Volume 19, Issue 3, March 2007
Index of content:

The evolution of largescale density perturbations is studied in a stably stratified, twodimensional flow governed by the Boussinesq equations. As is known, initially smooth density (or temperature) profiles develop into fronts in the very early stages of evolution. This results in a frontally dominated potential energy spectrum. The fronts, initially characterized by a relatively simple geometry, spontaneously develop into severely distorted sheets that possess structure at very fine scales, and thus there is a transfer of energy from large to small scales. It is shown here that this process culminates in the establishment of a kinetic energy spectrum, although its scaling extends over a shorter range as compared to the scaling of the potential energy spectrum. The establishment of the kinetic energyscaling signals the onset of enstrophy decay, which proceeds in a mildly modulated exponential manner and possesses a novel selfsimilarity. Specifically, the selfsimilarity is seen in the time invariant nature of the probability density function (PDF) associated with the normalized vorticity field. Given the rapid decay of energy at this stage, the spectral scaling is transient and fades with the emergence of a smooth, largescale, very slowly decaying, (almost) vertically sheared horizontal mode with most of its energy in the potential component, i.e., the PearsonLinden regime.
 LETTERS


Effect of concentrated energy deposition on the aerodynamic drag of a blunt body in hypersonic flow
View Description Hide DescriptionExperimental results on the effect of energy deposition using an electric arc discharge, upstream of a 60° half angle blunt cone configuration in a hypersonic flow stream is reported. Investigations involving drag measurements and high speed Schlieren flow visualization have been carried out in a hypersonic shock tunnel using air and argon as the test gases; and an unsteady drag reduction of about 50% (maximum reduction) has been observed in the energy deposition experiments done in argon environment. These studies also show that the effect of discharge on the flow field is more pronounced in argon environment as compared to air, which confirms that thermal effects are mainly responsible for flow alteration with discharge. It has also been observed that the interaction of the hypersonic flow with the discharge filament results in the development of an unsteady flow field.

On simulating scalar transport by mixing between Lagrangian particles
View Description Hide DescriptionLagrangian particles with mixing can be used as direct numerical simulations (DNS), large eddy simulations(LES), or filtered density function (FDF) methods depending on conditions of the simulations. We estimate major parameters associated with the DNS, LES, and FDF regimes and demonstrate that, under certain conditions specified in the paper, simulations using different mixing models approach the DNS limit.

A new application of the Korteweg–de Vries BenjaminOno equation in interfacial electrohydrodynamics
View Description Hide DescriptionWe consider waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. We use perturbation theory to identify canonical scalings and to derive a Korteweg–de Vries BenjaminOno equation arising in interfacial electrohydrodynamics. When the Bond number is equal to , dispersion disappears and the equation reduces to the BenjaminOno equation. In the additional limit of vanishing electric fields, we show how to obtain a new evolution equation that contains third and fifthorder dispersion as well as a nonlocal electric field term.

 ARTICLES


Interfacial Flows

Motion of a droplet near an evaporating liquidgas interface
View Description Hide DescriptionThe motion of a droplet placed in a gas phase near an evaporating, planar liquidgas interface is considered. Due to latent heat of evaporation, the gradients of temperature and vapor concentration are sustained in the system. The temperature gradient results in the thermocapillary force acting on the droplet and on the planar liquidgas interface causing thermocapillary flows in the three phases. The corresponding hydrodynamic and diffusion problems are solved using bispherical coordinates, and the velocity of the droplet as a function of the drop separation distance from the interface is found. It is shown that, in the absence of gravity, there exists a critical separation distance above which the drop escapes from the interface and below which the drop is captured by the interface. In the presence of gravity, it is shown that there exists a steadystate separation distance at which the drop can levitate above the interface.

Investigations on the impact of a drop onto a small spherical target
View Description Hide DescriptionThis paper reports on experimental and theoretical investigations of the impact of a droplet onto a spherical target. Spatial and temporal variation of film thickness on the target surface is measured. Three distinct temporal phases of the film dynamics are clearly visible from the experimental results, namely the initial drop deformation phase, the inertia dominated phase, and the viscosity dominated phase. Experiments are also conducted to study the effect of dropletReynolds number and targettodrop size ratio on the dynamics of the film flow on the surface of the target. It is observed that for a given targettodrop size ratio, the nondimensional temporal variation of film thickness collapses onto a single curve in the first and second phases. The transition to the viscosity dominated regime occurs earlier for the low Reynolds number cases and residual thickness is also larger. A simplified quasionedimensional approach has been used to model the flow on the spherical target. The theory accounts for the inertial and viscous effects. Gravity and the curvature of the target are also taken into account. An analytical expression for the timedependent film profile on the sphere is obtained for the inviscid, inertia dominated phase of spreading. Then, the evolution equation for the film thickness near the north pole in the viscosity dominated phase is obtained and solved. Good agreement is observed between the theoretical predictions and the measurements when the values of the drop and target diameters are comparable. No adjustable parameters have been used in the model.

