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Sep 2003

Volume 15, Issue 9, pp. L65-L71, 2469-2786

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Dynamics of distributed sources

E. A. Novikov

Phys. Fluids 15, L65 (2003); http://dx.doi.org/10.1063/1.1597451 (3 pages) | Cited 1 time

Online Publication Date: 11 July 2003

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The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling—from the Lagrangian invariants to dynamics. Possible applications of distributed sources and sinks to geophysical fluid dynamics and to the cosmology are indicated. © 2003 American Institute of Physics.
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47.32.C- Vortex dynamics
47.11.-j Computational methods in fluid dynamics
02.30.Jr Partial differential equations

A coupled Landau model describing the Strouhal–Reynolds number profile of a three-dimensional circular cylinder wake

G. J. Sheard, M. C. Thompson, and K. Hourigan

Phys. Fluids 15, L68 (2003); http://dx.doi.org/10.1063/1.1597471 (4 pages) | Cited 4 times

Online Publication Date: 23 July 2003

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A known bifurcation scenario describing the development and interaction of Mode A and Mode B vortex shedding modes of a circular cylinder wake is extended to predict the Strouhal–Reynolds number profile over the three-dimensional transitions. The mode amplitudes are described by coupled Landau equations and, with frequency information being included by the addition of complex coefficients, the model predicts the discontinuous nature of the Strouhal–Reynolds number shedding profile of the circular cylinder wake throughout the laminar three-dimensional transition regime. The model coefficients are determined from computations of the three-dimensional modes of a circular cylinder wake. © 2003 American Institute of Physics.
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47.15.Fe Stability of laminar flows
47.27.wb Turbulent wakes
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
47.32.C- Vortex dynamics
47.11.-j Computational methods in fluid dynamics
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Breakup length of forced liquid jets

A. Kalaaji, B. Lopez, P. Attané, and A. Soucemarianadin

Phys. Fluids 15, 2469 (2003); http://dx.doi.org/10.1063/1.1593023 (11 pages) | Cited 13 times

Online Publication Date: 17 July 2003

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The experimental breakup of liquid jets subjected to a sinusoidal perturbation is investigated in the Rayleigh and first wind-induced regimes. Stroboscopic illumination of the jet and laser photometry method are used. The ability of linear spatial and temporal theories to describe certain aspects of the phenomenon is stressed. A review of data in the literature shows that the limited experimental windows investigated so far do not allow definite conclusions to be drawn. Our results, obtained over a wide range of fluid viscosity and jet velocity values, show that the linear theory of Sterling and Sleicher accurately predicts the variation in breakup length with jet velocity. The exponential character of the initial growth of a monochromatic perturbation along the jet is also described quantitatively. These results were obtained by carefully controlling the initial jet surface perturbation. It is also shown that transient surface tension and jet contraction have to be taken into account to analyze the experimental results. © 2003 American Institute of Physics.
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68.03.Cd Surface tension and related phenomena
47.27.wg Turbulent jets
47.20.Dr Surface-tension-driven instability
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.55.D- Drops and bubbles
47.35.-i Hydrodynamic waves

Instability of interfaces in phase-separating binary fluids at a finite Reynolds number

Hirohito Kiwata

Phys. Fluids 15, 2480 (2003); http://dx.doi.org/10.1063/1.1592156 (6 pages) | Cited 1 time

Online Publication Date: 17 July 2003

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We investigate a stability of a lamellar domain in phase-separating binary fluids under an external flow. Using the Navier–Stokes and the Cahn–Hilliard equations, we take into account effects of diffusion and surface tension at an interface. Stability eigenvalues are evaluated for various values of the Péclet number, the spacing between the interfaces, and the Reynolds number. It is found that the lamellar domain becomes unstable at a finite wavenumber before the flow when the Reynolds number increases. The instability of the interface occurs on conditions that the interface is situated near a wall or the Péclet number is large. The instability stems from the interaction between disturbances of the flow and the diffusive interface. © 2003 American Institute of Physics.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.20.Dr Surface-tension-driven instability
64.75.-g Phase equilibria
68.03.Cd Surface tension and related phenomena

Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers

Sangmo Kang

Phys. Fluids 15, 2486 (2003); http://dx.doi.org/10.1063/1.1596412 (13 pages) | Cited 47 times

Online Publication Date: 21 July 2003

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Two-dimensional flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers has been numerically investigated in this study. For the study, numerical simulations are performed, using the immersed boundary method, in the ranges of 40 ⩽ Re ⩽ 160 and g∗<5, where Re and g∗ are, respectively, the Reynolds number and the spacing between the two cylinder surfaces divided by the cylinder diameter. Results show that a total of six kinds of wake patterns are observed over the ranges: antiphase-synchronized, in-phase-synchronized, flip-flopping, deflected, single bluff-body, and steady wake patterns. It is found that the characteristics of the flow significantly depend both on the Reynolds number and gap spacing, with the latter much stronger than the former. Instantaneous flow fields, time traces, flow statistics and so on are presented to identify the wake pattern and then to understand the underlying mechanism. Moreover, the bifurcation phenomena where either of two wake patterns can occur are found at certain flow conditions. © 2003 American Institute of Physics.
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47.27.wb Turbulent wakes
47.54.-r Pattern selection; pattern formation
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Mixing of concentrated oil-in-water emulsions measured by nuclear magnetic resonance imaging

Marcos A. d’Avila, Nina C. Shapley, Jeffrey H. Walton, Ronald J. Phillips, Stephanie R. Dungan, and Robert L. Powell

Phys. Fluids 15, 2499 (2003); http://dx.doi.org/10.1063/1.1583731 (13 pages) | Cited 6 times

Online Publication Date: 23 July 2003

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Mixing of concentrated oil-in-water emulsions in a horizontal, concentric-cylinder geometry was studied using nuclear magnetic resonance imaging. Time-of-flight and chemical shift imaging methods were used to measure velocity profiles and concentration maps in an emulsion that was mixed after being allowed to cream for several hours. The results revealed detailed information about mixing in concentrated emulsions. In the initial state, before mixing, the emulsion system formed three layers: an upper, oil-rich, “creamed” layer; a lower, water-rich layer; and a bulk concentration layer in between. It was found that the thickness of the creamed layer remained constant during mixing, while the oil concentration in that layer decayed exponentially as a function of time. It was also observed that most of the emulsion is quiescent while mixing occurs; the only motion detected occurs in a thin layer close to the rotating, outer cylinder. The velocity profile only begins to transition to its steady-state configuration after the emulsion becomes well mixed. A simple model is introduced that gives a plausible explanation of these experimental observations. These results indicate that the mixing mechanism in concentrated emulsions is significantly different from that in single-phase liquids. © 2003 American Institute of Physics.
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82.70.Kj Emulsions and suspensions
64.75.-g Phase equilibria

Time-dependent free-surface thin film flows over topography

Catherine Bielarz and Serafim Kalliadasis

Phys. Fluids 15, 2512 (2003); http://dx.doi.org/10.1063/1.1590978 (13 pages) | Cited 26 times

Online Publication Date: 23 July 2003

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The lubrication equation governing free-surface thin film flows over topography is solved numerically including the effects of inertia and intermolecular forces. We study the initial value problem for a variety of initial conditions and perturbations and demonstrate that the free surface is strongly stable and can only be destabilized with large values of the dimensionless Hamaker’s constant and large amplitude free-surface perturbations, both of which are difficult to achieve in practice. The strong stability of thin film flows over topography is in agreement with the recent analysis by Kalliadasis and Homsy [J. Fluid Mech. 448, 387 (2001)]. © 2003 American Institute of Physics.
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68.15.+e Liquid thin films
68.08.Bc Wetting
47.10.-g General theory in fluid dynamics

Multimode decomposition of spatially growing perturbations in a two-dimensional boundary layer

Anatoli Tumin

Phys. Fluids 15, 2525 (2003); http://dx.doi.org/10.1063/1.1597453 (16 pages) | Cited 19 times

