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Dec 2007

Volume 19, Issue 12, Articles (12xxxx)

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Phys. Fluids 19, 124102 (2007); http://dx.doi.org/10.1063/1.2813548 (11 pages)

J. P. Wilkinson and J. W. Jacobs
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Scalar flux spectrum in isotropic steady turbulence with a uniform mean gradient

Takeshi Watanabe and Toshiyuki Gotoh

Phys. Fluids 19, 121701 (2007); http://dx.doi.org/10.1063/1.2821906 (4 pages) | Cited 3 times

Online Publication Date: 18 December 2007

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The scaling law of a scalar flux spectrum (velocity-scalar cospectrum) in the inertial convective range of passive scalar turbulence under a uniform mean scalar gradient is examined using direct numerical simulation with a resolution of up to 20483 grid points. When the Reynolds number Reλ is increased up to Reλ = 585, the scalar flux spectrum tends to obey the power law k−7/3, as predicted by Lumley [J. Atmos. Sci. 21, 99 (1964); Phys. Fluids 10, 855 (1967)] , with a nondimensional constant of Cuθ = 1.50±0.08 at Reλ = 585. The Reλ effect on the scaling of the scalar flux spectrum is well compensated using the mean molecular destruction of the scalar flux mathuθ. The Reλ dependence of Cuθ is also compared with the results of previous studies, and its asymptotic state at an infinite Reynolds number is discussed.
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47.27.ek Direct numerical simulations
47.27.Gs Isotropic turbulence; homogeneous turbulence
47.27.te Turbulent convective heat transfer
47.11.-j Computational methods in fluid dynamics

Electrically tunable viscosity of dilute suspensions of carbon nanotubes

Chen Lin and Jerry W. Shan

Phys. Fluids 19, 121702 (2007); http://dx.doi.org/10.1063/1.2824398 (4 pages) | Cited 12 times

Online Publication Date: 28 December 2007

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The apparent viscosity of a dilute (volume fraction ϕ = 1.5×10−5), single-wall-carbon-nanotube(SWNT)/α-terpineol suspension was experimentally found to more than double at moderate shear rates under an external electric field of strength 160 V/mm. The electrorheological response is interpreted in terms of an electrostatic-polarization model, where the governing parameter is a modified Mason number giving the ratio of viscous to dipole-dipole forces. Analysis of the hydrodynamic and electrostatic forces suggests that the magnitude of the electrorheological response in the dilute SWNT suspension, which is much higher than conventional electrorheological fluids at comparable volume fractions, is due to the high aspect ratio of the nanotubes. Comparison is made to a suspension of glassy carbon spheres, in which a three-order-of-magnitude-higher volume fraction is required to achieve similar increases in the apparent viscosity under the same conditions.
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47.65.Gx Electrorheological fluids
83.80.Gv Electro- and magnetorheological fluids
82.70.Kj Emulsions and suspensions
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.60.Fg Shear rate dependent viscosity
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back to top Interfacial Flows

Linear instability of pressure-driven channel flow of a Newtonian and a Herschel-Bulkley fluid

K. C. Sahu, P. Valluri, P. D. M. Spelt, and O. K. Matar

Phys. Fluids 19, 122101 (2007); http://dx.doi.org/10.1063/1.2814385 (11 pages) | Cited 15 times

Online Publication Date: 6 December 2007

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The linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of a Herschel-Bulkley fluid. A pair of coupled Orr-Sommerfeld eigenvalue equations are derived and solved using an efficient spectral collocation method for cases in which unyielded regions are absent. An asymptotic analysis is also carried out in the long-wave limit, the results of which are in excellent agreement with the numerical predictions. Our analytical and numerical results indicate that increasing the dimensionless yield stress, prior to the formation of unyielded plugs below the interface, is destabilizing. Increasing the shear-thinning tendency of the lower fluid is stabilizing.
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47.55.Hd Stratified flows
47.20.-k Flow instabilities

