by the Cercignani–Lampis boundary condition are also reported. An analytical discrete-ordinates method is used to establish the reported numerical results, and when available results from a numerical solution of the linearized Boltzmann equation are used as reference values. In addition to the numerical work based on model equations, the important issue of how to define meaningful ways (appropriate mean-free paths) to compare the results for the various models is discussed. © 2002 American Institute of Physics.
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47.45.Gx Slip flows and accommodation
47.11.-j Computational methods in fluid dynamics

Nonlinear evolution of nonuniformly heated falling liquid films

Benoit Scheid, Alexander Oron, Pierre Colinet, Uwe Thiele, and Jean Claude Legros

Phys. Fluids 14, 4130 (2002); http://dx.doi.org/10.1063/1.1515270 (22 pages) | Cited 24 times

Online Publication Date: 18 October 2002

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The present theoretical study focuses on the dynamics of a thin liquid film falling down a vertical plate with a nonuniform, sinusoidal temperature distribution. The results are compared to those obtained in the case of the uniform temperature distribution. The governing evolution equation for the film thickness profile based on long-wave theory accounts for two instability mechanisms related to thermocapillarity. The first mechanism is due to an inhomogeneity of the temperature at the liquid–gas interface induced by perturbations of the film thickness, when heat transfer to the gas phase is present, while the second one is due to the nonuniform heating imposed at the plate and leads to steady-state deformations of the liquid–gas interface. For a moderate nonuniform heating the traveling waves obtained in the case of a uniform heating are modulated by an envelope. When the temperature modulation along the plate increases the shape of the liquid–gas interface becomes “frozen” and the oscillatory traveling wave regime is suppressed. The enhancement of the heat transfer due to permanent deformations and traveling waves is also assessed. The latter is found to have no significant effect on the heat transfer coefficient, while the former can increase it significantly. A good agreement between the theoretical model and the experimental data obtained for a step-wise temperature distribution at the plate is found and the reason for discrepancies is explained. © 2002 American Institute of Physics.
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47.20.-k Flow instabilities
68.15.+e Liquid thin films

An evaluation of cellular automata applied to ganglia dissolution

M. L. Johns and L. F. Gladden

Phys. Fluids 14, 4152 (2002); http://dx.doi.org/10.1063/1.1515772 (8 pages) | Cited 3 times

Online Publication Date: 18 October 2002

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The ability of a three-dimensional (3-D) cellular automaton (CA) approach to describe or mimic the dissolution of entrapped octanol ganglia, trapped in a porous media, into a mobile aqueous phase has been directly assessed using detailed 3-D visualizations of the dissolution process, as provided by magnetic resonance imaging (MRI). In the 3-D CA, both time and space are made discrete with the state of each geometric site being updated after each time increment according to the state of all neighboring sites. Good agreement is produced by a direct 3-D comparison of the CA results with the corresponding images of the dissolving ganglia. These experimental images are also supplemented by 3-D velocity maps of the mobile aqueous phase produced using either MRI or by a lattice-Boltzmann simulation. The velocity maps are used to validate the assumption that a consideration of the local velocity field is essential for an accurate description of the ganglia dissolution process. Based on this analysis, an appropriate length scale is proposed for the region, required to be considered in the respective vicinity of each ganglion, when describing their dissolution using a CA approach. © 2002 American Institute of Physics.
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47.56.+r Flows through porous media
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
64.75.-g Phase equilibria
92.40.-t Hydrology and glaciology; cryosphere

The effects of wall proximity on vortex shedding from a square cylinder: Three-dimensional effects

S. C. C. Bailey, R. J. Martinuzzi, and G. A. Kopp

Phys. Fluids 14, 4160 (2002); http://dx.doi.org/10.1063/1.1514972 (18 pages) | Cited 18 times