Online Publication Date: 24 July 2003

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Three-dimensional spatially growing perturbations in a two-dimensional incompressible boundary layer are considered within the scope of linearized Navier–Stokes equations. The Cauchy problem is solved under the assumption of a finite growth rate of the disturbances. It is shown that the solution can be presented as an expansion into a biorthogonal eigenfunction system. The result can be utilized for decomposition of flow fields derived from computational studies when pressure and all velocity components, together with their derivatives, are available. The method can be used also in a case where partial data are available when a priori information leads to consideration of a finite number of modes. In the case of a continuous spectrum, the problem of decomposition based on partial information is ill-posed, but the method might be applied under additional assumptions about the perturbations.© 2003 American Institute of Physics.
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47.15.Cb Laminar boundary layers
47.27.nb Boundary layer turbulence
47.10.-g General theory in fluid dynamics
47.11.-j Computational methods in fluid dynamics

Hysteretic behavior of the flow under a vertical sluice gate

Andrea Defina and Francesca Maria Susin

Phys. Fluids 15, 2541 (2003); http://dx.doi.org/10.1063/1.1596193 (8 pages) | Cited 5 times

Online Publication Date: 31 July 2003

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In the paper, the phenomenon of hysteresis which can develop in a supercritical channel flow approaching an obstacle is analyzed, and a simple theory to predict the occurrence of hysteresis is described. The results of an in-depth theoretical and experimental study of the case of flow under a vertical sluice gate in a rectangular channel are then presented. Possible flow regimes in the vicinity of a gate are classified on the basis of the nondimensional gate opening and the Froude number of the undisturbed approaching flow. It is shown that within a wide range of flow parameters both undisturbed and free outflow conditions may exist for the same gate opening. Within this range, the actual regime depends on the previous history of the flow, thus implying the hysteretic character of the flow. It is worth noting that a subcritical approaching flow may also exhibit such a hysteretic behavior provided the Froude number is greater than approximately 0.8. This occurrence, which has not previously been reported in the literature, is probably a result of the contraction affecting the flow issuing from under the gate. The results of an extensive series of experiments, performed over a wide range of flow parameters, are detailed in the paper and confirm theoretical predictions. © 2003 American Institute of Physics.
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47.60.-i Flow phenomena in quasi-one-dimensional systems

Characteristics of square cylinder wake transition flows

S. C. Luo, Y. T. Chew, and Y. T. Ng

Phys. Fluids 15, 2549 (2003); http://dx.doi.org/10.1063/1.1596413 (11 pages) | Cited 21 times

Online Publication Date: 31 July 2003

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The wake transition regime in square cylinder flow is investigated experimentally. Mode A and B transitions similar to those captured in circular cylinder flows are found to exist in this regime and by using dye- and laser-induced fluorescence visualization, the spanwise and streamwise vortex structures are captured. Upon comparison with their corresponding modes in circular cylinder flows, some differences are noted. Most notably, the critical Reynolds numbers at which Mode A and B occur for square cylinder flows were estimated to be approximately 160 and 200, respectively, and are lower than those found in circular cylinder flows, which are generally agreed to be approximately 188–190 and 230–260, respectively. Also, the spanwise wavelengths for the two modes in square cylinder flows (5.2 Ds and 1.2 Ds for Modes A and B, respectively) are longer than their counterparts in circular cylinder flows (3–4Do and 0.8–1Do, respectively). Furthermore, by using a hot wire to measure the shedding frequency, it was found that the Mode A transition here does not exhibit a hysteresis phenomenon, which is unlike the case in circular cylinder flows. The Mode A to B transition here is also not associated with a sudden increase in Strouhal number, which is again unlike the corresponding situation in circular cylinder flows. However, the vortical structures are noted to be similar between the corresponding modes for the two bluff body shapes, and hence the formation mechanism can be deemed to be similar. © 2003 American Institute of Physics.
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47.27.wb Turbulent wakes
47.15.Fe Stability of laminar flows
47.27.Cn Transition to turbulence
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.32.C- Vortex dynamics

Mixing rates and symmetry breaking in two-dimensional chaotic flow

Greg A. Voth, T. C. Saint, Greg Dobler, and J. P. Gollub

Phys. Fluids 15, 2560 (2003); http://dx.doi.org/10.1063/1.1596915 (7 pages) | Cited 34 times

