Volume 20, Issue 12, December 2008
Index of content:
A study of the mechanism by which disturbances can cause tripping between steady-flow regular and Mach reflection in the dual-solution domain is presented. Computational results indicate that the disturbance shock created as a result of the impact of dense particles on one of the shock-generating wedges can cause transition from regular to Mach reflection. The disturbance shock may also be generated by direct energy deposition on the wedge. Estimates of the lower bound of the required energy for transition to occur are presented and compared to values obtained computationally. Experiments were performed at Mach 4.0 in a Ludwieg tube that has a test duration of 100 ms. Proper starting of the flow necessitated operation with an upstream diaphragm and modifications in the dump tank. The reflection state was changed by rapid rotation of one of the shock-generating wedges. The flow in the facility is sufficiently quiet to permit entering the dual-solution domain to approximately its midpoint before spontaneous transition to the Mach reflection occurs. The short test time prompted a study of the effect of wedge rotation speed on the transition from regular to Mach reflection. Transition due to deposition of energy on one of the wedges was also examined by using a pulsed laser focused on one of the two wedges. Measurements of the minimum energy to bring about transition and of the rapid growth of the Mach stem to its steady-state are compared to numerical and theoretical predictions.
- Interfacial Flows
20(2008); http://dx.doi.org/10.1063/1.3026747View Description Hide Description
The prediction of the rise speed of large buoyant bubbles is a fundamental fluid mechanics problem relevant to a number of applications ranging from carbon sequestration technology to chemical engineering or astrophysics. Single large bubbles typically have a spherical cap shape with bubbles of larger volume rising faster than the ones of smaller volume. However, except in well-controlled experiments, the released gas splits into a leading cap bubble, followed by a crown of satellite bubbles that can contain up to 50% of the total volume of gas. We find that in this case the satellite bubbles rearrange in a characteristic toroidal crown and the leading bubble takes a lenticular shape. The rise speeds of these multipart bubble systems and the ratios of the torus radii to the leading cap curvature radii are quite constant and predictable in the mean and are furthermore independent of the gas partitioning between the leading lenticular bubble and the crown of satellite bubbles. We also find that this multipart bubble system rises slightly faster than a single cap bubble with the same total injected volume of gas.
20(2008); http://dx.doi.org/10.1063/1.3053827View Description Hide Description
Long nonlinear two-dimensional traveling waves on a liquid film driven by laminar flow of a gas with much smaller density and viscosity are investigated. The gas flow is assumed to be pressure driven. The method of particles for incompressible flow is used to solve Navier–Stokes equations. The influence of layer depth ratio, gas Reynolds number, and wavelength on wave amplitude and phase speed is studied and compared to the corresponding characteristics of gravity-capillary waves. The waves with equal amplitude but different phase speeds have been revealed, i.e., the phase speed of the gas driven waves is not always a single valued function of their amplitude. Self-similarity of velocity profiles in shear driven waves has also been demonstrated.
20(2008); http://dx.doi.org/10.1063/1.3054153View Description Hide Description
We report on an experimental study conducted to investigate the airside flow structure above an evaporative watersurface during natural convection. Two-dimensional airside velocity fields were measured using particle image velocimetry for three different surface heat flux conditions. Detailed analysis of the turbulentvelocity fields shows a complex flow structure due the local interactions of fluid motions in vertical, horizontal, and normal directions. The trends of turbulent intensity profiles on airside and waterside are found to be similar. However, the airside turbulent intensities are approximately 20 times stronger than that on the waterside. The spectral analysis of the turbulentvelocities showed the existence of two distinct power law regimes. In low wavenumber range, the buoyancy subrange is observed with a slope of whereas, in high wavenumber range, the inertial subrange with the classical slope of is observed. The results also indicate that the airside turbulentvelocity fields control the local evaporation rate, which in turn influences the watersurfacetemperature field and the waterside velocity field.
