Feedback | Help | Exit
Search:
   
 
 
 

BROWSE VOLUME

Year Range:  

BROWSE EARLY VOLUMES

November 2009

Volume 21, Issue 11,  partial issue

back to top

LETTERS

FREE

Localized edge states in plane Couette flow

Yohann Duguet, Philipp Schlatter, and Dan S. Henningson

Phys. Fluids 21, 111701 (2009) (4 pages)

Online Publication Date: 13 November 2009

Full Text: PDF (347 kB)

Show Abstract
The dynamics at the threshold of transition in plane Couette flow is investigated numerically in a large spatial domain for a certain type of localized initial perturbation, for Re between 350 and 1000. The corresponding edge state is an unsteady spotlike structure, localized in both streamwise and spanwise directions, which neither grows nor decays in size. We show that the localized nature of the edge state is numerically robust, and is not influenced by the size of the computational domain. The edge trajectory appears to transiently visit localized steady states. This suggests that basic spatiotemporally intermittent features of transition to turbulence, such as the growth of a turbulent spot, can be described as a dynamical system.
Show PACS
47.15.Fe, 47.10.Fg, 47.27.ed, 47.27.Cn
FREE

Spectrum of a passive scalar in moderate Reynolds number homogeneous isotropic turbulence

L. Danaila and R. A. Antonia

Phys. Fluids 21, 111702 (2009) (4 pages)

Online Publication Date: 16 November 2009

Full Text: PDF (159 kB)

Show Abstract
For moderate Reynolds numbers, the spectral scaling exponents of both velocity [E(k)[proportional]k−mu] and the transported passive scalar [Etheta(k)[proportional]k−mtheta] fields exhibit departures from the asymptotic prediction mu=mtheta=5/3. However, at the same Reynolds number, the passive scalar spectrum for homogeneous isotropic turbulence is closer to the universal asymptotic state than the dynamic velocity field that transports it. This paper provides a possible explanation for this behavior, in the case of a gaseous mixing with Prandtl (or Schmidt) number Pr~=1. A scenario of the scalar energy transfer toward higher wavenumbers is proposed and validated using experimental data, in which the velocity field itself is actively involved via its characteristic time. A direct relationship between velocity and scalar spectra and therefore between mu and mtheta is thus established.
Show PACS
47.27.-i
back to top

ARTICLES

Micro- and Nanofluid Mechanics

Note on the relation between thermophoresis and slow uniform flow problems for a rarefied gas

Shigeru Takata

Phys. Fluids 21, 112001 (2009) (7 pages)

Online Publication Date: 10 November 2009

Full Text: PDF (179 kB)

Show Abstract
A relation between the problem of thermophoresis of a sphere and that of a uniform flow past a sphere is discussed on the basis of the linearized Boltzmann equation. First pointed out is the disagreement between the relation predicted by the representation theorem recently developed by the author and that of the existing theory by Sharipov. The two contradicting predictions are assessed by the asymptotic theory for small Knudsen numbers, which results in showing the failure of the latter. The reason of this failure is also explained. Finally, new data of a slip coefficient, which is predominantly responsible for the thermal polarization in a slightly rarefied gas, are obtained for the hard-sphere Boltzmann equation by the use of the correct relation.
Show PACS
47.45.-n, 05.60.-k

Interfacial Flows

Spray and microjets produced by focusing a laser pulse into a hemispherical drop

S. T. Thoroddsen, K. Takehara, T. G. Etoh, and C.-D. Ohl

Phys. Fluids 21, 112101 (2009) (15 pages) Multimedia

Online Publication Date: 2 November 2009

Full Text: PDF (1535 kB)

Show Abstract
We use high-speed video imaging to study laser disruption of the free surface of a hemispheric drop. The drop sits on a glass surface and the Nd:YAG (yttrium aluminum garnet) laser pulse propagates through the drop and is focused near the free surface from below. We focus on the evolution of the cylindrical liquid sheet and spray which emerges out of the drop and resembles typical impact crowns. The tip of the sheet emerges at velocities over 1 km/s. The tip of the crown breaks up into fine spray some of which is sucked back into the growing cavity at about 100 m/s. We measure the size of the typical spray droplets to be about 3  µm. We also show the formation of fine microjets, which are produced when the laser is focused inside the drop and the shock front hits small bubbles sitting under the free surface. For water these microjets are 5–50  µm in diameter and exit at 100–250 m/s. For higher viscosity drops, these jets can emerge at over 500 m/s.
Show PACS
47.15.Uv, 47.27.wg, 47.55.dp, 47.40.Nm, 47.80.Jk, 66.20.-d

Convective instabilities in liquid layers with free upper surface under the action of an inclined temperature gradient

A. I. Mizev and D. Schwabe

Phys. Fluids 21, 112102 (2009) (12 pages)

