Volume 20, Issue 1, January 2008
Index of content:
Physics of Fluids celebrates its 50th anniversary with this issue. This brief history summarizes the launching of the journal in 1958 under its first editor François Frenkiel, who held the position for more than 20 years; reviews the next under the guidance of Andreas Acrivos, a fertile period during which the journal grew and spun off its sibling, Physics of Plasmas; and then reaches the current era under the present two editors.
- Interfacial Flows
Instability of a vertical chemical front: Effect of viscosity and density varying with concentration20(2008); http://dx.doi.org/10.1063/1.2829081View Description Hide Description
In this work we analyze the behavior of a chemical front in a vertical porous medium. A homogeneous autocatalytic reaction occurs in the liquid phase. The column is filled with a chemical species and the reaction is initiated at one end of the vertical column by instantaneously adding the product. The reaction occurs at the interface of the products and the reactants. This causes the reaction front to move down (up) when the product is added to the top (bottom). The front or interface demarcates the domain into two regions: one rich in the reactants and the other rich in products. In this work chemohydrodynamic instabilities are studied, when the density and viscosity of the reactants and products are different and concentration dependent. The dependency of these properties on concentration is explicitly considered. We assume the process to be isothermal and other properties such as diffusivity and permeability to be constant. A traveling wave of chemical concentration is generated in the upward direction (when the products are introduced at the bottom) as the product reacts at the interface. The stability of the interface is determined by the viscosity and density of the two fluids. A shooting method in combination with a Runge–Kutta fourth-order scheme is used for generating the base state of the traveling front. Here, the conditions at which an interfacial instability induced by the density gradients is stabilized due to the viscosity dependence on concentration are determined. Linear stability predictions are determined by inducing perturbations on the traveling wave base state and analyzing their evolution. The effect of various parameters on the stability of the flow was calculated and compared with the nonlinear simulations. The nonlinear problem is modeled using the stream-function, vorticity equations. These equations are solved using a second-order finite difference scheme in space and first-order forward difference scheme in time. The instability predicted from the linear stability analysis is validated with nonlinear simulations.
20(2008); http://dx.doi.org/10.1063/1.2832775View Description Hide Description
The purpose of this paper is to analyze the validation achieved in recent simulations of Rayleigh–Taylor unstable mixing. The simulations are already in agreement with experiment; mesh refinement or insertion of a calibrated subgrid model for mass diffusion will serve to refine this validation and possibly shed light on the role of unobserved long wavelength perturbations in the initial data. In this paper we present evidence to suggest that a subgrid model will have a barely noticeable effect on the simulation. The analysis is of independent interest, as it connects a validated simulation to common studies of mixing properties. The average molecular mixing parameter for the ideal and immiscible simulations is zero at a grid block level, as is required by the exact microphysics of these simulations. Averaging of data over volumes of to yields a conventional value , suggesting that fluid entrainment in front tracked simulations produces a result similar to numerical mass diffusion in untracked simulations. The miscible simulations yield a nonzero in agreement with experimental values. We find spectra in possible approximate agreement with the Kolmogorov theory. A characteristic upturn especially in the density fluctuation spectrum at high wave numbers suggests the need for a subgrid mass diffusionmodel, while the small size of the upturn and the analysis of suggest that the magnitude of the model will not be large. We study directly the appropriate settings for a subgrid diffusion coefficient, to be inserted into simulations modelingmiscibleexperiments. This is our most definitive assessment of the role for a subgrid model. We find that a Smagorinsky-type subgrid mass diffusionmodel would have a diffusion coefficient at most about 0.15% of the value of the physical mass diffusion for the (mass diffusive) experiment studied.
20(2008); http://dx.doi.org/10.1063/1.2828098View Description Hide Description
The transport of a solute in a straight microchannel of axially variable cross-sectional shape in the presence of an inhomogeneous flow field and an adsorption-desorption process on the wall is studied, motivated by applications to capillary electrophoresis and open-channel capillary electrochromatography. An asymptotic approach based on the long time limit is adopted that reduces the problem to the solution of a one-dimensional transport equation. The reduced model is integrated numerically to study the effects of inhomogeneous electro-osmotic flow and adsorption-desorption kinetics on solute migration and dispersion in a rectangular microchannel. The accuracy of the asymptotic equations is checked by the direct numerical solution of the original three-dimensional transport problem.