Online Publication Date: 18 October 2002

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The three-dimensional nature of turbulent vortex shedding from a square cylinder in the vicinity of a solid wall is investigated for a Reynolds number of 18 900 as a function of the gap height, S/D. Spanwise surface pressure measurements on the cylinder faces and on the solid wall are complemented by velocimetry data. It is observed that parallel and oblique shedding modes arise naturally. The number of vortex dislocations is clearly related to the variations in the oblique shedding angle. Dislocations occur with increasing probability as the gap height is decreased to S/D ≈ 0.7. The dislocations are strongly associated with Type A instabilities and vortex splitting, which contribute significantly to phase-jitter. For gap heights close to that for vortex shedding suppression (0.5<S/D<0.7), dislocations occur less frequently. The vortex formation process is increasingly two-dimensional in this range, resulting in strong spanwise correlations and lower phase-jitter. These changes are observed as more sharply peaked frequency spectra, which have been interpreted as shedding frequency “tuning” in earlier studies. © 2002 American Institute of Physics.
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47.32.C- Vortex dynamics
47.27.-i Turbulent flows
47.20.-k Flow instabilities

Schmidt number effects on turbulent transport with uniform mean scalar gradient

P. K. Yeung, Shuyi Xu, and K. R. Sreenivasan

Phys. Fluids 14, 4178 (2002); http://dx.doi.org/10.1063/1.1517298 (14 pages) | Cited 44 times

Online Publication Date: 18 October 2002

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We study by direct numerical simulations the effects of Schmidt number (Sc) on passive scalars mixed by forced isotropic and homogeneous turbulence. The scalar field is maintained statistically stationary by a uniform mean gradient. We consider the scaling of spectra, structure functions, local isotropy and intermittency. For moderately diffusive scalars with Sc = 1/8 and 1, the Taylor-scale Reynolds number of the flow is either 140 or 240. A modest inertial-convective range is obtained in the spectrum, with a one-dimensional Obukhov–Corrsin constant of about 0.4, consistent with experimental data. However, the presence of a spectral bump makes a firm assessment somewhat difficult. The viscous-diffusive range is universal when scaled by Obukhov–Corrsin variables. In a second set of simulations we keep the Taylor-microscale Reynolds number fixed at 38 but vary Sc from 1/4 to 64 (a range of over two decades), roughly by factors of 2. We observe a gradual evolution of a −1 roll-off in the viscous-convective region as Sc increases, consistent with Batchelor’s predictions. In the viscous-diffusive range the spectra follow Kraichnan’s form well, with a coefficient that depends weakly on Sc. The breakdown of local isotropy manifests itself through differences between structure functions with separation distances in directions parallel and perpendicular to the mean scalar gradient, as well as via finite values of odd-order moments of scalar gradient fluctuations and of mixed velocity-scalar gradient correlations. However, all these indicators show, to varying degrees, an increasing tendency to isotropy with increasing Sc. The moments of scalar gradients and the scalar dissipation rate peak at Sc ≈ 4. The intermittency exponent for the scale-range between the Kolmogorov and Batchelor scales is found to decrease with Sc, suggesting qualitative consistency with previous dye experiments in water [Sc = O(1000)]. © 2002 American Institute of Physics.
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47.27.T- Turbulent transport processes

The flow around a torsionally oscillating sphere

R. Hollerbach, R. J. Wiener, I. S. Sullivan, R. J. Donnelly, and C. F. Barenghi

Phys. Fluids 14, 4192 (2002); http://dx.doi.org/10.1063/1.1518029 (14 pages) | Cited 7 times

Online Publication Date: 21 October 2002

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We investigate, experimentally and numerically, the flow around a torsionally oscillating sphere. The oscillation frequency is sufficiently high that the thickness of the Stokes boundary layer is small compared with the radius of the sphere. In addition to this boundary layer the flow then consists of a radial jet of periodically fluctuating speed emanating from the equator of the sphere. As the oscillation amplitude is increased, these fluctuations gradually become more pronounced, until the faster portions of the jet overtake the slower ones, causing them to curl back on themselves to form vortex pairs. The experimental results show that even after the appearance of the vortices the flow remains predominantly axisymmetric, and also equatorially symmetric, for a distance considerably greater than one sphere radius away. A two-dimensional numerical code is therefore used to elucidate the precise details of the flow, with excellent agreement on the range of amplitudes over which the vortices and other structures gradually emerge, and on the variation of that range with frequency. The turbulent breakdown of the vortices at higher amplitudes is also studied experimentally, and a connection with previous results is suggested. © 2002 American Institute of Physics.
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47.32.C- Vortex dynamics