- Viscous and Non-Newtonian Flows
Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films20(2008); http://dx.doi.org/10.1063/1.3041150View Description Hide Description
The formation and presence of eddies within thick gravity-driven free-surface filmflow over a corrugated substrate are considered, with the governing equations solved semianalytically using a complex variable method for Stokes flow and numerically via a full finite element formulation for the more general problem when inertia is significant. The effect of varying geometry (involving changes in the film thickness or the amplitude and wavelength of the substrate) and inertia is explored separately. For Stokes-like flow and varying geometry, excellent agreement is found between prediction and existing flow visualizations and measured eddy center locations associated with the switch from attached to locally detached flow. It is argued that an appropriate measure of the influence of inertia at the substrate is in terms of a local Reynolds number based on the characteristic corrugation length scale. Since, for small local Reynolds numbers, the local flowstructure there becomes effectively decoupled from the inertia-dominated overlying film and immune from instabilities at the free-surface; the influence of inertia manifests itself as a skewing of the dividing streamline (separatrix). It is shown that the formation and presence of eddies can be manipulated in one of two ways. While an decrease/increase in the corrugation steepness leads to the disappearance/appearance of kinematically induced eddies, an increase/decrease in the inertia present in the system leads to the appearance/disappearance of inertially induced eddies. A critical corrugation steepness for a given film thickness is defined, demarking the transition from a kinematically to an inertially induced local eddyflowstructure and vice versa.
Flow of artificial microcapsules in microfluidic channels: A method for determining the elastic properties of the membrane20(2008); http://dx.doi.org/10.1063/1.3054128View Description Hide Description
The paper deals with a method to characterize the membranemechanical properties of microcapsules. The technique consists in flowing microcapsules into a microchannel of comparable dimensions, observing the deformation as a function of the flow rate, and deducing the membraneelastic modulus by means of an inverse method based on a numerical model of the flowing capsule. The method is tested on liquid-filled microcapsules (average diameter of ) with a membrane made of crossed-linked ovalbumin flowing inside a cylindrical channel. For a neo-Hookean constitutive law, the method yields a constant value for the membrane shear elastic modulus independently of capsule size or deformation. When the capsules are flowed into a square-section microchannel, an approximate analysis of the deformation yields the same value of the membraneshear modulus provided that the size ratio between the capsule and the channel is of order unity.
- Particulate, Multiphase, and Granular Flows
Asymptotic model of the inertial migration of particles in a dilute suspension flow through the entry region of a channel20(2008); http://dx.doi.org/10.1063/1.3032909View Description Hide Description
The inertial migration of particles in a dilute suspension flow through the entry region of a plane channel (or a circular pipe) is considered. Within the two-fluid approach, an asymptotic one-way coupling model of the dilute suspension flow in the entry region of a channel is constructed. The carrier phase is a viscous incompressible Newtonian fluid, and the dispersed phase consists of identical noncolloidal rigid spheres. In the interphase momentum exchange, we take into account the drag force, the virtual mass force, the Archimedes force, and the inertial lift force with a correction factor due to the wall effect and an arbitrary particle slip velocity. The channel Reynolds number is high and the particle-to-fluid density ratio is of order unity or significantly larger unity. The solution is constructed using the matched asymptotic expansion method. The problem of finding the far-downstream cross-channel profile of particle number concentration is reduced to solving the equations of the two-phase boundary layer developing on the channel walls. The full Lagrangian approach is used to study the evolution of the cross-flow particle concentration profile. The inertial migration results in particle accumulation on two symmetric planes (an annulus) distanced from the walls, with a nonuniform concentration profile between the planes (inside the annulus) and particle-free layers near the walls. When the particle-to-fluid density ratio is of order unity, an additional local maximum of the particle concentration on inner planes (an inner annulus) is revealed. The inclusion of the corrected lift force makes it possible to resolve the nonintegrable singularity in the concentration profile on the wall, which persisted in all previously published solutions for the dilute suspension flow in a boundary layer. The numerical results are compared to the tubular pinch effect observed in experiments, and a qualitative analogy is found.