Bifurcation and hysteresis phenomena in two-dimensional sail-sail-flow interactions

Takeshi Sugimoto

Phys. Fluids 19, 122102 (2007); http://dx.doi.org/10.1063/1.2818229 (13 pages)

Online Publication Date: 7 December 2007

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This is the first report of complex bifurcation and manyfold hysteresis phenomena in the physics behind a pair of sails set in a flow of two dimensions. The formalism is based on inviscid vorticity theory, and the basic equations consist of a pair of integro-differential equations subject to a pair of nonlinear integral constraints. The method of solution is built up with the boundary element method for the integro-differential equations as well as the Newton–Raphson method for parameter search by use of the nonlinear integral constraints. Three types of configurations are considered as case studies on effects due to overlapping of the jib sail upon the main sail. Numerical analyses predict three sets of solutions: The convex-convex sail shapes, the concave-convex sail shapes, and the concave-concave sail shapes as well as two- or threefold hysteresis in aerodynamic and structural characteristics. Experimental observations confirm the existence of all the three solution sets, and moreover another set, the convex-concave sail shapes, is found by the experiment. The three case studies show that too much overlap of sails fails to obtain high lift.
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47.85.Gj Aerodynamics
02.60.Nm Integral and integrodifferential equations
47.11.Hj Boundary element methods
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking

Marangoni instability in ultrathin two-layer films

A. A. Nepomnyashchy and I. B. Simanovskii

Phys. Fluids 19, 122103 (2007); http://dx.doi.org/10.1063/1.2819748 (14 pages) | Cited 10 times

Online Publication Date: 13 December 2007

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The development of instabilities under the joint action of the van der Waals forces and Marangoni stresses in a two-layer film on a heated or cooled substrate, is considered. The problem is solved by means of a linear stability theory and nonlinear simulations. Nontrivial change of the droplet shape in the presence of the Marangoni effect, which manifests itself as the deformation of a “plateau” into an “inkpot,” is observed. The appearance of the threshold oscillations predicted by the linear stability theory is confirmed by nonlinear simulations.
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47.55.Hd Stratified flows
47.20.-k Flow instabilities

Photo-Marangoni convection in a thin liquid film

A. A. Golovin and V. A. Volpert

Phys. Fluids 19, 122104 (2007); http://dx.doi.org/10.1063/1.2823573 (8 pages)

Online Publication Date: 18 December 2007

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Marangoni convection caused by a photochemical reaction of the type AmathB in a thin liquid film with deformable interface is studied. A system of two coupled nonlinear evolution equations for the film thickness and the reactant concentration is derived in the long-wave approximation. Linear stability analysis is performed and the conditions for Marangoni convection to occur are obtained. It is shown that the type of instability depends on the ratio of diffusivities of the reactant and the product of the photochemical reaction: If the diffusivities are equal, the instability is always monotonic, while when they are significantly different the instability can be oscillatory. Numerical simulations of the derived system of equations are performed. It is shown that in the case of the monotonic instability, the system develops a spotty pattern that ultimately leads to the film rupture. In the case of oscillatory instability, it is shown that photo-Marangoni convection can result in sustained wavy patterns with a square symmetry.
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47.55.P- Buoyancy-driven flows; convection
47.20.-k Flow instabilities
68.15.+e Liquid thin films
68.03.Cd Surface tension and related phenomena

Gravitational effects on the deformation of a droplet adhering to a horizontal solid surface in shear flow

P. Dimitrakopoulos

Phys. Fluids 19, 122105 (2007); http://dx.doi.org/10.1063/1.2821127 (14 pages) | Cited 1 time