Scaling parameters for underexpanded supersonic jets

K. Bülent Yüceil and M. Volkan Ötügen

Phys. Fluids 14, 4206 (2002); http://dx.doi.org/10.1063/1.1513796 (10 pages) | Cited 9 times

Online Publication Date: 22 October 2002

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An analysis and experiments were carried out to study the spreading and centerline property decay rates of underexpanded supersonic jets. The main purpose was to determine a suitable set of normalization parameters that would account for the initial expansion process and allow for a comparison of the asymptotic mixing rates of jets within a large range of exit-to-ambient pressure ratios. A set of expressions were developed for after-expansion equivalent jet exit diameter, velocity, temperature, and density to allow for a better collapse of jet spreading and centerline decay rates. Measurements were made for five different underexpanded sonic jets with jet exit-to-ambient pressure ratios of pe/pa = 1, 2.5, 7.5, 15.5, and 20.3, corresponding to (isentropically) fully expanded jet Mach numbers of Mj = 1, 1.68, 2.38, 2.85, and 3.03, respectively. For each jet, both centerline and profile measurements were made using special probes that simultaneously measured local total pressure, static pressure, total temperature in the jet, as well as ambient conditions. These measurements were made in the subsonic flow regime, in some cases, extending as far as 270 nozzle diameters from the exit plane. The experimental results were analyzed and the asymptotic jet properties were determined using the new renormalization parameters. © 2002 American Institute of Physics.
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47.27.wg Turbulent jets
47.40.Ki Supersonic and hypersonic flows

Nonlinear evolution of thin free viscous films in the presence of soluble surfactant

O. K. Matar

Phys. Fluids 14, 4216 (2002); http://dx.doi.org/10.1063/1.1516597 (19 pages) | Cited 12 times

Online Publication Date: 22 October 2002

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The rupture of thin free viscous films is studied in the presence of soluble surfactant. In the limit of rapid surfactant bulk diffusion, higher-order long wavelength theory is used to derive a one-dimensional (1D) nonlinear model for the film thickness, tangential velocity, surfactant surface, and bulk concentrations, the latter being cross-sectionally averaged. For slow diffusion, an approximate (1D) model for the bulk concentration is derived; the predictions of this model in this limit are compared with those of the fully two-dimensional (2D) concentration model. Linear stability is investigated in detail for the 1D rapid diffusion model and numerical simulations of the 1D and 2D models for the symmetric (squeeze) mode are also conducted; this allows a parametric study of the nonlinear rupture time to be performed. Finally, self-similar scaling exponents for all flow variables as rupture is approached are extracted. Our results indicate that scaling exponents for rupture derived in the surfactant-free case are preserved even in the presence of soluble surfactant and absence of surface viscosity. Inclusion of a concentration-independent surface viscosity, however, alters the scalings giving rise to new exponents. © 2002 American Institute of Physics.
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68.55.-a Thin film structure and morphology
66.20.-d Viscosity of liquids; diffusive momentum transport

Subgrid-scale energy and pseudo pressure in large-eddy simulation

B. Knaepen, O. Debliquy, and D. Carati

Phys. Fluids 14, 4235 (2002); http://dx.doi.org/10.1063/1.1514643 (7 pages) | Cited 7 times

Online Publication Date: 22 October 2002

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A dynamic model based on the Germano identity is proposed to evaluate the subgrid-scale energy in large-eddy simulations as a function of the large-scale velocity field only. The model is shown to allow the satisfactory reconstruction of the total energy contained in a direct numerical simulation from large-eddy simulations with different resolutions. The predicted subgrid-scale energy is given as a simple algebraic expression based on the Leonard tensor appearing in the dynamic procedure and does not require an additional transport equation. The model assumes a Kolmogorov spectrum and is implemented with and without the introduction of a dissipation cutoff in the high wave vector range. © 2002 American Institute of Physics.
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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
47.40.-x Compressible flows; shock waves
02.70.Dh Finite-element and Galerkin methods

Gas-dynamic boundary conditions of evaporation and condensation: Numerical analysis of the Knudsen layer

Andrey V. Gusarov and Igor Smurov

Phys. Fluids 14, 4242 (2002); http://dx.doi.org/10.1063/1.1516211 (14 pages) | Cited 21 times