A focused view of the behavior of granular flows down a confined inclined chute into the horizontal run-out zone20(2008); http://dx.doi.org/10.1063/1.3033490View Description Hide Description
In this paper a detailed approach is proposed for the behavior of two-dimensional cohesionless granular materials moving down a confined inclined plane chute into the horizontal run-out zone, where the upslope propagating bore is treated as a growing deposition heap. It deals with the theoretical-numerical and experimental treatments. The depth-averaged field equations of balance of mass and linear momentum are described in moving coordinates for general topography as prescribed by Tai and Kuo [Acta Mech.199, 71 (2008)]. A most simplistic approach to the erosion/deposition parameterization is proposed and the spatial coordinate coincides with the arc length of the variable basal surface. These equations describe the temporal evolution of the depth and velocity of the granular mass, especially the locations and shapes of the growing deposition heaps beneath the flowing layer. Experiments were carried out with different material supply rates and in two types of chutes, which differed by the bottom surface of the chute. In these experiments the sequential motions of the granular mass were recorded by a high-speed digital camera. The outlines of the deposition heap and flowing layers were obtained by successive images differences. Comparison of the experimental findings with the computational results proved to lead to good correspondence between experiment and theory. Even the development of the detailed geometry of the deposition heap is satisfactorily reproduced.
20(2008); http://dx.doi.org/10.1063/1.3035943View Description Hide Description
Observations of bubbles rising near a wall under conditions of large Reynolds and small Weber numbers have indicated that the velocity component of the bubbles parallel to the wall is significantly reduced upon collision with a wall. To understand the effect of such bubble-wall collisions on the flow of bubbly liquids bounded by walls, a model is developed and examined in detail by numerical simulations and theory. The model is a system of bubbles in which the velocity of the bubbles parallel to the wall is significantly reduced upon collision with the channel wall while the bubbles in the bulk are acted upon by gravity and linear drag forces. The inertial forces are accounted for by modeling the bubbles as rigid particles with mass equal to the virtual mass of the bubbles. The standard kinetic theory for granular materials modified to account for the viscous and gravity forces and supplemented with boundary conditions derived assuming an isotropic Maxwellianvelocity distribution is inadequate for describing the behavior of the bubble-phase continuum near the walls since the velocity distribution of the bubbles near the walls is significantly bimodal and anisotropic. A kinetic theory that accounts for such a velocity distribution is described. The bimodal nature is captured by treating the system as consisting of two species with the bubbles (modeled as particles) whose most recent collision was with a channel wall treated as one species and those whose last collision was with another bubble as the other species. The theory is shown to be in very good agreement with the results of numerical simulations and provides closure relations that may be used in the analysis of bidisperse particulate systems as well as bounded bubbly flows.
20(2008); http://dx.doi.org/10.1063/1.3041776View Description Hide Description
Suspensions of self-propelled particles, such as swimming micro-organisms, are known to undergo complex dynamics as a result of hydrodynamic interactions. To elucidate these dynamics, a kinetic theory is developed and applied to study the linear stability and the nonlinear pattern formation in these systems. The evolution of a suspension of self-propelled particles is modeled using a conservation equation for the particle configurations, coupled to a mean-field description of the flow arising from the stress exerted by the particles on the fluid. Based on this model, we first investigate the stability of both aligned and isotropic suspensions. In aligned suspensions, an instability is shown to always occur at finite wavelengths, a result that extends previous predictions by Simha and Ramaswamy [“Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles,” Phys. Rev. Lett.89, 058101 (2002)]. In isotropic suspensions, we demonstrate the existence of an instability for the active particle stress, in which shear stresses are eigenmodes and grow exponentially at long scales. Nonlinear effects are also investigated using numerical simulations in two dimensions. These simulations confirm the results of the stability analysis, and the long-time nonlinear behavior is shown to be characterized by the formation of strong density fluctuations, which merge and breakup in time in a quasiperiodic fashion. These complex motions result in very efficient fluid mixing, which we quantify by means of a multiscale mixing norm.
20(2008); http://dx.doi.org/10.1063/1.3039547View Description Hide Description
When loosely packed granular material in a long tube is tapped, the material collapses into a more dense state. For fine-grained material and with interstitial air present, this compaction occurs as waves of apparent avalanches transport the grains to a lower height. We find that these avalanches are due to a train of air bubbles rising within the material. We investigate how the formation of bubbles depends on the tilt angle of the tube, the size of granular particles, and the pressure of the interstitial gas between the particles. We estimate the interaction between the air and the granular medium that is necessary for the bubbles to form. The estimates are in quantitative agreement with our experimental observations.