Online Publication Date: 3 November 2009

Full Text: PDF (912 kB)

Show Abstract
We present the results of an experimental study of convective instabilities in a horizontal liquid layer with free upper surface under the action of an inclined temperature gradient, i.e., when horizontal and vertical temperature gradients are applied at the same time. Silicone oil of 10 cSt (Prandtl number Pr=102) was employed as the test fluid. We investigated the layers with different thicknesses to examine the influence of gravity on the formation of the convective patterns. It is found out that the system behavior appreciably depends on the dynamic Bond number, which shows a relation of buoyancy and thermocapillary forces. In the case of small dynamic Bond numbers, when the influence of buoyancy is minimal, four different flow patterns, according to the combination of the vertical and horizontal Marangoni numbers, have been found: steady parallel flow, Bénard–Marangoni cells, drifting Bénard–Marangoni cells, and longitudinal rolls. At larger dynamic Bond number, when the influence of buoyancy becomes considerable, new convective structures, named by us the “surface longitudinal rolls” and the “surface drifting cells,” appear in addition to the patterns listed above. These instabilities exist only in the surface part of the thermocapillary flow, whereas the return flow remains stable. Under large enough dynamic Bond number these patterns become the dominating ones, forcing out the classical Bénard–Marangoni instability. We give a phenomenological description of the obtained convective patterns and present the stability diagram in the plane of the vertical and the horizontal Marangoni numbers.
Show PACS
47.20.Bp, 47.54.De, 68.03.Cd, 47.55.pf, 47.55.nb

Onset of flow separation for the oblique water impact of a wedge

Yuriy A. Semenov and Bum-Sang Yoon

Phys. Fluids 21, 112103 (2009) (11 pages)

Online Publication Date: 9 November 2009

Full Text: PDF (482 kB)

Show Abstract
For the oblique impact of a wedge on a liquid half space, the limiting angles of the entry velocity and the wedge orientation corresponding to flow separation from the wedge vertex during the initial stage of the impact are investigated on the basis of an analytical solution of the problem. The liquid is assumed to be ideal and incompressible; gravity, surface tension, and air cushioning effects are ignored. The flow generated by the impact is two dimensional and potential. The solution is presented in terms of two governing expressions, which are the complex velocity and the derivative of the complex potential defined in a parameter region. These expressions are obtained using generalized integral formulas for solving mixed and uniform boundary-value problems for the first quadrant. They include two unknown functions, which are the velocity magnitude and angle to the free surface determined from the dynamic and kinematic boundary conditions. The obtained system of integral equations is solved by using the method of successive approximations. The effect of the horizontal component of the entry velocity is studied for various wedge orientations. The analysis of the computations revealed configurations of the impact such that the pressure along the whole length of one side of the wedge becomes less than the pressure on the free surface. Although air effects are not included in the analysis, such a pressure distribution provides conditions for the ventilation of the wedge side, which, in the presence of the air, starts from the contact point on the free surface and extends suddenly along the whole length of the wedge side, thus leading to flow separation from the wedge vertex. The theoretical predictions of flow separation and the experimental data on flow separation by Judge et al. [“Initial water impact of a wedge at vertical and oblique angles,” J. Eng. Math. 48, 279 (2004)] are remarkably close to each other.
Show PACS
47.15.Rq, 68.03.Cd, 02.60.Nm, 02.60.Lj

Time-resolved proper orthogonal decomposition of liquid jet dynamics

Marco Arienti and Marios C. Soteriou

Phys. Fluids 21, 112104 (2009) (15 pages)

Online Publication Date: 13 November 2009

Full Text: PDF (1834 kB)

Show Abstract
New insight into the mechanism of liquid jet in crossflow atomization is provided by an analysis technique based on proper orthogonal decomposition and spectral analysis. Data are provided in the form of high-speed videos of the jet near field from experiments over a broad range of injection conditions. For each condition, proper orthogonal modes (POMs) are generated and ordered by intensity variation relative to the time average. The feasibility of jet dynamics reduction by truncation of the POM series to the first few modes is then examined as a function of crossflow velocity for laminar and turbulent liquid injection. At conditions where the jet breaks up into large chunks of liquid, the superposition of specific orthogonal modes is observed to track long waves traveling along the liquid column. The temporal coefficients of these modes can be described as a bandpass spectrum that shifts toward higher frequencies as the crossflow velocity is increased. The dynamic correlation of these modes is quantified by their cross-power spectrum density. Based on the frequency and wavelength extracted from the videos, the observed traveling waves are linked to the linearly fastest growing wave of Kelvin–Helmholtz instability. The gas boundary layer thickness at the gas-liquid shear layer emerges at the end of this study as the dominant length scale of jet dynamics at moderate Weber numbers.
Show PACS
47.15.Uv, 47.20.-k, 47.15.Cb, 47.27.nb, 47.55.Ca, 47.27.wg