Online Publication Date: 19 December 2007

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In this paper we investigate the gravitational effects on the deformation of a three-dimensional droplet adhering to a horizontal rough solid surface in steady shear Stokes flows. Our study considers both positive and negative Bond numbers for viscous and inviscid droplets. When the interfacial system is initially at hydrostatic equilibrium, our study shows that the Bond number affects the deformation of viscous droplets with moderate and large initial contact angles in a different way than those for small angles owing to the interplay between the viscous and surface tension forces. Inviscid droplets with different initial contact angles show similar behavior as the Bond number increases, i.e., their deformation is monotonically decreased owing to the monotonic decrease of the droplets’ height and thus the exerted pressure force. Our study identifies the gravitational effects of the onset of interfacial sliding, i.e., on the portions of the contact line which slide first due to violation of the hysteresis condition. When the interfacial system is not at hydrostatic equilibrium at the flow initiation, its dynamic evolution is more complicated owing to the combined action of the shear flow with the gravitational forcing due to the difference between the initial shape with the hydrostatic one. Our computational results are accompanied with an analysis of the forces on the droplet which provides physical insight and identifies the three-dimensional nature of the interfacial deformation.
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47.55.dr Interactions with surfaces

Decomposition driven interface evolution for layers of binary mixtures. I. Model derivation and stratified base states

Uwe Thiele, Santiago Madruga, and Lubor Frastia

Phys. Fluids 19, 122106 (2007); http://dx.doi.org/10.1063/1.2824404 (23 pages) | Cited 18 times

Online Publication Date: 26 December 2007

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A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation and dewetting. The model is based on model-H describing the coupled transport of the mass of one component (convective Cahn-Hilliard equation) and momentum (Navier-Stokes-Korteweg equations) supplemented by appropriate boundary conditions at the solid substrate and the free surface. General transport equations are derived using phenomenological nonequilibrium thermodynamics for a general nonisothermal setting taking into account Soret and Dufour effects and interfacial viscosity for the internal diffuse interface between the two components. Focusing on an isothermal setting the resulting model is compared to literature results and its base states corresponding to homogeneous or vertically stratified flat layers are analyzed.
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47.55.Hd Stratified flows
47.55.N- Interfacial flows
47.50.Cd Modeling
68.08.Bc Wetting
47.10.A- Mathematical formulations
back to top Viscous and Non-Newtonian Flows

Measurement of tack of Newtonian liquids on porous substrates

Prateek K. Jha and Mahesh S. Tirumkudulu

Phys. Fluids 19, 123101 (2007); http://dx.doi.org/10.1063/1.2813586 (15 pages)

Online Publication Date: 3 December 2007

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Probe-tack experiments of Tirumkudulu et al. [Phys. Fluids 15, 1588 (2003)] have shown that squeeze flow of Newtonian liquids on flat, impermeable substrates can be successfully modeled using the lubrication approximation. Here, we present a model for squeeze flow of Newtonian liquids on porous substrates where the flow in the gap is coupled to the fluid flow in the porous media. The competition of spreading and imbibition of liquid on a partially saturated porous substrate determines the force versus gap profile in both the squeeze (compression) and pull-off (tension) modes. The finite difference method was used to discretize the lubrication equation in the gap while boundary element method was employed to solve for flow in the porous substrate. The model predicts a lower magnitude of force for porous substrates in both compression and tension modes compared to that for impermeable substrates. Experiments on porous alumina substrates with Newtonian liquids show close agreement with the model predictions in both compression and tension modes when the gap is corrected for the obliqueness of the confining surfaces. Cavitation is predicted for some cases in the tension mode when the pressure in the gap reduced below the vapor pressure of liquid.
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47.11.Bc Finite difference methods
47.11.Hj Boundary element methods
47.56.+r Flows through porous media
back to top Particulate, Multiphase, and Granular Flows

Phase diagram of vertically shaken granular matter

Peter Eshuis, Ko van der Weele, Devaraj van der Meer, Robert Bos, and Detlef Lohse

Phys. Fluids 19, 123301 (2007); http://dx.doi.org/10.1063/1.2815745 (11 pages) | Cited 12 times