Online Publication Date: 31 July 2003

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We experimentally determine the mixing rate for a magnetically forced two-dimensional time-periodic flow exhibiting chaotic mixing. The mixing rate, defined as the rate of decay of the root-mean square concentration inhomogeneity, grows with Reynolds number, but does not increase at the onset of nonperiodic (weakly turbulent) flow. The mixing rate increases linearly with a second non-dimensional parameter, the typical path length of a fluid element in one forcing period. The breaking of time-reversal symmetry and spatial reflection symmetry substantially increases the mixing rates. A theory by Antonsen et al. that predicts mixing rates in terms of the measured Lyapunov exponents of the flow is tested and found to predict mixing rates that are too large by approximately a factor of 10; the discrepancy is traced to the fact that large scale transport rather than stretching of fluid elements is the dominant rate limiting step when the system is sufficiently large compared to the velocity correlation length. An effective diffusion model gives a good account of the measured mixing rates. Finally, the formation of persistent recurrent patterns (also called strange eigenmodes) is shown to arise from a combination of stretching and effective diffusion. © 2003 American Institute of Physics.
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47.52.+j Chaos in fluid dynamics
64.75.-g Phase equilibria
47.65.-d Magnetohydrodynamics and electrohydrodynamics
05.45.-a Nonlinear dynamics and chaos

Diffuse interface modeling of the morphology and rheology of immiscible polymer blends

B. J. Keestra, P. C. J. Van Puyvelde, P. D. Anderson, and H. E. H. Meijer

Phys. Fluids 15, 2567 (2003); http://dx.doi.org/10.1063/1.1597454 (9 pages) | Cited 18 times

Online Publication Date: 31 July 2003

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A diffuse interface model is used to simulate a step-shear experiment of a binary immiscible polymer blend. The gradient theory used in diffuse interface modeling makes it possible to incorporate interfacial tension and governs the process of coalescence and breakup without any additional decision criteria. The interface tensor q, a direct outcome of the model, is used to relate microstructural information to the first-normal stress difference N1. The results obtained are in qualitative agreement with experiments reported in the literature.© 2003 American Institute of Physics.
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83.80.Rs Polymer solutions
61.25.H- Macromolecular and polymers solutions; polymer melts
64.75.-g Phase equilibria
68.03.Cd Surface tension and related phenomena

Heat and mass transfer during the violent collapse of nonspherical bubbles

Andrew J. Szeri, Brian D. Storey, Antony Pearson, and John R. Blake

Phys. Fluids 15, 2576 (2003); http://dx.doi.org/10.1063/1.1595647 (11 pages) | Cited 17 times

Online Publication Date: 1 August 2003

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The very high speed of collapse of cavitation bubbles is responsible for a number of phenomena of interest in science and engineering: Luminescence, sonochemistry, cavitation damage, ultrasonic cleaning, etc. Strongly forced bubbles may collapse with such violence that the relatively slow processes of diffusion of the heat of compression and of excess vapor to the bubble wall are obviated. This leads to an approximately adiabatic system with nearly constant mass during the final stages of extreme collapses, accompanied by the evolution of sharp thermal and compositional boundary layers on either side of the interface. It is shown that the boundary layers, which are involved in the determination of the interfacial temperature through the balance of sensible and latent heats, may profitably be described mathematically through integral equations. This complements well the boundary integral solution of the fluid dynamics, which has been the basis of much progress in the field. © 2003 American Institute of Physics.
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47.55.D- Drops and bubbles
47.27.T- Turbulent transport processes
47.55.dp Cavitation and boiling

Capillary driven flow in circular cylindrical tubes

Michael Stange, Michael E. Dreyer, and Hans J. Rath

Phys. Fluids 15, 2587 (2003); http://dx.doi.org/10.1063/1.1596913 (15 pages) | Cited 35 times