Numerical simulation of liquid sloshing in a partially filled container with inclusion of compressibility effects

Y. G. Chen and W. G. Price

Phys. Fluids 21, 112105 (2009) (16 pages)

Online Publication Date: 19 November 2009

Full Text: PDF (3106 kB)

Show Abstract
A numerical scheme of study is developed to model compressible two-fluid flows simulating liquid sloshing in a partially filled tank. For a two-fluid system separated by an interface as in the case of sloshing, not only a Mach-uniform scheme is required but also an effective way to eliminate unphysical numerical oscillations near the interface. By introducing a preconditioner, the governing equations expressed in terms of primitive variables are solved for both fluids (i.e., water, air, gas, etc.) in a unified manner. In order to keep the interface sharp and to eliminate unphysical numerical oscillations in unsteady fluid flows, the nonconservative implicit split coefficient matrix method is modified to construct a flux-difference splitting scheme in the dual-time formulation. The proposed numerical model is evaluated by comparisons between numerical results and measured data for sloshing in an 80% filled rectangular tank excited at resonance frequency. Through similar comparisons, the investigation is further extended by examining sloshing flows excited by forced sway motions in two different rectangular tanks with 20% and 83% filling ratios. These examples demonstrate that the proposed method is suitable to capture induced free surface waves and to evaluate sloshing pressure loads acting on the tank walls and ceiling.
Show PACS
47.55.Ca, 47.60.-i, 47.40.Dc, 47.35.-i, 47.20.Ma, 47.11.-j

Failure of thermocapillary-driven permanent nonwetting droplets

Peter T. Nagy and G. Paul Neitzel

Phys. Fluids 21, 112106 (2009) (8 pages)

Online Publication Date: 20 November 2009

Full Text: PDF (693 kB)

Show Abstract
A droplet may be prevented from molecular contact with a solid surface by providing a thin, lubricating film of surrounding fluid between the solid and liquid surfaces. In this study, we exploit thermocapillary convection, caused by a temperature difference maintained between the droplet and the unwetted surface, to provide this lubricating film. This state may be sustained indefinitely (permanent nonwetting) if the load applied to the droplet does not exceed a threshold. Failure of such systems may be categorized as either film or pinning failures, depending on whether the lubrication film is breached, resulting in a molecular contact between the droplet and the solid surface, or the droplet is forced from its support by losing its pinning contact line. In this work, loads that trigger film and pinning failures are quantified, and their mechanisms explained. Results show that larger loads can be sustained for systems with an elevated temperature difference and for droplets of higher viscosity.
Show PACS
47.55.dm, 47.55.nb, 47.55.nd, 47.55.pb, 68.15.+e, 66.20.Ej

Viscous and Non-Newtonian Flows

The friction of a mesh-like super-hydrophobic surface

Anthony M. J. Davis and Eric Lauga

Phys. Fluids 21, 113101 (2009) (8 pages)

Online Publication Date: 3 November 2009

Full Text: PDF (200 kB)

Show Abstract
When a liquid droplet is located above a super-hydrophobic surface, it only barely touches the solid portion of the surface, and therefore slides very easily on it. More generally, super-hydrophobic surfaces have been shown to lead to significant reduction in viscous friction in the laminar regime, so it is of interest to quantify their effective slipping properties as a function of their geometric characteristics. Most previous studies considered flows bounded by arrays of either long grooves, or isolated solid pillars on an otherwise flat solid substrate, and for which therefore the surrounding air constitutes the continuous phase. Here we consider instead the case where the super-hydrophobic surface is made of isolated holes in an otherwise continuous no-slip surface, and specifically focus on the mesh-like geometry recently achieved experimentally. We present an analytical method to calculate the friction of such a surface in the case where the mesh is thin. The results for the effective slip length of the surface are computed, compared to simple estimates, and a practical fit is proposed displaying a logarithmic dependence on the area fraction of the solid surface.
Show PACS
47.55.D-, 66.20.-d, 46.55.+d

Optimal shapes for best draining

J. D. Sherwood

Phys. Fluids 21, 113102 (2009) (7 pages)

Online Publication Date: 4 November 2009

Full Text: PDF (215 kB)

Show Abstract
The container shape that minimizes the volume of draining fluid remaining on the walls of the container after it has been emptied from its base is determined. The film of draining fluid is assumed to wet the walls of the container, and is sufficiently thin so that its curvature may be neglected. Surface tension is ignored. The initial value problem for the thickness of a film of Newtonian fluid is studied, and is shown to lead asymptotically to a similarity solution. From this, and from equivalent solutions for power-law fluids, the volume of the residual film is determined. The optimal container shape is not far from hemispherical, to minimize the surface area, but has a conical base to promote draining. The optimal shape for an axisymmetric mixing vessel, with a hole at the center of its base for draining, is also optimal when inverted in the manner of a washed wine glass inverted and left to drain.
Show PACS
47.15.Rq