Online Publication Date: 6 December 2007

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A shallow, vertically shaken granular bed in a quasi-two-dimensional container is explored experimentally yielding a wider variety of phenomena than in any previous study: (1) bouncing bed, (2) undulations, (3) granular Leidenfrost effect, (4) convection rolls, and (5) granular gas. These phenomena and the transitions among them are characterized by dimensionless control parameters and combined in a full experimental phase diagram.
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45.70.Mg Granular flow: mixing, segregation and stratification
47.57.Gc Granular flow

A reduced-order model of diffusive effects on the dynamics of bubbles

A. T. Preston, T. Colonius, and C. E. Brennen

Phys. Fluids 19, 123302 (2007); http://dx.doi.org/10.1063/1.2825018 (12 pages) | Cited 10 times

Online Publication Date: 19 December 2007

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We propose a new reduced-order model for spherical bubble dynamics that accurately captures the effects of heat and mass diffusion. The objective is to reduce the full system of partial differential equations to a set of coupled ordinary differential equations that are efficient enough to implement into complex bubbly flow computations. Comparisons to computations of the full partial differential equations and of other reduced-order models are used to validate the model and establish its range of validity.
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47.55.dd Bubble dynamics
back to top Laminar Flows

Achieving large slip with superhydrophobic surfaces: Scaling laws for generic geometries

Christophe Ybert, Catherine Barentin, Cécile Cottin-Bizonne, Pierre Joseph, and Lydéric Bocquet

Phys. Fluids 19, 123601 (2007); http://dx.doi.org/10.1063/1.2815730 (10 pages) | Cited 55 times

Online Publication Date: 3 December 2007

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We investigate the hydrodynamic friction properties of superhydrophobic surfaces and quantify their superlubricating potential. On such surfaces, the contact of the liquid with the solid roughness is minimal, while most of the interface is a liquid-gas one, resulting in strongly reduced friction. We obtain scaling laws for the effective slip length at the surface in terms of the generic surface characteristics (roughness length scale, depth, solid fraction of the interface, etc.). These predictions are successfully compared to numerical results in various geometries (grooves, posts or holes). This approach provides a versatile framework for the description of slip on these composite surfaces. Slip lengths up to 100 μm are predicted for an optimized patterned surface.
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46.55.+d Tribology and mechanical contacts

Maximizing mixing and alignment of orientable particles for reaction enhancement

T. John and I. Mezić

Phys. Fluids 19, 123602 (2007); http://dx.doi.org/10.1063/1.2819343 (15 pages) | Cited 3 times

Online Publication Date: 10 December 2007

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We present a model for the evolution of concentrations of orientable species undergoing a collisional binary reaction and examine the dependence of the concentration of the reaction product on flow parameters in Poiseuille flow. Interesting patterns of concentration are obtained depending on parameters. We use the model to investigate the reaction in a microfluidic device known as the shear superposition micromixer. Simulation results over a range of Péclet, Damköhler, and rotational Péclet numbers indicate that this micromixer is well suited to enhance the rate of reaction via the mechanism of simultaneous mixing and alignment of the orientable species. Connections to biological systems are discussed.
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47.61.Ne Micromixing
47.85.Np Fluidics
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.70.Fw Chemically reactive flows

Transient buoyancy-driven front dynamics in nearly horizontal tubes

T. Séon, J. Znaien, D. Salin, J. P. Hulin, E. J. Hinch, and B. Perrin

Phys. Fluids 19, 123603 (2007); http://dx.doi.org/10.1063/1.2813581 (11 pages) | Cited 16 times

Online Publication Date: 10 December 2007

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The interpenetration of light and heavy liquids has been studied in a long tube inclined at small angles α to the horizontal. For angles greater than a critical angle αc (whose value decreases when the density contrast measured by the Atwood number At increases), the velocity of the interpenetration front is controlled by inertia and takes the steady value Vf = ki(At gd)1/2, with ki ≃ 0.7. At lower angles, the front is initially controlled by inertia, but later limited by viscous effects. The transition occurs at a distance Xfc, which increases indefinitely as α increases to αc. Once the viscous effects act, the velocity of the front decreases in time to a steady value Vf∞ which is proportional to sin α. For a horizontal tube in the viscous regime, the velocity of the front decreases to zero as t−1/2. At the same time, the profile of the interface h(x,t) only depends on the reduced variable x/t1/2. A quasi-unidirectional model reproduces well the variation of the velocity of the front and the profiles of the interface, both in inclined and horizontal tubes. In the inclined tube, the velocity of the front is determined by matching rarefaction waves to a shock wave.
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47.40.Nm Shock wave interactions and shock effects