- Laminar Flows
20(2008); http://dx.doi.org/10.1063/1.3021477View Description Hide Description
Hydraulic permeabilities of fiber networks are of interest for many applications and have been studied extensively. There is little work, however, on permeability calculations in three-dimensional random networks. Computational power is now sufficient to calculate permeabilities directly by constructing artificial fiber networks and simulating flow through them. Even with today’s high-performance computers, however, such an approach would be infeasible for large simulations. It is therefore necessary to develop a correlation based on fiber volume fraction, radius, and orientation, preferably by incorporating previous studies on isotropic or structured networks. In this work, the direct calculations were performed, using the finite element method, on networks with varying degrees of orientation, and combinations of results for flows parallel and perpendicular to a single fiber or an array thereof, using a volume-averaging theory, were compared to the detailed analysis. The detailed model agreed well with existing analytical solutions for square arrays of fibers up to fiber volume fractions of 46% for parallel flow and 33% for transverse flow. Permeability calculations were then performed for isotropic and oriented fiber networks within the fiber volume fraction range of 0.3%–15%. When drag coefficients for spatially periodic arrays were used, the results of the volume-averaging method agreed well with the direct finite element calculations. On the contrary, the use of drag coefficients for isolated fibers overpredicted the permeability for the volume fraction range that was employed. We concluded that a weighted combination of drag coefficients for spatially periodic arrays of fibers could be used as a good approximation for fiber networks, which further implies that the effect of the fiber volume fraction and orientation on the permeability of fiber networks are more important than the effect of local network structure.
Viscous and inviscid flows generated by wall-normal injection into a cylindrical cavity with a headwall20(2008); http://dx.doi.org/10.1063/1.3045738View Description Hide Description
An analysis of viscous and inviscid steady flows in a cylindrical cavity of a circular cross section with a headwall is presented. The flow is induced by wall-normal injection from both the sidewall and the headwall which includes the zeroth tangential velocity at the injecting boundaries. It is shown that in the inviscid limit the functional vorticity-stream function relation is essentially nonlinear and singular becoming linear far downstream.
- Instability and Transition
20(2008); http://dx.doi.org/10.1063/1.3029703View Description Hide Description
Three-dimensional (3D) calculations of the flow through a curved duct of square cross section are conducted by use of the spectral method. The main concern of this paper is to clarify 3D structures of periodic solutions which have been obtained by two-dimensional (2D) calculations assuming uniformity in the main-flow direction. It is found that traveling-wave solutions are realized by 3D numerical simulations in the parameter region where periodic solutions were obtained by 2D simulations. Exact traveling-wave solutions are obtained by the iteration method from an initial guess given by the time-evolution calculations. The flow patterns of a 3D traveling wave observed in a cross section are very similar to those of 2D periodic solutions.
Floquet analysis of secondary instability of boundary layers distorted by Klebanoff streaks and Tollmien–Schlichting waves20(2008); http://dx.doi.org/10.1063/1.3040302View Description Hide Description
Previous studies of the interaction between boundary layer streaks and Tollmien–Schlichting (TS) waves have shown puzzling effects. Streaks were shown to reduce the growth rate of primary TS waves and, thereby, to delay transition; however, they can also promote transition by inducing a secondary instability. The outcome of the interaction depends on the spanwise wavelength and intensity of the streaks as well as on the amplitude of the TS waves. A Floquet analysis of secondary instability is able to explain many of these features. The base state is periodic in two directions: it is an Ansatz composed of a saturated TS wave (periodic in ) and steady streaks (periodic in ). Secondary instability analysis is extended to account for the doubly periodic base flow. Growth rate computations show that, indeed, the streak can either enhance or diminish the overall stability of the boundary layer. The stabilizing effect is a reduction in the growth rate of the primary two-dimensional TS wave; the destabilizing effect is a secondary instability. Secondary instability falls into two categories, depending on the spanwise spacing of the streaks. The response of one category to perturbations is dominated by fundamental and subharmonic instability; the response of the other is a detuned instability.