Online Publication Date: 22 October 2002

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The gas-dynamic Euler equations require two boundary conditions to be specified at the surface of evaporated condensed phase and one condition at the surface of condensation. In the commonly considered three-parameter space of the temperature and pressure ratios and the Mach number this corresponds to a three-dimensional curve in the case of evaporation and to a surface in the case of condensation. To obtain the conditions of evaporation and condensation the steady-state Knudsen layer is numerically studied by the discrete velocity method applied to a Boltzmann equation with a relaxation collision term. Simple models of Mott-Smith type based on the conservation laws and analytical approximations of the velocity distribution function in the Knudsen layer may give satisfactory description of the gas-dynamic evaporation and condensation conditions while in general they inadequately represent the detailed structure of the distribution function. One of the reasons why the models deviate from the calculations is that they do not allow different parallel and perpendicular temperatures of the velocity distribution. Under evaporation, the Knudsen layer thickness increases with the Mach number M. Under condensation, it is inversely proportional to M when M is low. Numerical results are obtained and an analytical model is proposed for the vapor temperature considerably less than the condensed phase one (up to 10 times) what is typical for back condensation under pulsed laser ablation. © 2002 American Institute of Physics.
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47.45.-n Rarefied gas dynamics
47.55.Kf Particle-laden flows
64.70.F- Liquid-vapor transitions

Variable sphere molecular model for inverse power law and Lennard-Jones potentials in Monte Carlo simulations

Hiroaki Matsumoto

Phys. Fluids 14, 4256 (2002); http://dx.doi.org/10.1063/1.1517602 (10 pages) | Cited 6 times

Online Publication Date: 29 October 2002

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The variable sphere (VS) molecular model for the Monte Carlo simulation of rarefied gas flow is introduced to provide consistency for diffusion and viscosity cross-sections with those of any realistic intermolecular potential. It is then applied to the inverse power law (IPL) and Lennard-Jones (LJ) potentials. The VS model has a much simpler scattering law than either the variable hard sphere (VHS) or variable soft sphere (VSS) models; also, it has almost the same computational efficiency as the VHS and VSS models. A simulation of velocity relaxation in a homogeneous space and two comparative simulations of molecular diffusion in a homogeneous heat-bath gas and normal shock wave structure in a monatomic gas are made to examine VS model validity. The relaxation to a Maxwellian distribution function and equipartition between all degrees of freedom are well established; good agreement is shown in the molecular diffusion and shock wave structure between the VS model and the IPL and LJ potentials. The VS model is combined with the statistical inelastic cross-section (SICS) model and applied to simulation of translational and rotational energy relaxation in a homogeneous space. The VS model shows the relaxation of Maxwellian and Boltzmann distribution functions and equipartition between all degrees of freedom. Comparative calculation between the VS model with the SICS (VS-SICS) model and the VSS model with the SICS (VSS-SICS) model is made for rotational relaxation in a nitrogen normal shock wave. Good agreement is shown in the shock wave structure and rotational energy distribution function between the VS-SICS model and the VSS-SICS model. This study demonstrates that diffusion and viscosity cross-sections, rather than the scattering law of each molecular collision, affect macroscopic transport phenomena. © 2002 American Institute of Physics.
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47.45.-n Rarefied gas dynamics
61.20.Ja Computer simulation of liquid structure

Transport properties of heavy particles in high Reynolds number turbulence

Piero Olla

Phys. Fluids 14, 4266 (2002); http://dx.doi.org/10.1063/1.1517296 (12 pages) | Cited 6 times

Online Publication Date: 30 October 2002

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The statistical properties of heavy particle trajectories in high Reynolds numbers turbulent flows are analyzed. Dimensional analysis assuming Kolmogorov scaling is compared with the result of numerical simulation using a synthetic turbulence advecting field. The non-Markovian nature of the fluid velocity statistics along the solid particle trajectories is put into evidence, and its relevance in the derivation of Lagrangian transport models is discussed. © 2002 American Institute of Physics.
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47.27.-i Turbulent flows
47.55.Kf Particle-laden flows

Some dynamical properties of a differential model for the bursting cycle in the near-wall turbulence

A. Porporato and L. Ridolfi

Phys. Fluids 14, 4278 (2002); http://dx.doi.org/10.1063/1.1517601 (6 pages)