Rollover instability due to double diffusion in a stably stratified cylindrical tank

William B. Zimmerman and Julia M. Rees

Phys. Fluids 19, 123604 (2007); http://dx.doi.org/10.1063/1.2827488 (18 pages) | Cited 2 times

Online Publication Date: 28 December 2007

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Double diffusion of a viscous fluid is simulated for heat leakage driven by buoyant convection under cryogenic storage conditions in a cylindrical tank with laminar flow. If the tank is stably stratified, there is a potential instability due to the inability of the fluid in the lower layer to release heat to the top vapor space, whereas the upper liquid layer can exchange heat and mass through sensible heat transfer and evaporation with the vapor space. Eventually, the lower layer becomes less dense due to thermal expansion and is no longer constrained in the stratification. The rapid rise and overturning of the fluid is termed rollover, and can be accompanied by a potentially explosive release of vapor. In this paper, hydrodynamics and heat and mass transport are used to study the stability characteristics of rollover. The transient state is used as a base state for a linear stability analysis which shows the transition from a “corner eddy” mode spinning down to spinning up is the driver for the rollover instability. Four different vapor-liquid interfacial boundary conditions are tested, with similar results for the time to rollover. Surprisingly, the long time prerollover state is dominated in the laminar flow regime by heat conduction and diffusion, as the expected double roll structure is suppressed and advection plays a small roll in the majority of the prerollover period. Scalings are suggested for controlling dimensionless groups on this prerollover basis that can be used as a guideline to determine the regime of double diffusion—a single roll or a double roll stratification, as well as the severity of the eventual rollover event. An energy analysis demonstrates the switch from practically advection free to free convection regimes.
Show PACS
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.20.-k Flow instabilities
47.27.N- Wall-bounded shear flow turbulence
back to top Instability and Transition

Rayleigh–Bénard flow of a rarefied gas and its attractors. III. Three-dimensional computer simulations

S. Stefanov, V. Roussinov, and C. Cercignani

Phys. Fluids 19, 124101 (2007); http://dx.doi.org/10.1063/1.2815729 (13 pages) | Cited 4 times

Online Publication Date: 3 December 2007

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We investigate the three-dimensional Rayleigh–Bénard flow for a set of different Knudsen and Froude numbers at a fixed temperature ratio r = 0.1, as well as for different aspect ratios. We observe a variety of stable vortex structures in the form of rolls, squares, and more complicated polygonal patterns. For sufficiently low Knudsen numbers, the existence of irregular regimes was confirmed. Two numerical approaches (the direct simulation Monte Carlo method and a finite-difference method for the Navier–Stokes equation) are used and the results show a satisfactory agreement.
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47.45.-n Rarefied gas dynamics
47.20.-k Flow instabilities
47.32.cd Vortex stability and breakdown
47.11.Bc Finite difference methods

Experimental study of the single-mode three-dimensional Rayleigh-Taylor instability

J. P. Wilkinson and J. W. Jacobs

Phys. Fluids 19, 124102 (2007); http://dx.doi.org/10.1063/1.2813548 (11 pages) | Cited 6 times