Viscous and NonNewtonian Flows

Capillary pinching in a pinched microchannel
View Description Hide DescriptionWe report a study of the capillary pinching of a gas bubble by a wetting liquid inside a pinched channel. The capillary pinching induces very reproducible bubbling, at a very welldefined frequency. There are two regimes associated with drip and jet bubbling. In the latter, we show that highly monodispersed bubbles are formed by our pinched channel. The dynamics of the bubble formation also shows two distinct regimes: a longduration elongation of the air bubble and a rapid relaxation of the interface after interface breakup. The slow regime depends on the flux imposed and the channel geometry. The rapid deformation dynamic regime depends very weakly on the boundary conditions. Scaling arguments are proposed in the context of the lubrication approximation to describe the two regimes.

Thermophoresis of a slightly deformed aerosol sphere
View Description Hide DescriptionAn analytical study is presented for the thermophoreticmotion of a freely suspended aerosol particle with an arbitrary, slightly deformed spherical surface in a uniformly prescribed temperature gradient. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the surface of the particle. A first attempt is made to obtain analytical approximations for the thermophoreticvelocity of the particle in the limit of vanishing Peclet and Reynolds numbers. To the first order in the small parameter characterizing the deformation of the spherical shape of the particle, explicit expressions are derived for its drift and rotational velocities. The angular velocity of a particle undergoing thermophoresis is found to be zero for any shape, which is the first indication that the fluid motion around a single thermophoretic particle of an arbitrary shape is irrotational, as is known to be in the case of thindoublelayer electrophoresis. A comparison of our firstorder approximation for the thermophoreticvelocity of a spheroid with the available exact solution shows that the agreement is quite good, even for relatively large deformations of the spherical shape of the particle. Our results for the motion of a spheroid demonstrate that its relative physical and surface properties, its aspect ratio, and its orientation relative to the imposed temperature gradient can have significant effects on its thermophoretic mobility.

Pore scale mixing and macroscopic solute dispersion regimes in polymer flows inside twodimensional model networks
View Description Hide DescriptionA change of solutedispersion regime with the flow velocity has been studied both at the macroscopic and pore scales in a transparent array of capillary channels, using an optical technique allowing for simultaneous local and global concentration mappings. Two solutions of different polymer concentrations ( and ) have been used at different Péclet numbers. At the macroscopic scale, the displacement front displays a diffusive spreading: for , the dispersivity is constant with and increases with the polymer concentration; for , increases as and is similar for the two concentrations. At the local scale, a time lag between the saturations of channels parallel and perpendicular to the mean flow has been observed and studied as a function of the flow rate. These local measurements suggest that the change of dispersion regime is related to variations of the degree of mixing at the junctions. For , complete mixing leads to pure geometrical dispersion enhanced for shear thinning fluids; for , weaker mixing results in higher correlation lengths along flow paths parallel to the mean flow and in a combination of geometrical and Taylor dispersion.

Particulate, Multiphase, and Granular Flows

An experimental study of the size effect on adiabatic gasliquid twophase flow patterns and void fraction in microchannels
View Description Hide DescriptionAdiabatic gasliquidflow patterns and void fractions in microchannels were experimentally investigated. Using nitrogen and water, experiments were conducted in rectangular microchannels with hydraulic diameters of , and , respectively. Gas and liquid superficial velocities were varied from and , respectively. The main objective is focused on the effects of microscale channel sizes on the flow regime map and void fraction. The instability of flow patterns was observed. Four groups of flow patterns including bubbly slug flow, slugring flow, dispersedchurn flow, and annular flow were observed in microchannels of and, . In the microchannel of , the bubbly slug flow became the slug flow and the dispersedchurn flow disappeared. The current flow regime maps showed the transition lines shifted to higher gas superficial velocity due to a dominant surface tension effect as the channel size was reduced. The regime maps presented by other authors for minichannels were found to not be applicable for microchannels. Timeaveraged void fractions were measured by analyzing 8000 high speed video images for each flow condition. The void fractions hold a nonlinear relationship with the homogeneous void fraction as opposed to the relatively linear trend for the minichannels. A new correlation was developed to predict the nonlinear relationship that fits most of the current experimental data and those of the diameter tube reported by Kawahara et al. [Int. J. Multiphase Flow28, 1411 (2002)] within .