Simultaneous particle-image velocimetry–planar laser-induced fluorescence measurements of Richtmyer–Meshkov instability growth in a gas curtain with and without reshock20(2008); http://dx.doi.org/10.1063/1.3041705View Description Hide Description
The structure of the concentration and velocity fields in a light-heavy-light fluid layer subjected to an impulsive acceleration by a shock wave (Richtmyer–Meshkov instability) is studied using simultaneous particle-image velocimetry and planar laser-induced fluorescence (PLIF) measurements (performed in such flows for the first time). The initial condition prior to shock impact is accurately characterized using calibrated PLIF measurements to enable comparisons of the evolving structure to numerical simulations. Experiments performed on a curtain in air (Atwood number, ), after single shock by a Mach 1.2 shock wave and reshock by the reflected wave, show that the reshock wave has a dramatic impact on the evolution of the unstable structure. After first shock and in the absence of reshock(s), the structure widths agree well with an analytical extension to the nonlinear point vortex model [J. W. Jacobs et al., “Nonlinear growth of the shock-accelerated instability of a thin fluid layer,” J. Fluid Mech.295, 23 (1995)] that accounts for the nonuniform spacing of the row of counter-rotating vortices that drive the flow. However, upon reshock, the width deviates significantly from the singly shocked case, and a substantial rise in the growth rate is observed. Enhanced mixing, destruction of the ordered velocity field, and an increase in both the positive and negative circulations ensue. Large velocity fluctuations relative to the mean flow, and the advection of a wide spectrum of vortex scales combine to mix the flow well and create turbulent conditions in the reshocked structure.
20(2008); http://dx.doi.org/10.1063/1.3054146View Description Hide Description
We report the results of an experimental investigation into fluid motion induced by the deceleration to rest of a rigidly rotating fluid-filled torus. Transition to a transient turbulent state is found where the onset of the complicated motion is triggered by a small-scale wavelike instability. The wave forms on a front that propagates from the inner wall of the toroidal container after it is stopped. We reveal the origins of the front through a combination of careful experimental measurements, boundary-layer analysis, and computation of the axisymmetric Navier–Stokes equations.
- Turbulent Flows
20(2008); http://dx.doi.org/10.1063/1.3013635View Description Hide Description
A commonplace view of pressure-driven turbulence in pipes and channels is as “cascades” of streamwise momentum toward the viscous layer at the wall. We present in this paper an alternative picture of these flows as “inverse cascades” of spanwise vorticity in the cross-stream direction but away from the viscous sublayer. We show that there is a constant spatial flux of spanwise vorticity due to vorticity conservation and that this flux is necessary to produce pressure drop and energy dissipation. The vorticitytransport is shown to be dominated by viscous diffusion at distances closer to the wall than the peak Reynolds stress, well into the classical log layer. The Perry–Chong model based on “representative” hairpin/horseshoe vortices predicts a single sign of the turbulentvorticity flux over the whole log layer, whereas the actual flux must change sign at the location of the Reynolds-stress maximum. Sign reversal may be achieved by assuming a slow power-law decay of the Townsend “eddy-intensity function” for wall-normal distances greater than the hairpin length scale. The vortex-cascade picture presented here has a close analog in the theory of quantum superfluids and superconductors, the “phase slippage” of quantized vortex lines. Most of our results should therefore apply as well to superfluidturbulence in pipes and channels. We also discuss issues about drag reduction from this perspective.