Particulate, Multiphase, and Granular Flows

A unified sweep-stick mechanism to explain particle clustering in two- and three-dimensional homogeneous, isotropic turbulence

S. W. Coleman and J. C. Vassilicos

Phys. Fluids 21, 113301 (2009) (10 pages)

Online Publication Date: 3 November 2009

Full Text: PDF (2365 kB)

Show Abstract
Our work focuses on the sweep-stick mechanism of particle clustering in turbulent flows introduced by Chen et al. [L. Chen, S. Goto, and J. C. Vassilicos, “Turbulent clustering of stagnation points and inertial particles,” J. Fluid Mech. 553, 143 (2006)] for two-dimensional (2D) inverse cascading homogeneous, isotropic turbulence (HIT), whereby heavy particles cluster in a way that mimics the clustering of zero-acceleration points. We extend this phenomenology to three-dimensional (3D) HIT, where it was previously reported that zero-acceleration points were extremely rare. Having obtained a unified mechanism we quantify the Stokes number dependency of the probability of the heavy particles to be at zero-acceleration points and show that in the inertial range of Stokes numbers, the sweep-stick mechanism is dominant over the conventionally proposed mechanism of heavy particles being centrifuged from high vorticity regions to high strain regions. Finally, having a clustering coincidence between particles and zero-acceleration points, both in 2D and 3D HIT, motivates us to demonstrate the sweep and stick parts of the mechanism in both dimensions. The sweeping of regions of low acceleration regions by the local fluid velocity in both flows is demonstrated by introducing a velocity of the acceleration field. Finally, the stick part is demonstrated by showing that heavy particles statistically move with the same velocity as zero-acceleration points, while moving away from any nonzero-acceleration region, irrespective of their Stokes number. These results explain the clustering of inertial particles given the clustering of zero-acceleration points.
Show PACS
47.27.-i, 47.11.-j

Multibubble cavitation inception

Masato Ida

Phys. Fluids 21, 113302 (2009) (13 pages)

Online Publication Date: 19 November 2009

Full Text: PDF (583 kB)

Show Abstract
The inception of cavitation in multibubble cases is studied numerically and theoretically to show that it is different from that in single-bubble cases in several aspects. Using a multibubble model based on the Rayleigh–Plesset equation with an acoustic interaction term, we confirmed that the recently reported suppression of cavitation inception due to the interaction of nonidentical bubbles can take place not only in liquid mercury but also in water, and we found that a relatively large bubble can significantly decrease the cavitation threshold pressure of a nearby small bubble. By examining in detail the transition region where the dynamics of the suppressed bubble changes drastically as the interbubble distance changes, we determined that the explosive expansion of a bubble under negative pressure can be interrupted and turn into collapse even though the far-field liquid pressure well exceeds the bubble's threshold pressure. Numerical results suggest that the interruption of expansion occurs when the bubble radius is exceeded by the instantaneous unstable equilibrium radius of the bubble determined using the total pressure acting on the bubble. When we extended the discussion to systems of larger numbers of bubbles, we found that a larger number of bubbles have a stronger suppression effect. The present findings would be useful in understanding the complex behavior of cavitation bubbles in practical applications where, in general, many cavitation nuclei exist and may interact with each other.
Show PACS
47.55.dp, 47.11.-j, 47.55.dd

Instability and Transition

Effect of electric field on the stability of an oscillatory contaminated film flow

Arghya Samanta

Phys. Fluids 21, 114101 (2009) (8 pages)

Online Publication Date: 3 November 2009

Full Text: PDF (423 kB)

Show Abstract
The stability of the viscous liquid film on an oscillating plane is investigated in the presence of both insoluble surfactant on the film surface and uniform electric field, acting normal to the plane. In this problem main motivation is to study the combine effect of surfactant and electric field on the stability of the liquid film. Here liquid is treated as a perfect conductor and the air above the liquid film is also treated as a perfect dielectric. The linear stability analysis is performed using the long-wave perturbation method based on Floquet theory. It is observed that two Floquet modes exist due to the presence of surfactant and both modes can be unstable. The growth rate corresponding to the Floquet modes increase with the presence of an electric field and decrease with the presence of surfactant.
Show PACS
47.20.Gv, 47.65.-d, 47.15.gm

Global mode analysis of axisymmetric bluff-body wakes: Stabilization by base bleed

E. Sanmiguel-Rojas, A. Sevilla, C. Martínez-Bazán, and J.-M. Chomaz

Phys. Fluids 21, 114102 (2009) (13 pages)

Online Publication Date: 6 November 2009

Full Text: PDF (1314 kB)