Dissipative particle dynamics simulation of multiphase fluid flow in microchannels and microchannel networks
View Description Hide DescriptionMultiphase fluid motion in microchannels and microchannel networks involves complicated fluid dynamics and is fundamentally important to diverse practical engineering applications such as inkjet printing, DNA and protein micro/nanoarraying, and fabrication of particles and capsules for controlled release of medicines. This paper presented the simulations of multiphase fluid motion in microchannels and microchannel networks using a modified dissipative particle dynamics method that employs a new conservative particleparticle interaction combining shortrange repulsive and longrange attractive interactions to simulate multiphase systems. This new conservative particleparticle interaction allows the behavior of multiphase systems consisting of gases, liquids, and solids to be simulated. Three numerical examples that are closely related to engineering applications were simulated. These examples involve multiple fluid motions in (i) a simple microchannel within two parallel plates; (ii) an inverted Yshaped microchannel junction consisting of a vertical channel that divides into two branch channels with the same aperture; and (iii) a microchannel network. The numerical results obtained by using DPD agreed well with those from other sources, and clearly demonstrated the potential value of this DPD method for modeling and analyzing multiphase flow in microchannels and microchannel networks.

Instability and Transition

Linear stability analysis of PoiseuilleRayleighBénard flows in binary fluids with Soret effect
View Description Hide DescriptionTemporal and spatiotemporal instabilities of PoiseuilleRayleighBénard flows in binary fluids with Soret effect have been investigated by a Chebyshev collocation method. Both situations corresponding to the fluid layer heated from below or from above have been studied. When heating is from below and for positive separation factors, the critical thresholds strongly increase when the throughflow is applied, and the boundary curves between absolute and convective instabilities increase as well, but more steeply. For large enough positive separation factors, there exist three local minima in the neutral curves (Rayleigh number against wavenumber) for moderate Reynolds numbers (Re), which results in the discontinuity of the critical wavenumber curve and the nonsmoothness of the critical Rayleigh number curve when the Reynolds number is varied. For negative separation factors, there exists a contact point between the critical Rayleigh number curve and the boundary curve at which the fluid system is directly changed from stable to absolutely unstable without crossing the convectively unstable region. This contact point has been characterized and localized for different negative separation factors. When heating is from above, the main observation is that the stationary curve obtained at is replaced by two critical curves, one stationary and the other oscillatory, when a throughflow is applied. An energy budget analysis for the binary fluid system is also performed. A better insight into the role played by the solutal buoyancy contribution in the different situations is thus obtained.

Stability of the viscous flow of a polymeric fluid past a flexible surface
View Description Hide DescriptionThe instability in plane Couette flow of a viscoelastic fluid past a deformable surface is examined using the temporal linear stability theory in the zero Reynolds number limit. The polymeric fluid is described using the OldroydB model and the flexible wall is modeled as a linear viscoelastic solid surface. The analysis shows that the wall flexibility tends to reduce the decay rate of the stable discrete modes for the polymericflow past a rigid wall, and one of the discrete modes becomes unstable when the wall deformability parameter exceeds a certain critical value . Here, is the topplate velocity, is the zero shear viscosity of the polymeric fluid, is the shear modulus of the wall, and is the width of the fluid layer. The analysis reveals the presence of two classes of modes, the first of which becomes unstable for perturbations with wavelength comparable to the channel width (finite wavelength modes), and the second becomes unstable for perturbations with wavelength small compared to the channel width (short wave modes). The latter class of modes are found to be absent for the highly concentrated polymer solutions with , where is the ratio of solventtosolution viscosity. We have mapped out the regions in the parameter space where the finite wavelength and short wave modes are unstable, where , and is the relaxation time of the viscoelastic fluid. Fluid elasticity is found to have a stabilizing influence on the unstable mode, such that when the shortwave instability is absent for , the flow becomes stable for any Weissenberg number . Here, increases proportional to for . However, when the shortwave instability is present, the instability persists for . The behavior of both classes of modes with respect to the parameters, like , , , and the ratio of solidtofluid viscosity, is examined.