Online Publication Date: 1 August 2003

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Capillary-driven flow of a perfectly wetting liquid into circular cylindrical tubes is studied. Based on an analysis of previous approaches, a comprehensive theoretical model is presented which is not limited to certain special cases. This model considers the meniscus reorientation, the dynamic contact angle as well as inertia, convective, and viscous losses inside the tube and the reservoir. The capillary-driven flow is divided into three successive phases where first inertia then convective losses and finally viscous forces counteract the driving capillary force. This leads to an initial meniscus height increase proportional to the square of time followed by a linear dependence and finally the Lucas–Washburn behavior where the meniscus height is proportional to the square root of time. The three phases are separated by two characteristic transition times which are determined by the Ohnesorge number and the inertia of the liquid. Experiments were carried out under microgravity condition in a carefully chosen range of Ohnesorge numbers and initial liquid heights to cover the complete process from the initial meniscus development to the final Lucas–Washburn behavior. Good agreement of experimental and theoretical data is found throughout the complete range of experiment parameters. The existence of all three flow regimes predicted by the theory is verified by the experiments. © 2003 American Institute of Physics.
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47.60.-i Flow phenomena in quasi-one-dimensional systems
47.27.T- Turbulent transport processes
68.03.Cd Surface tension and related phenomena

Velocity streak structure modifications induced by flow manipulation

Gaetano Iuso, Gaetano Maria Di Cicca, Michele Onorato, Pier Giorgio Spazzini, and Riccardo Malvano

Phys. Fluids 15, 2602 (2003); http://dx.doi.org/10.1063/1.1597680 (11 pages) | Cited 4 times

Online Publication Date: 1 August 2003

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The present research is based on the belief that the observation of the response of near wall turbulent organized motions to external perturbations is a powerful technique for investigating the physics of turbulence regeneration. The low speed streak behavior in the buffer layer of a flat plate turbulent boundary layer under the action of transversal wall oscillation has been statistically analyzed by observing particle image velocimetry velocity fields in a plane parallel to the wall at a distance of 20 wall units. It was found that the observed reduction in turbulence activity (velocity variance and Reynolds stress) is accompanied by an increase of the averaged velocity streaks width, spacing and waviness and by a reduction of their strength. The increase in streak width and spacing has been attributed mainly to coalescence processes between neighboring streaks. The occurrence of velocity streaks strength reduction, associated with the consequent decrease of the number of unstable low speed streaks, is believed to be the main reason leading to the reduction of turbulent activity. The interpretation of the present results supports the concept that the so-called streak regeneration cycle plays an important role in the near wall turbulence reproduction process. © 2003 American Institute of Physics.
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47.27.nb Boundary layer turbulence
47.35.-i Hydrodynamic waves
47.85.L- Flow control

Second-order slip laws in microchannels for helium and nitrogen

Jean Maurer, Patrick Tabeling, Pierre Joseph, and Herve Willaime

Phys. Fluids 15, 2613 (2003); http://dx.doi.org/10.1063/1.1599355 (9 pages) | Cited 79 times

Online Publication Date: 1 August 2003

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We perform gas flow experiments in a shallow microchannel, 1.14±0.02 μm deep, 200 μm wide, etched in glass and covered by an atomically flat silicon wafer. The dimensions of the channel are accurately measured by using profilometry, optical microscopy and interferometric optical microscopy. Flow-rate and pressure drop measurements are performed for helium and nitrogen, in a range of averaged Knudsen numbers extending up to 0.8 for helium and 0.6 for nitrogen. This represents an extension, by a factor of 3 or so, of previous studies. We emphasize the importance of the averaged Knudsen number which is identified as the basic control parameter of the problem. From the measurements, we estimate the accommodation factor for helium to be equal to 0.91±0.03 and that for nitrogen equal to 0.87±0.06. We provide estimates for second-order effects, and compare them with theoretical expectations. We estimate the upper limit of the slip flow regime, in terms of the averaged Knudsen number, to be 0.3±0.1, for the two gases. © 2003 American Institute of Physics.
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47.45.Gx Slip flows and accommodation

Instability mechanisms in swirling flows

F. Gallaire and J.-M. Chomaz

Phys. Fluids 15, 2622 (2003); http://dx.doi.org/10.1063/1.1589011 (18 pages) | Cited 10 times

Online Publication Date: 5 August 2003

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We investigate the stability of the screened Rankine vortex with added plug flow where the azimuthal velocity decreases abruptly outside the core of the vortex. The jump in circulation is known to induce centrifugal and azimuthal Kelvin–Helmholtz instabilities. Their effect on the stability of the different azimuthal wave number m is discussed using physical considerations associated with asymptotic expansions and numerical computations of the dispersion relation. It is shown that the axial shear and centrifugal instability are active for all m, and that modes with ∣m∣ ≥ 2 are also destabilized by azimuthal shear. In contrast, the bending modes m = ±1 are stabilized by a coupling with Kelvin waves in the core. Effects of rotation on the absolute/convective transition are also discussed. The absolute instability of positive helical modes is seen to be promoted by centrifugal instability and azimuthal shear. © 2003 American Institute of Physics.
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47.32.C- Vortex dynamics
47.20.-k Flow instabilities