Show Abstract
The flow around a slender body with a blunt trailing edge is unstable in most situations of interest. Usually the flow instabilities are generated within the wake behind the bluff body, inducing fluctuating forces and introducing the possibility of resonance mechanisms with modes of the structure. Base bleed is a simple and well-known means of stabilizing the wake. In the present research, we investigate the global instability properties of the laminar-incompressible flow that develops behind a cylinder with sharp edges and axis aligned with the free stream using a spectral domain decomposition method. In particular, we describe the flow instability characteristics as a function of the Reynolds number, Re=rhoW[infinity]D/µ, and the bleed coefficient, defined as the bleed-to-free-stream velocity ratio, Cb=Wb/W[infinity], where D is the diameter of the body and rho and µ the density and viscosity of the free stream, respectively. For a truncated cylinder of aspect ratio L/D=5, where L is the length of the body, our calculations reveal the presence of a first steady bifurcation in the wake at Re~=391, as well as a second oscillatory one at Re~=715 with an associated Strouhal number St~=0.0905 for the most unstable azimuthal mode |m|=1. In addition, we report the existence of two critical values of the bleed coefficient C<sub>b1</sub><sup>*</sup>(Re,|m|) and C<sub>b2</sub><sup>*</sup>(Re,|m|)<C<sub>b1</sub><sup>*</sup>, which vary with the aspect ratio of the body, needed to stabilize both the first and second bifurcations in the range of Reynolds numbers under study, 0<=Re<=2200. Finally, the numerical results for the oscillatory mode obtained for a bulletlike body of aspect ratio L/D=2 without base bleed are compared with experiments performed in a wind tunnel using hot-wire anemometry, showing the limitations of using an axisymmetric basic flow at Reynolds numbers higher than the critical one corresponding to the first steady bifurcation in the global stability analysis.
Show PACS
47.15.Tr, 47.20.Ky, 47.27.wb

Small-amplitude perturbations in the three-dimensional cylindrical Richtmyer–Meshkov instability

M. Lombardini and D. I. Pullin

Phys. Fluids 21, 114103 (2009) (18 pages)

Online Publication Date: 6 November 2009

Full Text: PDF (1941 kB)

Show Abstract
We first study the linear stability of an interface between two fluids following the passage of an imploding or exploding shock wave. Assuming incompressible flow between the refracted waves following shock impact, we derive an expression for the asymptotic growth rate for a three-dimensional combination of azimuthal and axial perturbations as a function of the Atwood ratio, the axial and azimuthal wave numbers, the initial radial position and perturbation amplitude of the interface, and the interface velocity gain due to the shock interaction. From the linearized theory, a unified expression for the impulsive asymptotic growth rate in plane, cylindrical, and spherical geometries is obtained which clearly delineates the effects of perturbation growth due to both geometry and baroclinic vorticity deposition. Several different limit cases are investigated, allowing recovery of Mikaelian's purely azimuthal theory and Richtmyer's plane model. We discuss the existence of three-dimensional perturbations with zero growth, typical of curvilinear geometries, as first observed by Mikaelian. The effect of shock proximity on the interface growth rate is studied in the case of a reflected shock. Analytical predictions of the effect of the incident shock strength and the perturbation wave numbers are then compared with results obtained from highly resolved numerical simulations of cylindrical imploding Richtmyer–Meshkov instability for ideal gases. A parallel is made with the instability growth in spherical and plane geometry. In particular, we propose a representation of the perturbation growth by considering the volume of the perturbed layer. This volume is found to grow faster in the plane case than in the imploding cylindrical geometry, among other results.
Show PACS
47.20.-k, 47.40.Nm

Shock tube experiments and numerical simulation of the single-mode, three-dimensional Richtmyer–Meshkov instability

C. C. Long, V. V. Krivets, J. A. Greenough, and J. W. Jacobs

Phys. Fluids 21, 114104 (2009) (9 pages)

Online Publication Date: 16 November 2009

Full Text: PDF (610 kB)

Show Abstract
A vertical shock tube is used to perform experiments in which an interface is formed using opposed flows of air and SF6. A three-dimensional single-mode perturbation is created by the periodic vertical motion of the gases within the shock tube. Richtmyer–Meshkov instability is produced by an impulsive acceleration by a weak shock wave (Ms=1.2). Planar laser induced fluorescence produces still images, and planar Mie scattering produces movies of the experiment. A three-dimensional numerical simulation of this experiment utilizing the Eulerian adaptive mesh refinement code, RAPTOR, was also conducted. Good agreement is obtained between experiments and the simulations. However, existing late time models, which have a 1/t dependence, disagree with measurements of the late time instability development. In contrast, both the experiments and simulation suggest a t−0.54 late time dependence for the overall growth rate. Comparisons with individual bubble and spike velocities show the bubbles appear to decay approximately at 1/t and the spikes to decay at a much slower rate of t−0.38.
Show PACS
47.40.Nm, 47.80.Jk, 47.20.Ma