Turbulent Flows

The spatial relationships between dissipation and production rates and vortical structures in turbulent boundary and mixing layers
View Description Hide DescriptionA novel approach for studying the spatial relationship between the production and dissipation rates of turbulent kinetic energy and vortical structures is presented. Two turbulent flows were investigated: the zero pressure gradient boundary layer and the twostream mixing layer. In both flows, a multisensor hotwire probe was used to measure the velocity components in all three coordinate directions, as well as six components of the velocity gradient tensor. The remaining three velocity gradients were determined using Taylor’s hypothesis. With these data, the “instantaneous” production and dissipation rates, defined by and , respectively, were determined. Crosscorrelating the fluctuations of these two signals reveals that they are not randomly distributed in time with respect to each other; rather they display significant levels of correlation. Plotting the crosscorrelation coefficients versus a dimensionless length scale, defined as , reveals an asymmetric pattern that persists at several crossstream locations for both flows. Furthermore, correlating both the dissipation and production rates with a vortex identifier, , also reveals consistent crossstream patterns. The magnitude of these correlations and their persistent shapes across the flows suggest that the spatial separation between regions of concentrated dissipation and production rates is associated with the presence of quasistreamwise vortices in both of these flows. More specifically, they imply that regions of concentrated rates of dissipation are primarily in the cores of the vortices, whereas regions of rates of production are more concentrated on their periphery.

On the performance of the moment approximation for the numerical computation of fiber stress in turbulent channel flow
View Description Hide DescriptionFiberinduced drag reduction can be studied in great detail by means of direct numerical simulation [J. S. Paschkewitz et al., J. Fluid Mech.518, 281 (2004)]. To account for the effect of the fibers, the NavierStokes equations are supplemented by the fiber stress tensor, which depends on the distribution function of fiber orientation angles. We have computed this function in turbulent channel flow, by solving the FokkerPlanck equation numerically. The results are used to validate an approximate method for calculating fiber stress, in which the second moment of the orientation distribution is solved. Since the moment evolution equations contain higherorder moments, a closure relation is required to obtain as many equations as unknowns. We investigate the performance of the eigenvaluebased optimal fitted closure scheme [J. S. Cintra and C. L. Tucker, J. Rheol.39, 1095 (1995)]. The closurepredicted stress and flow statistics in twoway coupled simulations are within 10% of the “exact” FokkerPlanck solution.

Scalings and decay of fractalgenerated turbulence
View Description Hide DescriptionA total of 21 planar fractal grids pertaining to three different fractal families have been used in two different wind tunnels to generate turbulence. The resulting turbulent flows have been studied using hot wire anemometry. Irrespective of fractal family, the fractalgenerated turbulent flows and their homogeneity, isotropy, and decay properties are strongly dependent on the fractal dimension of the grid, its effective mesh size (which we introduce and define) and its ratio of largest to smallest bar thicknesses, . With relatively small blockage ratios, as low as , the fractal grids generate turbulent flows with higher turbulence intensities and Reynolds numbers than can be achieved with higher blockage ratio classical grids in similar wind tunnels and wind speeds . The scalings and decay of the turbulence intensity in the direction along the tunnel’s center line are as follows (in terms of the normalized pressure drop and with similar results for and ): (i) for fractal cross grids , ; (ii) for fractal I grids, , where is the tunnel width and is the maximum bar length on the grid; (iii) for spacefilling fractal square grids, the turbulence intensity builds up as the turbulence is convected downstream until a distance from the grid is reached where the turbulence intensity peaks and then decays exponentially, , where increases linearly with , ( being the minimum bar length on the grid), and ( being the kinematic viscosity of the air and being the Taylor microscale); remains approximately constant during decay at . The longitudinal and lateral integral length scales also remain approximately constant during decay at .

Particle acceleration in turbulent flows: A class of nonlinear stochastic models for intermittency
View Description Hide DescriptionThe problem of modeling the velocity and acceleration of inertial particles in turbulent flows is discussed. Particular attention is focused on the modeling of the particle Lagrangianvelocity increment, especially, but not exclusively, in the case in which only the low frequencies of the carrier turbulent flow field are available. The need for suitable models arises in the simulation of particle laden flows by the means of new computational techniques such as largeeddy simulation. For this, stochastic differential equations, sde, are often introduced, though there is a lack of clarity in how such models should deal with the experimental observed far from Gaussian statistics, intermittency, and heavy tailed probability density function for particle acceleration. It is well known that Langevintype equations are not capable of reproducing such features. It is first shown how the stochastic model for the particle Lagrangianvelocity increments is far from being a Langevin equation, and it is characterized by nonlinear drift and diffusion; the statistical characteristics of this first model are shown to be in qualitative agreement with experimental findings. These results suggest an improved model for the particle dynamics based upon a more general family of nonlinear sde; the family, which is generated by a single parameter, includes both the Langevin equation and the first model as special cases. An analysis of the statistical properties of the new sde shows that the model is capable of accurately reproducing the strong deviations from Gaussianity observed in recent experiments.