Online Publication Date: 10 December 2007

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The three-dimensional Rayleigh-Taylor instability is studied in a low Atwood number (A ≈ 0.15) miscible fluid system. The two fluids are contained within a Plexiglas tank that is mounted on vertical rails and accelerated downward by a weight and pulley system. A net acceleration between 13 and 23 m/s2 can be maintained, resulting in an effective body force equivalent to 0.33–1.35 times Earth’s gravity. A single-mode, three-dimensional perturbation is produced by oscillating the tank, which has a square cross section, along its diagonal. Early time measured growth rates are shown to have good agreement with linear stability theory. At late time, the instability exhibits a nonconstant vertical interfacial velocity in agreement with the recent numerical computations of Ramaprabhu et al. [Phys. Rev. E 74, 066308 (2006)] . Both the late-time bubble and spike velocities have values greater than those predicted by both the simple buoyancy-drag model developed by Oron et al. [Phys. Plasmas 8, 2883 (2001)] and the potential flow model of Goncharov [Phys. Rev. Lett. 88, 134502 (2002)] . The disagreement with the models can be attributed to the formation of vortices, in this case vortex rings, observed in the experiments but not accounted for by the models.
Show PACS
47.20.-k Flow instabilities
47.32.-y Vortex dynamics; rotating fluids
47.27.-i Turbulent flows
47.55.D- Drops and bubbles

Turbulent spots and waves in a model for plane Poiseuille flow

Maher Lagha

Phys. Fluids 19, 124103 (2007); http://dx.doi.org/10.1063/1.2821912 (10 pages) | Cited 1 time

Online Publication Date: 14 December 2007

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The structure of a turbulent spot in plane Poiseuille flow is investigated using a model derived from the Navier–Stokes equations through a Galerkin method. The mean profile of the streamwise velocity inside the turbulent spot has the characteristic flat profile of a turbulent Poiseuille flow. The waves developing at the wing tips of the spot have an asymmetric streamwise velocity with respect to the channel centerline, whereas their associated wall-normal velocity component is symmetric. On the outskirts of the spot, a large-scale flow occupying the full gap between the plates is observed. It is characterized by a streamwise inflow toward the spot and a spanwise outflow from the spot. A detailed comparison with the numerical simulations and the experiments in the literature shows that these results are in fair agreement with the main features of the transitional plane Poiseuille flow.
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47.15.Rq Laminar flows in cavities, channels, ducts, and conduits

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer

M. C. Charrier-Mojtabi, B. Elhajjar, and A. Mojtabi

Phys. Fluids 19, 124104 (2007); http://dx.doi.org/10.1063/1.2821460 (14 pages) | Cited 10 times

Online Publication Date: 18 December 2007

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We present an analytical and numerical stability analysis of Soret-driven convection in a porous cavity saturated by a binary fluid. Both the mechanical equilibrium solution and the monocellular flow obtained for particular ranges of the physical parameters of the problem are considered. The porous cavity, bounded by horizontal infinite or finite boundaries, is heated from below or from above. The two horizontal plates are maintained at different constant temperatures while no mass flux is imposed. The influence of the governing parameters and more particularly the role of the separation ratio, ψ, characterizing the Soret effect and the normalized porosity, ε, are investigated theoretically and numerically. From the linear stability analysis, we find that the equilibrium solution loses its stability via a stationary bifurcation or a Hopf bifurcation depending on the separation ratio and the normalized porosity of the medium. The role of the porosity is important, when it decreases, the stability of the equilibrium solution is reinforced. For a cell heated from below, the equilibrium solution loses its stability via a stationary bifurcation when the separation ratio ψ>ψ0(Le,ε), while for ψ<ψ0(Le,ε), it loses stability via a Hopf subcritical bifurcation. The oscillatory solution is unstable and becomes stationary. For a cell heated from above, the equilibrium solution is linearly stable if ψ>0, while a stationary or an oscillatory bifurcation occurs if ψ<0. The results obtained from the linear stability analysis are widely corroborated by direct 2D numerical simulations. In the case of long-wave disturbances, for ψ<0 and for ψ higher than a particular value called ψmono, we observe that the monocellular flow leads to a separation of the species between the two ends of the cell. First, we determined the velocity, temperature, and concentration fields analytically for monocellular flow. Then we studied the stability of this flow. For a cell heated from below and for ψ>ψmono the monocellular flow loses stability via a Hopf bifurcation. As the Rayleigh number increases, the resulting oscillatory solution evolves to a stationary multicellular flow. For a cell heated from above and ψ<0, the monocellular flow remains linearly stable. We verified numerically that this problem admits other stable multicellular stationary solutions for this range of parameters.
Show PACS
47.20.-k Flow instabilities
02.60.-x Numerical approximation and analysis
44.25.+f Natural convection
47.27.te Turbulent convective heat transfer
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
back to top Turbulent Flows