Continuous spectrum analysis of roughness-induced transient growth

N. A. Denissen and E. B. White

Phys. Fluids 21, 114105 (2009) (13 pages)

Online Publication Date: 18 November 2009

Full Text: PDF (474 kB)

Show Abstract
Continuous spectrum amplitude distributions are calculated for transiently growing roughness-induced perturbations in a flat-plate boundary layer. A direct method is employed when the complete flow is known via direct numerical simulation. A new method using regularizing functionals is developed for calculating the distributions when only partial experimental data are available. These amplitude distributions provide a way of rigorously characterizing the boundary layer receptivity to surface roughness. Contrasting the present results to optimal theory results conclusively demonstrates that roughness-induced disturbances cannot be described by optimal disturbance calculations. The continuous spectrum analysis demonstrates the linearity of the perturbations by correctly reproducing the flow evolution over the measurement domain. Extracting the continuous spectrum amplitudes using the partial data technique reveals the underlying vortex behavior that creates transient growth. The method described is amenable to future work with realistic distributed roughness and complex surface geometries.
Show PACS
47.27.ek, 47.11.-j, 47.32.-y, 47.27.nb, 02.60.-x

Turbulent Flows

The velocity spectra and turbulence length scale distributions in the near to intermediate regions of a round free turbulent jet

Hachimi Fellouah and Andrew Pollard

Phys. Fluids 21, 115101 (2009) (9 pages)

Online Publication Date: 9 November 2009

Full Text: PDF (897 kB)

Show Abstract
Stationary and flying single hot-wire measurements were made to investigate the near to intermediate field in a round free turbulent jet. Measurements were carried out at Reynolds numbers ReD based on the jet exit mean velocity and the nozzle diameter, between 6000 and 100 000. The objective of this study was to investigate the concept of a mixing transition proposed by Dimotakis [“The mixing transition in turbulent flows,” J. Fluid Mech. 409, 69 (2000)]. This was done through the measurement of the velocity spectra and the calculation of Kolmogorov lambdaK, Taylor microscale lambdaT, the Liepmann–Taylor microscale lambdaL, and the viscous length scale lambdanu at different positions in the near to intermediate regions of a round free jet. The present results demonstrate the local nature of mixing transition. It is found that the Kolmogorov, Taylor, and viscous length scales all decrease in magnitude with the local Reynolds number Redelta based on the local center line mean velocity and the local time-averaged diameter of the jet and appear to be only weakly dependent on the radial position, although the ratio ReT/Redelta1/2 varies nonlinearly across the jet radius. The ratio of the laminar to viscous length scale exceeds unity beyond the potential core of the jet. Moreover, the skewness of the axial velocity is approximately −0.4 over 30<ReT<400.
Show PACS
47.27.wg, 47.60.Kz, 47.27.nf, 47.27.-i, 47.80.-v, 66.20.-d

Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube

J. Znaien, Y. Hallez, F. Moisy, J. Magnaudet, J. P. Hulin, D. Salin, and E. J. Hinch

Phys. Fluids 21, 115102 (2009) (10 pages)

Online Publication Date: 9 November 2009

Full Text: PDF (478 kB)

Show Abstract
Buoyancy-driven turbulent mixing of fluids of slightly different densities [At=Deltarho/(2<rho>)=1.15×10−2] in a long circular tube tilted at an angle theta=15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|>~0.36  d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube.
Show PACS
47.27.nb, 47.27.wj, 47.60.Dx, 47.27.nf, 47.32.-y, 47.80.Cb, 66.20.-d

Study on the characteristics of turbulent drag-reducing channel flow by particle image velocimetry combining with proper orthogonal decomposition analysis

W.-H. Cai, F.-C. Li, H.-N. Zhang, X.-B. Li, B. Yu, J.-J. Wei, Y. Kawaguchi, and K. Hishida

Phys. Fluids 21, 115103 (2009) (12 pages)

Online Publication Date: 12 November 2009

Full Text: PDF (2112 kB)