Online Publication Date: 6 November 2002

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In the last years several investigations have been devoted to model the bursting cycle in the near-wall turbulence by means of low-dimensional systems, with the aim of having simple mathematical models for the dynamics of coherent structures. The present paper deals with a low-dimension differential model, recently proposed by the authors. It is directly deduced from the velocity time series measured in a turbulent flow and well mimics the velocity oscillations typical of the bursting events. After studying the linear stability of the model, its behavior when an external forcing is added, both deterministic and stochastic, is analyzed. It is found that the essential characteristic of the dynamics described by the model is a Hopf bifurcation that, when excited by a stochastic forcing, produces time series with fluctuations that have similarities with the real turbulence signals. © 2002 American Institute of Physics.
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47.27.-i Turbulent flows
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Finite amplitude Faraday waves induced by a random forcing

R. Repetto and V. Galletta

Phys. Fluids 14, 4284 (2002); http://dx.doi.org/10.1063/1.1518690 (6 pages) | Cited 2 times

Online Publication Date: 6 November 2002

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In the present contribution we study the waves arising on the free surface of a liquid in a rectangular container undergoing vertical oscillations. Our aim in the work is to investigate the role of a random forcing characterized by a narrow-band spectrum on the wave amplitude close to subharmonic resonant conditions. The analysis is carried out theoretically by means of a weakly nonlinear analysis, assuming the ratio a0 between the acceleration of the tank and the gravitational acceleration to be small. We consider irrotational flow and take into account viscous effects by adding a linear dissipative term to the amplitude equation following Miles [“Nonlinear Faraday resonance,” J. Fluid Mech. 146, 285 (1984)]. Comparing the results with those obtained in the case of a monochromatic forcing, it appears that the range of unstable frequencies significantly widens. This finding agrees with the theoretical results found in the linear context by Zhang, Casademunt, and Viñals [“Study of the parametric oscillator driven by a narrow band noise to model the response of a fluid surface to time-dependent accelerations,” Phys. Fluids A 5, 3147 (1993)]. The maximum equilibrium amplitude of the free surface waves for the random forcing case turns out to be smaller than that of the monochromatic forcing and it decreases as the spectrum width is increased. © 2002 American Institute of Physics.
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47.35.-i Hydrodynamic waves

Calculations of the near-wall thermophoretic force in rarefied gas flow

M. A. Gallis, D. J. Rader, and J. R. Torczynski

Phys. Fluids 14, 4290 (2002); http://dx.doi.org/10.1063/1.1518692 (12 pages) | Cited 11 times

Online Publication Date: 6 November 2002

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The thermophoretic force on a near-wall, spherical particle in a rarefied, monatomic gas flow is calculated numerically. The rarefied gas flow is calculated with the Direct Simulation Monte Carlo (DSMC) method, which provides the molecular velocity distribution. The force is calculated from the molecular velocity distribution using a force Green’s function. Calculations are performed over a Knudsen-number range from 0.0475 to 4.75 using Maxwell and hard-sphere collision models. Results are presented for the thermophoresis parameter, ξ, a dimensionless quantity proportional to the thermophoretic force. The spatial profiles of ξ show a clear progression from free-molecular conditions (ξ is constant throughout the domain) to near-continuum conditions (ξ is constant in the interior but increases in the Knudsen layers). For near-continuum conditions, the DSMC calculations and Chapman–Enskog theory are in excellent agreement in the interior, suggesting that their velocity distributions are similar in this region. For all conditions examined, ξ lies between the continuum and free-molecular limits, which differ by only 10%. Moreover, the near-wall ξ values differ from the interior values by less than 5% for a fully diffuse wall, in sharp contrast with most previous studies. An approximate theory for the wall effect is presented that agrees reasonably well with the calculations. © 2002 American Institute of Physics.
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47.45.-n Rarefied gas dynamics

Stability analysis of thermosolutal convection in a vertical packed porous enclosure

Mahmoud Mamou

Phys. Fluids 14, 4302 (2002); http://dx.doi.org/10.1063/1.1518996 (13 pages) | Cited 8 times