Experimental study of an active grid-generated shearless mixing layer and comparisons with large-eddy simulation20(2008); http://dx.doi.org/10.1063/1.3001796View Description Hide Description
A shearless mixing layer characterized by interactions between two regions with different turbulence intensities but without mean shear is investigated experimentally in a wind tunnel. Reynolds numbers higher than those of prior studies [B. Gilbert, “Diffusion mixing in grid turbulence without mean shear,” J. Fluid Mech.100, 349 (1980); S. Veeravalli and Z. Warhaft, “The shearless turbulent mixing layer,” J. Fluid Mech.207, 191 (1989); B. Knaepen, O. Debliquy, and D. Carati, “Direct numerical simulation and large-eddy simulation of a shear-free mixing layer,” J. Fluid Mech.514, 153 (2004); D. Tordella and M. Iovieno, “Numerical experiments on the intermediate asymptotics of shear-free turbulent transport and diffusion,” J. Fluid Mech.549, 429 (2006); D. A. Briggs, J. H. Ferziger, J. R. Koseff, and S. G. Monismith, “Entrainment in a shear-free turbulent mixing layer,” J. Fluid Mech.310, 215 (1996)] are achieved by using an active grid with rotating winglets on one-half of its cross section. Stationary flow-conditioning fine meshes are used to avoid mean velocity gradients. Measurements are performed at five different downstream wind-tunnel locations using an X-type hot-wire probe and a stereoscopic particle image velocimetry system. The Reynolds numbers based on the Taylor microscale in the high- and low-kinetic energy regions are 170 and 88, respectively. The energy and integral length-scale ratios between the two regions are 4.27 and 1.73, respectively. The inlet turbulence in the upper and lower portions of the shearless mixing layer is not fully isotropic, with the streamwise velocityfluctuations being between 6% and 13% higher than the cross-stream ones. Fundamental statistical properties of the flow are documented and analyzed at various scales using band-pass box-filtered velocities. Downstream evolution of variance and half-width of the mixing layer, skewness and flatness factors, as well as the statistics of two-point velocity increments at various displacements are presented. It is found that much of the deviations from Gaussian statistics originate from large-scale motions. The data are well suited to be used as initial condition for simulations and as test for large-eddy simulation(LES)models and codes. Comparison studies for three LESmodels including Smagorinsky, dynamic Smagorinsky, and dynamic mixed nonlinear models are implemented in simulations of temporally decaying shearless mixing layer using a pseudospectral code. Initial conditions are prescribed by matching the longitudinal energy spectra at all heights across the layer for both streamwise and cross-stream velocity components. LES with all three subgrid scale models tested underpredicts the kinetic energy and exhibits deviations from the measured non-Gaussian behaviors. Overall, the dynamic Smagorinsky model predicts statistics slightly better than the other two models.
- Compressible Flows
20(2008); http://dx.doi.org/10.1063/1.3026074View Description Hide Description
The flow structure inside the valveless standing wave pump is investigated experimentally. The two-dimensional velocity fields inside the chamber of this novel pump at different phases of the excitation signal are measured using the synchronized particle imagevelocimetry technique. The variations in the pump flow rate, pressure loss coefficients, and rectification capability of the diffuser-nozzle element are analyzed. According to the results obtained in this paper, the net flow rate of the pump increases with an increase in the pressure (or Reynolds number). The interactions of three different flow fields inside the pump chamber (pumping flow, acoustic, and streaming velocities) are studied. It is found that, while the pumping flow has an effect on the acoustic velocity patterns only around the inlet and outlet orifices, the streaming velocity structures are drastically affected by the pumping flow.
20(2008); http://dx.doi.org/10.1063/1.3035992View Description Hide Description
Molecular simulations in a dilute monatomic gas were carried out to characterize the mutual interactions of impinging planar shocks of up to Mach 3 with transverse microvortices having core sizes comparable to the thickness of the shock. Time dependent simulations were performed using the direct simulation Monte Carlo method and then analyzed by applying transport theory to the sampled molecular results. Several flow cases were computed for initially stationary, composite vortices. The results reveal the generic features of the interaction, the effect of vortex size, and the effects of shock strength. In all cases, the applied straining compression in the shock was of the same order as the time scale of the vortex rotation. Most of the features found in shock interaction with a macroscale vortex of the same type were also found at microscale. These include acoustic wave formation, shock diffraction and refraction, vortex deformation and displacement, and dilatational vorticity generation greater than baroclinic vorticity generation. However, the major characteristic that dominated at microscale was the viscous attenuation of the vortex. In contrast to the net vorticity production due to interaction that has been demonstrated at macroscale, the attenuation overwhelmed the vorticity generation mechanisms at microscale, within the parameter ranges studied. The data allowed for the direct computation of the dissipation rate of kinetic energy, which was found to be high inside the shock wave throughout the interaction and significantly higher than a local thermodynamic equilibrium rate computed using the Newtonian continuum constitutive law with Stokes’ hypothesis. The differences between the two rates were substantial for a Mach 3 shock; but at Mach 2 they were close enough to decompose the continuum rate expression to infer the contributions of the various forms of dissipation to the actual rate.