- Viscous and Non-Newtonian Flows
20(2008); http://dx.doi.org/10.1063/1.2835312View Description Hide Description
The dynamics of confined droplets in shear flow is investigated using computational and experimental techniques for a viscosity ratio of unity. Numerical calculations, using a boundary integral method (BIM) in which the Green’s functions are modified to include wall effects, are quantitatively compared with the results of confined droplet experiments performed in a counter-rotating parallel plate device. For a viscosity ratio of unity, it is experimentally seen that confinement induces a sigmoidal droplet shape during shear flow. Contrary to other models, this modified BIM model is capable of predicting the correct droplet shape during startup and steady state. The model also predicts an increase in droplet deformation and more orientation toward the flow direction with increasing degree of confinement, which is all experimentally confirmed. For highly confined droplets, oscillatory behavior is seen upon startup of flow, characterized by an overshoot in droplet length followed by droplet retraction. Finally, in the case of a viscosity ratio of unity, a minor effect of confinement on the critical capillary number is observed both numerically and experimentally.
- Particulate, Multiphase, and Granular Flows
20(2008); http://dx.doi.org/10.1063/1.2833468View Description Hide Description
The human nasal cavities with an effective length of only feature a wide array of basic flow phenomena because of their complex geometrics. Employing a realistic nasal airway model and demonstrating that laminar, quasisteady airflow can be assumed, dilute nanoparticle suspension flow and nanoparticle deposition are simulated and analyzed for and . The understanding and quantitative assessment of mixture flow fields and local nanoparticle wall concentrations in nasal airways with a thin mucus layer are very important for estimating the health risks of inhaled toxic aerosols, determining proper drug-aerosol delivery to target sites such as the olfactory regions and developing algebraic transfer functions for overall nasal dose-response analyses. Employing a commercial software package with user-supplied programs, the validated computer modeling results can be summarized as follows: (i) Most of the air flows through the middle-to-low main passageways. Higher airflow rates result in stronger airflow in the olfactory region and relatively lower flow rates in the meatuses. (ii) Nanoparticle deposition in human nasal airways is significant for tiny nanoparticles, i.e., , which also represent some vapors. The smaller the nanoparticle size and the lower the flow rate, the higher are the total deposition efficiencies because of stronger diffusion and longer residence times. (iii) Nanoparticles with flow preferentially through the middle-to-low main passageway along with the major portion of the airflow. For relatively large nanoparticles, due to the low diffusivities, fewer particles will deposit onto the wall leaving a much thinner nanoparticle gradient layer near the wall, i.e., such nanoparticles pass through the nasal cavities more uniformly with minor wall deposition. (iv) Secondary flows may enhance nanoparticle transport and deposition, especially in the meatuses by convecting nanoparticles into these particular regions. (v) For the olfactory region, an optimal particle size may exist due to the combined effects of nanoparticle transport and local deposition mechanisms. However, because of the low deposition flux and small surface area, the olfactory channels account for only very small total deposition values. (vi) A compact correlation for predicting nanoparticle deposition in human nasal airways has been developed.
- Instability and Transition
20(2008); http://dx.doi.org/10.1063/1.2824401View Description Hide Description
We model and analyze the influence of small amplitude transverse wall oscillations on the evolution of velocity perturbations in channel flows. We quantify the effect of stochastic outside disturbances on velocity perturbation energy and develop a framework for the optimal selection of transverse oscillation parameters for turbulence suppression. A perturbation analysis is used to demonstrate that depending on the wall oscillation frequency the energy of velocity perturbations can be increased or decreased compared to the uncontrolled flow. Our results elucidate the capability of properly designed oscillations to reduce receptivity of the linearized Navier-Stokes equations to stochastic disturbances, which entails decreased levels of variance in wall-bounded shear flows.
20(2008); http://dx.doi.org/10.1063/1.2831493View Description Hide Description
The stability of circular Couette flow in discontinuous axisymmetric geometries is investigated using numerical simulations and physical experiments. By contouring the geometry of the inner cylinder, Taylor vortices can be made to appear in discrete sections along the length of the cylinder while adjoining sections remain stable. The disparate flows are connected by transition regions that arise from the stability of the axially nonuniform base flow state. The geometry of the inner cylinder can be tailored to produce the simultaneous onset of Taylor vortices of different wavelength in neighboring sections. In another variant, a stack of inner cylinders of common radius are made to rotate independently to produce adjacent regions of stable and unstable flow.