Online Publication Date: 6 November 2002

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A linear stability theory is performed to investigate the stability of the quiescent state and fully developed thermosolutal convection within a vertical porous enclosure subject to horizontal opposing gradients of temperature and solute. The fluid motion is modeled using the unsteady form of Darcy’s law coupled with energy and species conservation equations. The effect of different thermal and solutal boundary conditions is considered. The linearized governing equations are solved numerically using a finite element method. The thresholds for oscillatory and stationary convection are determined as functions of the governing parameters. It is concluded that the porosity and the acceleration parameter of the porous medium have a strong effect on the onset of overstability for a confined enclosure and on the wave number for an infinite enclosure. The stability analysis of fully developed flows within a slender enclosure reveals that an increase in the porosity and the acceleration parameter of the porous media delays the appearance of oscillatory finite amplitude flows. A nonlinear numerical solution is also computed by solving the full governing equations using a finite element method. Within the overstable regime, nonlinear traveling waves exist within slender enclosures, subject to Dirichlet thermal and solutal boundary conditions.© 2002 American Institute of Physics.
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47.27.T- Turbulent transport processes
47.56.+r Flows through porous media

Nonlinear electrokinetic ejection and entrainment due to polarization at nearly insulated wedges

Sunil Kumar Thamida and Hsueh-Chia Chang

Phys. Fluids 14, 4315 (2002); http://dx.doi.org/10.1063/1.1519530 (14 pages) | Cited 46 times

Online Publication Date: 6 November 2002

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We examine a singular electrokinetic flow around a corner or a wedge in micro-channels constructed from dielectric materials whose permittivity is small but finite compared to that of the electrolyte. When the wedge angle is less than 180°, the applied electric field, which is tangential far from the corner, develops a normal surface component that becomes singular at the corner. This normal field leakage causes opposite polarization at the two sides of the wedge and produces a converging singular tangential electrokinetic flow that ejects liquid from the tip. By expanding in cylindrical harmonics, we estimate this ejecting flow as a function of the permittivity ratio, applied electric field, angle of the wedge and the microscopic corner curvature that suppresses the singularity. The ejecting flow entrains tangential flow on the front side of the wedge and produces a vortex on the downstream side. This entrainment offers a long-range attractive hydrodynamic force that complements short-range electrostatic DLVO (Derjaguin–Landau–Verwey–Overbeek) and dielectrophoretic forces to enhance corner deposition and aggregation of colloids and proteins during electrophoresis/electro-osmosis. © 2002 American Institute of Physics.
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82.45.-h Electrochemistry and electrophoresis
47.55.Hd Stratified flows
77.22.Ch Permittivity (dielectric function)
47.32.C- Vortex dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems

Transient effects in the signaling problem

José M. Gordillo and Miguel Pérez-Saborid

Phys. Fluids 14, 4329 (2002); http://dx.doi.org/10.1063/1.1514654 (15 pages) | Cited 3 times

Online Publication Date: 6 November 2002

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We have obtained a uniformly valid asymptotic solution which accounts for the transient effects which take place during the response to the periodic forcing in the linear signaling problem. This solution complements the results of classical references [Huerre and Monkewitz, J. Fluid Mech. 159, 151 (1985); Annu. Rev. Fluid Mech. 22, 473 (1990); Huerre, in Perspectives in Fluid Dynamics (Cambridge University Press, Cambridge, 2000), pp. 159–229] by determining the spatiotemporal limits for the transition region separating the zone where the response has reached the periodic regime from that free of disturbances. The method of solution is based on the well-known steepest descent technique and does not invoke any type of causality arguments of the type resorted to in above-mentioned works. In addition, our technique provides one with a procedure, alternative to that presented in the above-mentioned works, which permits to identify very easily the direction of propagation (downstream or upstream) of the waves associated with the different spatial eigenvalues of the problem. The asymptotic solution obtained using the general procedure described in this paper has been validated with the numerical results for two relatively simple problems: the forced one-dimensional Ginzburg–Landau equation, and the forced Kelvin–Helmholtz problem. © 2002 American Institute of Physics.
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47.11.-j Computational methods in fluid dynamics
47.20.-k Flow instabilities
47.52.+j Chaos in fluid dynamics
47.27.T- Turbulent transport processes