Properties of d- and k-type roughness in a turbulent channel flow

S. Leonardi, P. Orlandi, and R. A. Antonia

Phys. Fluids 19, 125101 (2007); http://dx.doi.org/10.1063/1.2821908 (6 pages) | Cited 11 times

Online Publication Date: 17 December 2007

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Roughness is classified by the so-called roughness function, which represents the downward shift of the velocity profile relative to a smooth wall. The dependence of the roughness function on the Reynolds number is discussed with the aim of clarifying the difference between d-type and k-type behaviors. This difference has been traditionally associated with the stability of the flow within the roughness elements. The present direct numerical simulation results indicate that the difference more correctly reflects the different contributions from the frictional drag and pressure drag to the total stress.
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47.27.N- Wall-bounded shear flow turbulence
47.50.-d Non-Newtonian fluid flows
47.60.-i Flow phenomena in quasi-one-dimensional systems

Unsteady turbulent round jets and vortex motion

Neerav Abani and Rolf D. Reitz

Phys. Fluids 19, 125102 (2007); http://dx.doi.org/10.1063/1.2821910 (13 pages) | Cited 5 times

Online Publication Date: 18 December 2007

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A new model to predict the velocity distribution in round jets with time-varying injection profiles has been formulated as an extension of steady jet theory. The approach introduces an effective injection velocity within the jet based on a representative response time. It is assumed that the instantaneous injection velocity affects the velocity within the jet with an exponential response function and that the response time is related to the fluid particle’s residence time within the jet, consistent with the theory of translation of jet vortex rings from Helmholtz’s vortex motion analysis [ P. G. Tait, London Edinburgh Dublin Philos. Mag. J. Sci. 33, 485 (1867) ]. The Helmholtz theory is also shown to reduce to the well-known velocity decay rate in the case of steady turbulent gas jets. A Duhamel superposition integral is used to determine the effective injection velocity for time-varying injection rates. The model is tested with different injection profiles and different ambient densities. The results are also compared with numerical results from a computational fluid dynamics code. The comparisons agree very well and the new model is shown to offer an efficient method to predict jet tip penetrations for unsteady jets.
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47.20.-k Flow instabilities
47.32.C- Vortex dynamics
47.27.wg Turbulent jets

Direct and large-eddy simulations of a pure thermal plume

M. V. Pham, F. Plourde, and K. S. Doan

Phys. Fluids 19, 125103 (2007); http://dx.doi.org/10.1063/1.2813043 (13 pages) | Cited 4 times

Online Publication Date: 18 December 2007

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A turbulent natural convection flow (Gr = 2.2×1010) arising from a heated and finite size source in a quiescent and infinite environment was numerically investigated by means of direct numerical simulation (DNS) and large eddy simulation. Several subgrid-scale models (SGS) were tested and specific attention was paid to dynamic models. The well known dynamic model was compared to the Lagrangian dynamic model which was applied to both dynamic coefficient and turbulent Prandtl number. DNS results show good agreement with experimental results while the Lagrangian dynamic model and especially the extended Lagrangian dynamic model to Prandtl number estimation were found to significantly improve the prediction of pure thermal plume evolution, especially in the turbulent region in which the main turbulent characteristics fitted DNS results. The puffing phenomenon, i.e., unsteady vortex shedding concentration that occurs in the very close vicinity of the finite size source, was not correctly predicted by SGS models but only required sufficient grid resolution.
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47.15.Fe Stability of laminar flows
47.27.Cn Transition to turbulence
47.32.-y Vortex dynamics; rotating fluids
47.27.ek Direct numerical simulations
47.27.ep Large-eddy simulations
47.27.te Turbulent convective heat transfer
47.11.-j Computational methods in fluid dynamics