- Turbulent Flows
The turbulence dissipation constant is not universal because of its universal dependence on large-scale flow topology20(2008); http://dx.doi.org/10.1063/1.2832778View Description Hide Description
The dimensionless dissipation rate constant of homogeneous isotropic turbulence is such that where is a dimensionless function of which tends to 0.26 (by extrapolation) in the limit where (as opposed to just ) if the assumption is made that a finite such limit exists. The dimensionless number reflects the number of large-scale eddies and is therefore nonuniversal. The nonuniversal asymptotic values of stem, therefore, from its universal dependence on . The Reynolds number dependence of at values of close to and not much larger than 1 is primarily governed by the slow growth (with Reynolds number) of the range of viscous scales of the turbulence. An eventual Reynolds number independence of can be achieved, in principle, by an eventual balance between this slow growth and the increasing non-Gaussianity of the small scales. The turbulence is characterized by five length-scales in the following order of increasing magnitude: the Kolmogorov microscale , the inner cutoff scale , the Taylor microscale , the voids length scale , and the integral length scale .
20(2008); http://dx.doi.org/10.1063/1.2832779View Description Hide Description
Turbulent duct flows in a uniform magnetic field are examined at low magnetic Reynolds number. Large-eddy simulation is conducted to reveal a sidewall effect on the skin friction. The duct has a square cross section and entirely insulated walls. The duct flow has two kinds of boundary layers: Hartmann layer and sidewall layer. The Hartmann layer is located on the wall perpendicular to the magnetic field, while the sidewall layer exists on the wall parallel to the magnetic field. As the magnetic field increases in the range of turbulent flows, the Hartmann layer becomes thin because of the “Hartmann flattening”—a flattening effect of the flow by the Lorentz force. The sidewall layer, however, becomes thick because of the turbulence suppression until the laminarization takes place. When the Reynolds number, Re, based on the hydraulic diameter, molecular viscosity, and bulk velocity is 5 300, the Hartmann and sidewall layers are laminarized at the same Hartmann number that is proportional to the magnetic field. When the Hartmann layer is laminarized at , the sidewall layer remains turbulence. This is due to a sidewall effect and is the condition that a local maximum takes place in the skin friction profile. When the sidewall layer is laminarized, the flow totally becomes laminar and the skin friction becomes minimum.
20(2008); http://dx.doi.org/10.1063/1.2832780View Description Hide Description
An experimental investigation of the turbulent flow downstream of a planar sudden expansion has been performed by means of a 2D particle imagevelocimetry(PIV) technique. Flow fields at the Reynolds number of have been measured in several mutually perpendicular planes of a channel having an expansion ratio of 3 and an aspect ratio of 10. As usual for large expansion ratios, the separated flow exhibits a strong asymmetry about the expansion axis and, consequently, very different reattachment lengths on the two side walls of the channel. The mean flow turns out to be substantially symmetric about the midspan plane and strong three-dimensional effects are observed in wide portions of the separation bubbles adjacent to the upper and lower walls. The reattachment lengths exhibit significant spanwise variations that are particularly pronounced in the longer reattachment line. Measurements performed in a single flow plane at show that the influence of the Reynolds number on the mean flow is not completely negligible in the considered variation range. Based on a careful analysis of the PIV data, a model of the three-dimensional mean flow structure in the separation bubbles has been conjectured and it is provided in the paper. The present investigation contributes to clarifying the controversial three-dimensional character of the turbulent flow in a planar sudden expansion and provides accurate and detailed reference data for numerical simulations.
- Compressible Flows
20(2008); http://dx.doi.org/10.1063/1.2831135View Description Hide Description
Computations using the direct simulation Monte Carlo (DSMC) method are presented for hypersonic flow on power-law shaped leading edges. The primary aim of this paper is to examine the geometry effect of such leading edges on the shock-wave structure. The sensitivity of the shock-wave shape, shock-wave thickness, and shock-wave standoff distance to shape variations of such leading edges is investigated by using a model that classifies the molecules in three distinct classes: (1) undisturbed freestream, (2) reflected from the boundary, and (3) scattered, i.e., molecules that had been indirectly affected by the presence of the leading edge. The analysis showed that, for power-law shaped leading edge with exponent between and 1, the shock wave follows the body shape. It was found that, at the vicinity of the nose, the shock-wave power-law exponent is . Far from the nose, calculations showed that the shock-wave shape is in surprising qualitative agreement with that predicted by the hypersonic small disturbance theory for the flow conditions considered.