Show Abstract
Turbulent drag reduction of 30 ppm cetyltrimethyl ammonium chloride (CTAC) solution flow in a channel was investigated with particle image velocimetry (PIV) combining with proper orthogonal decomposition (POD). Measurements were made at inlet fluid temperature of 304 K and at Reynolds number 2.5×104 (based on the channel height, bulk velocity, and solvent viscosity) for both water and CTAC solution flows with 70.0% drag reduction rate. The two-component velocity fields in the streamwise-wall normal plane were recorded by PIV. In order to study the characteristics of turbulent drag-reducing channel flow, POD was performed to identify the near-wall coherent structures based on PIV-measured data. POD is a powerful low-dimensional analysis tool that can be used to identify coherent structures embedded in the turbulent shear flow. We mainly studied a comparison between the first dominant POD eigenmodes of water and drag-reducing CTAC solution flows. Coherent structures were seen as the sum of several eigenmodes that possess a dominant energy of the flow, say 90%. It was obtained that the amount of eigenmodes required for capturing the coherent structures was 233 and 195 for water and CTAC solution flows, respectively, which means the decrease in the complexity in CTAC solution flow. Based on the analysis of POD eigenmodes of water and CTAC solution flows, we captured the processes that can reflect the ejection motion of low-speed fluid from the wall and sweep motion of high-speed fluid toward the wall associating with turbulent bursting events. The results showed that CTAC additives can inhibit the turbulent bursting processes (both strength and occurrence frequency), resulting in a great decrease in turbulent contribution to frictional drag and drag reduction, which is sufficient to understand deeply the mechanism of turbulent drag reduction.
Show PACS
47.27.nd, 47.60.Dx, 47.80.Cb

Scaling and correlation of vorticity fluctuations in turbulent channels

Ronald L. Panton

Phys. Fluids 21, 115104 (2009) (11 pages)

Online Publication Date: 17 November 2009

Full Text: PDF (1695 kB)

Show Abstract
Data from direct numerical simulations have been correlated to examine the effects of Reynolds number on vorticity fluctuation profiles. Three different scalings are found: two in the inner region and the third in the outer region. In the inner region a two-term asymptotic expansion is required to represent the mean square vorticity profiles; <omegaomega>#=<omegaomega><sub>0</sub><sup>#</sup>+<omegaomega><sub>1</sub><sup>+</sup>u*/U0. The first scaling <omegaomega><sub>0</sub><sup>#</sup>=<omegaomega>0/(u<sub>*</sub><sup>3</sup>U0/nu2) is for inactive motions that do not generate Reynolds shear stress. It applies to the streamwise and spanwise components. However, the zero-order term is zero for the normal vorticity component. The scrubbing of the inactive motions over the wall generates vorticity, which is a maximum at the wall, and diffuses out to about y+=50 before it decays. The fluctuating viscous wall shear stress is due entirely to this motion, and as a result the stress ratio (rms/mean) tau[prime]/tau0=Csqrt(U[sub 0]/u[sub *]) depends on the Reynolds number. The second scaling <omegaomega><sub>1</sub><sup>+</sup>=<omegaomega>1/(u<sub>*</sub><sup>4</sup>/nu2), the same scaling as the Reynolds shear stress, is active motions. All three components participate in these motions, which are zero at the wall, rise to a peak at about y+=13–20, and fall to zero at about y+=400. This is consistent with the fact that the Reynolds shear stress is identically zero at the wall. The third scaling correlates data in the outer region using the Kolmogorov time scale <omegaomega>/(u<sub>*</sub><sup>3</sup>/hnu). Matching between the inner and outer regions has a common part (the equivalent of the log law) of ~C/y+ or ~C/Y for all three components. All components decrease further and become isotropic as the centerline is approached. Scaling with the Kolmogorov scale implies that dissipation is the important activity. The correlated data are fitted to simplified equations that can be formed into composite expansions to predict profiles at any Reynolds number.
Show PACS
47.32.-y, 47.60.Dx, 47.27.nd, 47.11.-j, 47.27.ek

Inertial range scaling of the scalar flux spectrum in two-dimensional turbulence

W. J. T. Bos, B. Kadoch, K. Schneider, and J.-P. Bertoglio

Phys. Fluids 21, 115105 (2009) (8 pages)

Online Publication Date: 18 November 2009

Full Text: PDF (1051 kB)

Show Abstract
Two-dimensional statistically stationary isotropic turbulence with an imposed uniform scalar gradient is investigated. Dimensional arguments are presented to predict the inertial range scaling of the turbulent scalar flux spectrum in both the inverse cascade range and the enstrophy cascade range for small and unity Schmidt numbers. The scaling predictions are checked by direct numerical simulations and good agreement is observed.
Show PACS
47.27.Gs, 47.10.ad

Compressible Flows

Composite self-similar solutions for relativistic shocks: The transition to cold fluid temperatures

Margaret Pan and Re'em Sari

Phys. Fluids 21, 116101 (2009) (10 pages)

Online Publication Date: 13 November 2009

Full Text: PDF (263 kB)

Show Abstract
The flow resulting from a strong ultrarelativistic shock moving through a stellar envelope with a polytropelike density profile has been studied analytically and numerically at early times while the fluid temperature is relativistic—that is, just before and after the shock breaks out of the star. Such a flow should expand and accelerate as its internal energy is converted to bulk kinetic energy; at late enough times, the assumption of relativistic temperatures becomes invalid. Here we present a new self-similar solution for the postbreakout flow when the accelerating fluid has bulk kinetic Lorentz factors much larger than unity but is cooling through p/n of order unity to subrelativistic temperatures. This solution gives a relation between a fluid element's terminal Lorentz factor and that element's Lorentz factor just after it is shocked. Our numerical integrations agree well with the solution. While our solution assumes a planar flow, we show that corrections due to spherical geometry are important only for extremely fast ejecta originating in a region very close to the stellar surface. This region grows if the shock becomes relativistic deeper in the star.
Show PACS
52.27.Ny, 52.30.-q