The transient rise of a bubble subject to shape or volume changes

B. Yang, A. Prosperetti, and S. Takagi

Phys. Fluids 15, 2640 (2003); http://dx.doi.org/10.1063/1.1592800 (9 pages) | Cited 4 times

Online Publication Date: 5 August 2003

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This paper deals with two problems in which the rectilinear rise of a gas bubble in a liquid undergoes a transient behavior. In the first problem, the bubble is released with a spherical, oblate, prolate, or oval shape and its evolution to steady state is simulated numerically. Contrary to some recently reported experiments, it is found that the terminal velocity and final shape are independent of the initial shape. This result suggests that the experimental observations may be influenced by uncontrolled effects rather than a genuine multivaluedness of the fluid-dynamic solution for a steadily rising bubble. The second problem concerns the ascent of a bubble which expands, or contracts, due to a change in the ambient pressure. The ensuing behavior of the rise velocity is strongly influenced by added mass effects. © 2003 American Institute of Physics.
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47.55.Kf Particle-laden flows
47.55.D- Drops and bubbles
47.10.-g General theory in fluid dynamics
47.11.-j Computational methods in fluid dynamics

Reversible and irreversible dispersion in a porous medium

A. A. Khrapitchev and P. T. Callaghan

Phys. Fluids 15, 2649 (2003); http://dx.doi.org/10.1063/1.1596914 (12 pages) | Cited 26 times

Online Publication Date: 5 August 2003

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Pulsed gradient spin echo nuclear magnetic resonance (PGSE NMR) has been used to examine the approach to asymptotic dispersion for flow of water in a randomly packed array of 500 μm latex spheres in a cylindrical tube of inner diameter 10 mm. Measurements have been performed using single pulse pair and double pulse pair PGSE NMR in directions both transverse to and co-linear with the flow direction, Péclet numbers (Pe) covering a range from 2.8×103 to 8.4×103. In the case of longitudinal flow we find evidence for both reversible and irreversible dispersion over observation times of up to 10τv where τv is the correlation time associated with flow across one bead diameter. The fluctuating component of the velocity field appears to obey a simple Ornstein–Uhlenbeck correlation function with a single correlation time in close agreement with τv. In transverse dispersion, no stationary velocity distribution is evident and the correlation time for fluctuation is much smaller, over the entire range of Pe values. © 2003 American Institute of Physics.
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76.60.Lz Spin echoes
47.80.-v Instrumentation and measurement methods in fluid dynamics
47.56.+r Flows through porous media
82.70.-y Disperse systems; complex fluids

Onset of thermal convection in a vertical porous cylinder with conducting wall

Kjetil B. Haugen and Peder A. Tyvand

Phys. Fluids 15, 2661 (2003); http://dx.doi.org/10.1063/1.1597452 (7 pages) | Cited 13 times

Online Publication Date: 5 August 2003

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The onset of Rayleigh–Bénard convection in a finite circular porous cylinder with vertical axis is investigated analytically. The cylinder is heated from below, and its top and bottom are assumed impermeable and perfectly heat-conducting. The impermeable sidewall of the cylinder is assumed to be heat-conducting so that the temperature perturbation there is zero. The eigenvalue problem is split into two different Helmholtz equations. The resulting eigenmode is expressed in terms of Bessel functions. The preferred mode at the onset of convection is found to be axisymmetric. The critical Rayleigh number is a smooth function of the aspect ratio of the cylinder, in contrast to the standard case of an insulating sidewall. © 2003 American Institute of Physics.
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47.27.T- Turbulent transport processes
47.56.+r Flows through porous media

Regularization of Grad’s 13 moment equations: Derivation and linear analysis

Henning Struchtrup and Manuel Torrilhon

Phys. Fluids 15, 2668 (2003); http://dx.doi.org/10.1063/1.1597472 (13 pages) | Cited 74 times