Turbulent mixing of two-layer stratified fluid

J. A. Whitehead and Ian Stevenson

Phys. Fluids 19, 125104 (2007); http://dx.doi.org/10.1063/1.2821913 (7 pages) | Cited 2 times

Online Publication Date: 19 December 2007

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A two-layer salt-stratified tank of water was mixed by turbulence generated by many excursions of a horizontally moving vertical rod. The objective is to observe the time-dependent response of the mean density field for ranges of Richardson number Ri>0.9 and Reynolds Number Re>600. As the density profile of the fluid gradually evolves from a single step to a mixed state over a wide range of time, there is an almost perfect collapse of all the profiles to one universal profile as a function of a similarity variable. Although the turbulent diffusion is not constant, the value in the limit of small stratification has similar magnitude to values found by others.
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47.27.wj Turbulent mixing layers
47.55.Hd Stratified flows
47.27.tb Turbulent diffusion
47.51.+a Mixing

Front dynamics and macroscopic diffusion in buoyant mixing in a tilted tube

T. Séon, J. Znaien, B. Perrin, E. J. Hinch, D. Salin, and J. P. Hulin

Phys. Fluids 19, 125105 (2007); http://dx.doi.org/10.1063/1.2821733 (7 pages) | Cited 10 times

Online Publication Date: 20 December 2007

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The buoyancy driven interpenetration of two fluids of different densities has been studied in a long tilted tube in the strong mixing regime for which the mean concentration profile along the tube length satisfies a macroscopic diffusion equation. Variations of the corresponding macroscopic diffusion coefficient D and of the front velocity Vf are studied as a function of the Atwood number At, the viscosity ν, the tube diameter d, and the tilt angle θ. Introducing the characteristic inertial velocity Vt and the Reynolds number Ret, the normalized front velocity Vf/Vt and dispersion coefficient D/(Vtd) are observed to scale, respectively, as Ret−3/4 and Ret−3/2 for Ret≲1000. Also, Vf increases linearly with tan θ and the ratio (D/Vf2) remains of the order of (35±10)d/Vt in a wide range of values of the tilt angle and of the other control parameters. This close relation observed between the variations of D and Vf2 is discussed in terms of the characteristic time for transverse mixing across the flow channel.
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45.70.Mg Granular flow: mixing, segregation and stratification
47.51.+a Mixing

Natural convection boundary layer in a 5:1 cavity

D. G. Barhaghi and L. Davidson

Phys. Fluids 19, 125106 (2007); http://dx.doi.org/10.1063/1.2815746 (15 pages) | Cited 4 times

Online Publication Date: 21 December 2007

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The natural convection boundary layer in a tall cavity with an aspect ratio of AR = 5 is studied numerically. The Rayleigh number based on the width of the cavity is RaW = 4.028×108. The large eddy simulation method together with different subgrid scale models are used to study the near-wall behavior of the boundary layer and the turbulence structure. It is found that the dynamic subgrid scale model is the most accurate model in terms of predicting the transition location. Results also indicate that the conventional grid resolutions expressed in viscous units that are used for forced convection flows are not appropriate in the case of the natural convection flows and higher grid resolutions are necessary. The turbulence statistics are studied in both the turbulent and the transition regions. Although the results of the fully turbulent region show no important grid dependency, it is found that the accuracy of the results in the transition region is highly grid dependent, suggesting that the subgrid scale fluctuations in the transition region are of different nature compared to the fully turbulent region. The budget of the momentum, temperature, and Reynolds stress transport equations are studied and the behavior of the important terms in the boundary layer is investigated.
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44.25.+f Natural convection
47.27.Cn Transition to turbulence
47.27.ep Large-eddy simulations
47.27.nb Boundary layer turbulence
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