Optimal large-eddy simulation of forced Burgers equation

Arup Das and Robert D. Moser

Phys. Fluids 14, 4344 (2002); http://dx.doi.org/10.1063/1.1516212 (8 pages) | Cited 11 times

Online Publication Date: 6 November 2002

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To explore the properties of optimal large eddy simulation (LES) formulations, they have been applied to the case of forced one-dimensional Burgers equation with a Fourier cutoff filter, rather than three-dimensional turbulence for which this approach was developed. This simplified model problem allows more complex models to be evaluated than was possible in three-dimensional turbulence. Further, in “Burgers turbulence,” the small scales consist of shocks, and the evolution of Fourier filtered shocks can be constructed with high accuracy. Thus, the lower bound on the modeling error in this case is known to be very small, if not zero, which makes it possible to correctly interpret the observed errors in the optimal LES models. Optimal LES models were used in Burgers equation LES, and it was found that the solution exhibits shocks similar to the exact solution but that the Gibbs phenomenon that exists in the exact filtered solution is gradually eliminated. This also produced poor results for the high wavenumber spectrum. In contrast, previous optimal LES studies in isotropic turbulence yielded very good results for the spectra. The differences and similarities in performance on Burgers equation and three-dimensional turbulence are instructive for characterizing the properties of optimal LES models. © 2002 American Institute of Physics.
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47.27.E- Turbulence simulation and modeling
47.40.Nm Shock wave interactions and shock effects

A model for preferential concentration

H. Sigurgeirsson and A. M. Stuart

Phys. Fluids 14, 4352 (2002); http://dx.doi.org/10.1063/1.1517603 (10 pages) | Cited 37 times

Online Publication Date: 6 November 2002

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The preferential concentration of inertial particles in a turbulent velocity field occurs when the particle and fluid time constants are commensurate. We propose a straightforward mathematical model for this phenomenon and use the model to study various scaling limits of interest and to study numerically the effect of interparticle collisions. The model comprises Stokes’ law for the particle motions, and a Gaussian random field for the velocity. The primary advantages of the model are its amenability to mathematical analysis in various interesting scaling limits and the speed at which numerical simulations can be performed. The scaling limits corroborate experimental evidence about the lack of preferential concentration for a large and small Stokes number and make new predictions about the possibility of preferential concentration at large times and lead to stochastic differential equations governing this phenomenon. The effect of collisions is found to be negligible for the most part, although in some cases they have an interesting antidiffusive effect. © 2002 American Institute of Physics.
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47.27.-i Turbulent flows

The effects of high-frequency ultrasound on turbulent liquid mixing with a rapid chemical reaction

Yasumasa Ito, Kouji Nagata, and Satoru Komori

Phys. Fluids 14, 4362 (2002); http://dx.doi.org/10.1063/1.1518508 (10 pages) | Cited 5 times

Online Publication Date: 6 November 2002

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The effects of high-frequency ultrasound and mean fluid shear on turbulent mixing with a rapid chemical reaction were experimentally investigated in three types of liquid mixing-layer flow downstream of a turbulence-generating grid; pure grid-generated turbulence, grid-generated turbulence with high-frequency ultrasonic irradiation, and grid-generated turbulence with mean fluid shear. Instantaneous velocity and concentration were simultaneously measured using the combination of a laser-Doppler velocimeter and a laser-induced fluorescence method. The results show that turbulent mixing and chemical reaction are promoted by ultrasonic irradiation and mean fluid shear. The amount of chemical product in grid-generated turbulence with high-frequency ultrasonic irradiation is much larger than that in grid-generated turbulence with mean fluid shear, despite turbulent mass transport being enhanced at an equivalent level in both flows. This is attributed to the difference in turbulent mass transport at small scales. Ultrasonic irradiation more enhances the mass transport at smaller scales than by mean fluid shear, whereas mean shear can promote the mass transport only at larger scales. As a result, high-frequency ultrasound can be regarded as a better tool for promoting turbulent mixing and chemical reaction than mean fluid shear. © 2002 American Institute of Physics.
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64.75.-g Phase equilibria
47.27.-i Turbulent flows
47.70.Fw Chemically reactive flows
43.35.-c Ultrasonics, quantum acoustics, and physical effects of sound
47.80.-v Instrumentation and measurement methods in fluid dynamics
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