Online Publication Date: 5 August 2003

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A new closure for Grad’s 13 moment equations is presented that adds terms of Super-Burnett order to the balances of pressure deviator and heat flux vector. The additional terms are derived from equations for higher moments by means of the distribution function for 13 moments. The resulting system of equations contains the Burnett and Super-Burnett equations when expanded in a series in the Knudsen number. However, other than the Burnett and Super-Burnett equations, the new set of equations is linearly stable for all wavelengths and frequencies. Dispersion relation and damping for the new equations agree better with experimental data than those for the Navier–Stokes–Fourier equations, or the original 13 moments system. The new equations also allow the description of Knudsen boundary layers. © 2003 American Institute of Physics.
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47.45.-n Rarefied gas dynamics
47.10.-g General theory in fluid dynamics

Thermal expansion models of viscous fluids based on limits of free energy

S. E. Bechtel, M. G. Forest, F. J. Rooney, and Q. Wang

Phys. Fluids 15, 2681 (2003); http://dx.doi.org/10.1063/1.1597874 (13 pages) | Cited 5 times

Online Publication Date: 5 August 2003

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Many viscous flows are mechanically incompressible, yet thermally expand and shrink. Approximations of the compressible Navier–Stokes equations are routinely utilized to model diverse phenomena that share these properties, with a primary goal to remove rapid timescales associated with sound waves. Most models are derived from thermodynamic assumptions coupled with application-specific, scale separation assumptions in time and space. The Boussinesq model for laboratory-scale, buoyancy-driven thermal convection patterns [Spiegel and Veronis, Astrophys. J. 131, 442 (1960)] and the anelastic model for atmospheric-scale, density-stratification phenomena [Emanuel, Atmospheric Convection (Oxford University Press, New York, 1994)] are two important examples. Some engineering models of thermal expansion are fluid specific, e.g., for molten glasses and polymers, and rest upon thermodynamic assumptions alone. These models postpone specification of flow conditions, since applications range from slow confined flows for mold filling, to film flows, to high-speed, free surface fiber flows. The aims of this paper are to systematize the implementation of thermodynamic assumptions to derive thermal expansion models; to benchmark this class of models with respect to near-equilibrium physical behavior; and to pose candidate models for thermal expansion which may be used for a diverse set of flow conditions. By casting thermodynamic assumptions as limits of free energy, we reduce the full Navier–Stokes system in a straightforward way, and parametrize the limits of linearized compressible modes and their propagation properties. The thermodynamic assumptions are uncoupled from flow-dependent scale separation conditions, which can be subsequently augmented for specific applications. Indeed, one conclusion of this analysis is that the traditional thermal expansion assumption, where density is slaved to the temperature field, must be coupled with additional flow or thermal assumptions or else the model equations possess unphysical properties (e.g., instability of thermodynamic equilibrium or negative specific heat). Two new models for thermal expansion are deduced solely from a limit condition on free energy, which pass the minimal benchmark of non-negativity of bulk modulus, squared sound speed, and specific heat. We close with an indication of viscous flow applications of one of the new thermal expansion models. © 2003 American Institute of Physics.
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65.20.-w Thermal properties of liquids
51.30.+i Thermodynamic properties, equations of state
47.55.Hd Stratified flows
47.27.T- Turbulent transport processes
47.10.-g General theory in fluid dynamics

Free convection of binary liquid with variable Soret coefficient in thermogravitational column: The steady parallel base states

G. Labrosse

Phys. Fluids 15, 2694 (2003); http://dx.doi.org/10.1063/1.1597875 (34 pages) | Cited 10 times