A study of swirling turbulent pipe and jet flows
View Description Hide DescriptionAxially rotating turbulent pipe flow is an example in which the rotation strongly affects the turbulence, which then also influences the mean flow properties. For instance, in the fully developed flow as well, the fluid is not in solid body rotation due to the influence of the crossstream Reynolds stress. The present paper reports new measurements from a rotating pipe flow and the streamwise mean velocity distribution is compared with recent scaling ideas of Oberlack [J. Fluid Mech.379, 1 (1999)] and good agreement is found. A second part of the paper deals with the initial stages when the flow leaves the pipe and forms a swirling jet. The measurements in the jet show that at some distance downstream (approximately five jet diameters) the central part of the jet actually rotates in the opposite direction as compared to the rotation of the pipe. This effect is explained by the influence of the crossstream Reynolds shear stress.

Analysis of the gradientdiffusion hypothesis in largeeddy simulations based on transport equations
View Description Hide DescriptionThe gradientdiffusion hypothesis is frequently used in numerical simulations of turbulent flows involving transport equations. In the context of largeeddy simulations(LES) of turbulent flows, one modeling trend involves the use of transport equations for the subgridscale (SGS) kinetic energy and SGS scalar variance. In virtually all models using these equations, the diffusion terms are lumped together, and their joint effect is modeled using a “gradientdiffusion” model. In this work, direct numerical simulations of homogeneous isotropic turbulence are used to analyze the local dynamics of these terms and to assess the performance of the “gradientdiffusion” hypothesis used in their modeling. For this purpose a priori tests are used to assess the influence of the Reynolds and Schmidt numbers and the size of the implicit grid filter in this modeling assumption. The analysis uses correlations, variances, skewnesses, flatnesses, probability density functions, and joint probability density functions. The correlations and joint probability density functions show that provided the filter width is within or close to the dissipative range the diffusion terms pertaining to the SGS kinetic energy and SGS scalar variance transport equations are well represented by a gradientdiffusion model. However, this situation changes dramatically for both equations when considering inertial range filter sizes and high Reynolds numbers. The reason for this lies in part in a loss of local balance between the SGS turbulent diffusion and diffusion caused by grid/subgridscale (GS/SGS) interactions, which arises at inertial range filter sizes. Moreover, due to the deficient modeling of the diffusion by SGS pressurevelocity interactions, the diffusion terms in the SGS kinetic energy equation are particularly difficult to reconcile with the gradientdiffusion assumption. In order to improve this situation, a new model, inspired by Clark’s SGS model, is developed for this term. The new model shows very good agreement with the exact SGS pressurevelocity term in a priori tests and better results than the classical model in a posteriori(LES) tests.

A stochastic subgrid model with application to turbulent flow and scalar mixing
View Description Hide DescriptionA new computationally cheap stochastic Smagorinsky model which allows for backscatter of subgrid scale energy is proposed. The new model is applied in the large eddy simulation of decaying isotropic turbulence, rotating homogeneous shear flow and turbulent channel flow at . The results of the simulations are compared to direct numerical simulation data. The inclusion of stochastic backscatter has no significant influence on the development of the kinetic energy in homogeneous flows, but it improves the prediction of the fluctuation magnitudes as well as the anisotropy of the fluctuations in turbulent channel flow compared to the standard Smagorinsky model with wall damping of . Moreover, the stochastic model improves the description of the energy transfer by reducing its length scale and increasing its variance. Some improvements were also found in isotropic turbulence where the stochastic contribution improved the shape of the enstrophy spectrum at the smallest resolved scales and reduced the time scale of the smallest resolved scales in better agreement with earlier observations.

On the turbulent structure in the wake of Taylor bubbles rising in vertical pipes
View Description Hide DescriptionThe development of gasliquid slug flow along pipes is governed by the interaction between consecutive elongated bubbles. It is commonly accepted that the trailing bubble’s shape and velocity are affected by the flow field in the liquid phase ahead of it. Particle image velocimetry(PIV)measurements of the velocity field in the wake of an elongated Taylor bubble are performed for different pipe diameters and various Reynolds numbers. Experiments are carried out in both laminar and turbulent background flows. Ensembleaveraged quantities in the frame of reference moving with the Taylor bubble are calculated. Peculiarities regarding the variation of the mean velocity distributions, as well as of the normal and shear Reynolds stresses, with the distance from the Taylor bubble bottom are discussed.