20(2008); http://dx.doi.org/10.1063/1.2827584View Description Hide Description
Solving transport equations in heterogeneous flows might give rise to scale dependent transport behavior with effective large scale transport parameters differing from those found on smaller scales. For incompressible velocity fields, homogenization methods have proven to be powerful in describing the effective transport parameters. In this paper, we aim at studying the effective drift of transport problems in heterogeneous compressible flows. Such a study was done by Vergassola and Avellaneda in Physica D106, 148 (1997). There, it was shown that for static compressible flow without mean drift, impacts on the large scale drift do not occur. We will first discuss the impact of a mean drift and show that static compressible flow with mean drift can produce a heterogeneity driven large scale drift (or ballistic transport). For the case of Gaussian stationary random processes, we derive explicit results for the large scale drift. Moreover, we show that the large scale or effective drift depends on the small scale diffusion coefficients and thus on the molecular weights of the particles. This study could be applied to weight-based particle separation. Numerical simulations are presented to illustrate these phenomena.
20(2008); http://dx.doi.org/10.1063/1.2813042View Description Hide Description
Counterflow drag reduction by supersonic jet for a apex angle blunt cone flying at hypersonic Mach number is investigated for two different flowenthalpies using conventional and free piston driven hypersonic shock tunnels. Enhancement in drag reduction has been observed with increase in freestream stagnation enthalpy. It is shown that the percentage of drag reduction goes up by a factor of 2 when the flowenthalpy increases by a factor of 2.5 for a given ratio of total pressure of supersonic jet and freestream flow.
20(2008); http://dx.doi.org/10.1063/1.2837172View Description Hide Description
An experimental study has been conducted to examine the interaction of shock wave induced vortices with a flat plate and a perforated plate. The experiments were carried out using a internal diameter shock-tube at Mach numbers 1.31, 1.49, and 1.61 under critical driver conditions. Air was used both in the driver and driven sections. High-speed schlieren photography was employed to study the flow development and the resulting interactions with the plates. Wall pressure measurements on both plates were also carried out in order to study the flow interactions quantitatively. The experimental results indicated that a region of strong flow development is generated near the wall surface, due to the flow interactions of reflected waves and oncoming induced vortices. This flow behavior causes the generation of multiple pressure fluctuations on the wall. In the case of the perforated plate, a weaker initial reflected wave is produced, which is followed by compression waves, due to the internal reflections within the plate. The transmitted wave is reduced in strength, compared to the initial incident shock wave.
- Geophysical Flows
20(2008); http://dx.doi.org/10.1063/1.2830983View Description Hide Description
We numerically study the induction mechanisms generated from an array of helical motions distributed along a cylinder. Our flow is a very idealized geometry of the columnar structure that has been proposed for the convective motion inside the Earth’s core. Using an analytically prescribed flow, we apply a recently introduced iterative numerical scheme [M. Bourgoin, P. Odier, J.-F. Pinton, and Y. Richard, Phys. Fluids16, 2529 (2004)] to solve the induction equation and analyze the flow response to externally applied fields with simple geometries (e.g., azimuthal, radial). Symmetry properties allow us to build selected induction modes whose interactions lead to dynamo mechanisms. Using an induction operator formalism, we show how dipole and quadrupole dynamos can be envisioned from such motions. The method identifies the main induction mechanisms that generate dynamo action in the selected geometry. Here, it emphasizes the competition between -effect and field expulsion as well as the role of scale separation.
20(2008); http://dx.doi.org/10.1063/1.2834731View Description Hide Description
We present the results of fully nonlinear numerical simulations of the geostrophic adjustment of a pressure front over topography, represented by an escarpment with a linear slope. The results of earlier simulations in the linear regime are confirmed and new essentially nonlinear effects are found. Topography influences both fast and slow components of motion. The fast unbalanced motion corresponds to inertia-gravity waves (IGW). The IGW emitted during initial stages of adjustment break and form the localized dissipation zones. Due to topography, the IGW activity is enhanced in certain directions. The slow balanced motion corresponds to topographic Rossby waves propagating along the escarpment. As shown, at large enough nonlinearities they may trap fluid/tracer and carry it on. There are indications that nonlinear topographic waves form a soliton train during the adjustment process. If the coastal line is added to the escarpment at the shallow side (continental shelf), secondary fronts related to the propagation of the coastal Kelvin waves appear.