Online Publication Date: 5 August 2003

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An exhaustive identification is made of the steady parallel base states which might occur in a thermogravitational column, with a constant horizontal thermal gradient, and a Soret coefficient depending both on temperature and composition, ST(T,C). It is shown that the horizontal dynamics is mainly governed by the Soret thermal sensitivity, and the vertical separation by its compositional one. Published ST(T,C) empirical laws are used to define a generic model which allows one to carry out a “normal mode” analysis of these flows. To account for the possible complete species vertical separation, the Boussinesq approximations are updated. To the leading order in the Soret coefficient amplitude, the horizontal dynamics is seen to be controlled by the solutal Péclet number, Pe, and a vertical stratification parameter, both drifting very slowly along the vertical. Stabilizing and potentially unstable vertical stratifications of the species are predicted, and, for each, the steady parallel flows are described for every thermal sensitivity of the Soret coefficient. Then an accurate determination of the vertical stratification profile is given for a constant and linear C-dependence of ST. The determinant peculiarity of the C-dependence is shown to be the number of zeroes that ST possesses in C ∊ ]0,1[. Some suggestions are made regarding the way the Soret coefficient measurement could benefit from this first analysis. It is shown, in particular, that the vertical separation slope may be misleading in real molecular mixtures, such as the 0.5 N NaCl solution about T = 12.09 °C, where the Soret term is mainly linear with temperature. © 2003 American Institute of Physics.
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47.27.T- Turbulent transport processes
66.10.C- Diffusion and thermal diffusion
47.55.Hd Stratified flows

Instability of the interface between two inviscid fluids inside a rotating annulus in the absence of gravity

L. A. Dávalos-Orozco and E. Vázquez-Luis

Phys. Fluids 15, 2728 (2003); http://dx.doi.org/10.1063/1.1597682 (12 pages)

Online Publication Date: 5 August 2003

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In this paper we investigate the linear instability of two superposed inviscid fluids between two rotating concentric cylinders. In the hydrostatic state the two fluids rotate as a rigid body with the same angular velocity as the annulus. Two problems are investigated. First, calculations are made of the instability of the liquid layer coating the outside of a cylinder under rotation. Second, results are obtained of the instability of two stratified fluids between two concentric cylinders. The first case is the most unstable condition of the second case when the outer fluid is absent. Therefore, in the second case only the instability of a system with a heavier fluid located outside the interface was investigated. It was found that the introduction of the inner cylinder produces new and interesting results about the axial and azimuthal modes not previously published in the literature. In particular, when a liquid layer coats the outside of a cylinder it was found that the azimuthal mode, n = 1, is the most important in a range of the nondimensional surface tension where the purely axial mode dominated in the absence of the inner cylinder. Additionally, it was found that some azimuthal spiral modes with a finite wavenumber appear as the most unstable in the presence of the inner cylinder. It was shown that the larger the centrifugal force is, the larger the nondimensional radius of the inner cylinder should be to make the instability more sensitive to the presence of the inner cylinder. An equation for the growth rate was obtained in the limit of very thin liquid layers and it was found that the maxima of growth rate agree very well with the experimental results of a fluid layer coating the outside of a rotating cylinder. © 2003 American Institute of Physics.
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47.20.Ma Interfacial instabilities (e.g., Rayleigh-Taylor)
47.55.Hd Stratified flows
68.03.Cd Surface tension and related phenomena
47.60.-i Flow phenomena in quasi-one-dimensional systems

Database analysis of errors in large-eddy simulation

Johan Meyers, Bernard J. Geurts, and Martine Baelmans

Phys. Fluids 15, 2740 (2003); http://dx.doi.org/10.1063/1.1597683 (16 pages) | Cited 61 times

Online Publication Date: 5 August 2003

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A database of decaying homogeneous, isotropic turbulence is constructed including reference direct numerical simulations at two different Reynolds numbers and a large number of corresponding large-eddy simulations at various subgrid resolutions. Errors in large-eddy simulation as a function of physical and numerical parameters are investigated. In particular, employing the Smagorinsky subgrid parametrization, the dependence of modeling and numerical errors on simulation parameters is quantified. The interaction between these two basic sources of error is shown to lead to their partial cancellation for several flow properties. This leads to a central paradox in large-eddy simulation related to possible strategies that can be followed to improve the accuracy of predictions. Moreover, a framework is presented in which the global parameter dependence of the errors can be classified in terms of the “subgrid activity” which measures the ratio of the turbulent to the total dissipation rate. Such an analysis allows one to quantify refinement strategies and associated model parameters which provide optimal total simulation error at given computational cost. © 2003 American Institute of Physics.
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47.11.-j Computational methods in fluid dynamics
47.27.-i Turbulent flows
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