20(2008); http://dx.doi.org/10.1063/1.2823561View Description Hide Description
A convective transport model is developed to study the role of thermal diffusion, or the Ludwig–Soret effect, in nanofluid systems with temperature gradients. The study deals with a fluid suspension of nanoparticles enclosed between two differentially heated horizontal, relatively closely spaced plates (Bénard configuration). An order-of-magnitude analysis is performed to identify the relevant parameters of the problem. Three-dimensional simulations are performed taking into account different conditions, including normal or microgravity conditions, gravity orientation, and positive or negative Soret effect. Different modes of convective instabilities are shown to be present in the system, which are associated with the gravity force and the density differences induced by concentration gradients. The characteristic flow patterns and instability developments are in agreement with the experimental findings obtained by independent investigators on colloidal suspensions. The onset of instabilities, their characteristic time scales, and flow patterns corresponding with different geometrical configurations, gravity levels, and gravity orientation are shown.
20(2008); http://dx.doi.org/10.1063/1.2830328View Description Hide Description
The asymptotic dynamics of finite-size particles is governed by a slow manifold that is globally attracting for sufficiently small Stokes numbers. For neutrally buoyant particles (suspensions), the slow dynamics coincide with that of infinitesimally small particles, therefore the suspension dynamics should synchronize with Lagrangian particle motions. Paradoxically, recent studies observe a scattering of suspension dynamics along Lagrangian particle motions. Here we resolve this paradox by proving that despite its global attractivity, the slow manifold has domains that repel nearby passing trajectories. We derive an explicit analytic expression for these unstable domains; we also obtain a necessary condition for the global attractivity of the slow manifold. We illustrate our results on neutrally buoyant particle motion in a two-dimensional model of vortex shedding behind a cylinder in crossflow and on the three-dimensional steady Arnold–Beltrami–Childress flow.
20(2008); http://dx.doi.org/10.1063/1.2832777View Description Hide Description
This study analyzes heat transfer effects inside vacuum packaged microelectromechanical system(MEMS)devices. A packaged device is simplified as four plates forming a square cavity, the bottom plate represents a hot chip, while the other three plates are maintained at room temperature. For a highly rarefied free molecular internal gas flow scenario, the corresponding detailed density and temperature fields are analytically determined with a proposed speculation. This speculation indicates that for a steady free molecular gas flow inside a convex closure domain formed by walls maintained at different temperatures: (1) the velocity distribution functions for those molecules diffusely reflected at different walls and traveling away from them are Maxwellian with different number densities; (2) for each distribution, is a constant, where is the number density for the group of reflected molecules, and is the temperature for the plate. For a near continuum flow scenario, the governing energy equation degenerates to Laplace’s equation with several temperature-jump wall boundary conditions. This study also includes discussions and comparisons among analytical results, simulation results from the direct simulation Monte Carlo method, and results by solving the Navier–Stokes equations with proper wall boundary conditions. The approach used in this study is generally applicable to study internal flows and heat transfer effects in other vacuum packaged MEMSdevices with different shapes.
20(2008); http://dx.doi.org/10.1063/1.2831153View Description Hide Description
We study the flow of a liquid metal in a square duct past a circular cylinder in a strong externally imposed magnetic field. In these conditions, the flow is quasi-two-dimensional, which allows us to model it using a two-dimensional (2D) model. We perform a parametric study by varying the two control parameters and ( is the ratio of Lorentz to viscous forces) in the ranges [0…6000] and [0…2160], respectively. The flow is found to exhibit a sequence of four regimes. The first three regimes are similar to those of the non-magnetohydrodynamic (non-MHD) 2D circular wake, with transitions controlled by the friction parameter . The fourth one is characterized by vortices raising from boundary layer separations at the duct side walls, which strongly disturbs the Kármán vortex street. This provides the first explanation for the breakup of the 2D Kármán vortex street first observed experimentally by Frank, Barleon, and Müller [Phys. Fluids13, 2287 (2001)]. We also show that, for high values of , the transition to the fourth regime occurs for , and that it is accompanied by a sudden drop in the Strouhal number. In the first three regimes, we show that the drag coefficient and the length of the steady recirculation regions located behind the cylinder are controlled by the parameter . Also, the free shear layer that separates the recirculation region from the free stream is similar to a free MHD parallel layer, with a thickness of the order of that is quite different to that of the non-MHD case, and therefore strongly influences the dynamics of this region. We also present one case at and , where this layer undergoes an instability of the Kelvin–Helmholtz-type.