Geophysical Flows

Tidal flow over three-dimensional topography in a stratified fluid

Benjamin King, H. P. Zhang, and Harry L. Swinney

Phys. Fluids 21, 116601 (2009) (10 pages)

Online Publication Date: 9 November 2009

Full Text: PDF (2365 kB)

Show Abstract
Our laboratory experiments and numerical simulations of stratified tidal flow past model topography (a half sphere on a horizontal plane) reveal several three-dimensional flow features, including an unexpected flow perpendicular to the forcing plane (the vertical plane through the center of the sphere, in the direction of the oscillating tide). This perpendicular flow has a time-independent component and a component oscillating at twice the tidal frequency. Our results show that the time-independent part of the perpendicular flow forms a large-scale horizontal circulation, which could enhance material transport and mixing near bottom topography in the oceans. In addition, for small forcing amplitude we find that the azimuthal dependence of the internal wave field is described by the functional form cos phi, as predicted by linear inviscid theory. At higher forcing amplitude, the internal wave energy is more concentrated in the forcing direction. Finally, we observe a wave intensity asymmetry in the polar direction and explain the asymmetry using a geometrical argument.
Show PACS
92.10.Hm, 45.70.Mg, 47.55.Hd, 47.11.-j, 47.35.-i, 47.85.-g

Inertial oscillations in a confined monopolar vortex subjected to background rotation

M. Duran-Matute, L. P. J. Kamp, R. R. Trieling, and G. J. F. van Heijst

Phys. Fluids 21, 116602 (2009) (13 pages)

Online Publication Date: 11 November 2009

Full Text: PDF (534 kB)

Show Abstract
We study the axisymmetric inertial oscillations in a confined monopolar vortex under the influence of background rotation. By first focusing on the inviscid linear dynamics, and later studying the effects of viscosity and of a no-slip bottom, we characterize the effects of rotation and confinement. It was found that background rotation allows for oscillations outside the vortex core even with frequencies larger than 2Omega, with Omega the background rotation rate. However, confinement is necessary for the system to sustain oscillations with frequencies smaller than 2Omega. Through the analytical solution for a small perturbation of a Rankine vortex, we obtain five regimes where the oscillations are qualitatively different, depending on their frequency. Numerical results for the linear inviscid waves sustained by a Lamb–Oseen vortex show a similar behavior. The effects of viscosity are twofold: the oscillations are damped and the vortex sustaining the oscillations is modified. When a no-slip bottom is considered, a boundary layer drives a secondary motion superimposed on the inertial oscillations. In this case, the vortex is quickly damped, but the oscillations persist due to the background rotation.
Show PACS
47.35.-i, 47.15.ki, 47.32.-y, 66.20.-d, 47.15.Cb

Von Kármán vortex streets on the sphere

George Chamoun, Eva Kanso, and Paul K. Newton

Phys. Fluids 21, 116603 (2009) (10 pages)

Online Publication Date: 20 November 2009

Full Text: PDF (433 kB)

Show Abstract
We consider streamline patterns associated with single and double von Kármán point vortex streets on the surface of a nonrotating sphere, with and without pole vortices. The full family of streamline patterns are identified and the topological bifurcations from one pattern to another are depicted as a function of latitude and pole strength. The process involves first finding appropriate vortex strengths so that the configuration forms a relative equilibrium, then calculating the angular rotation of the configuration about the center-of-vorticity vector. We move in a rotating frame of reference so that the configuration is fixed, identify the separatrices in the flowfield, and plot the global streamline patterns as a function of the pole strengths and latitudinal positions of the rings. We carry the procedure out for single and double von Kármán vortex streets, with and without pole vortices. The single von Kármán street configurations are comprised of n evenly spaced vortices on each of two rings that symmetrically straddle the equator and are skewed with respect to each other by half a wavelength, while the double von Kármán ring configurations are made up of four rings of n evenly spaced vortices symmetrically straddling the equator.
Show PACS
47.32.Ef

Others

Negatively buoyant starting jets

C. Marugán-Cruz, J. Rodríguez-Rodríguez, and C. Martínez-Bazán

Phys. Fluids 21, 117101 (2009) (14 pages)

Online Publication Date: 2 November 2009

Full Text: PDF (2024 kB)

Show Abstract
The initial development of negatively buoyant jets has been investigated experimentally and numerically, focusing on the role played by gravity in the evolution of the leading vortex ring. Under the experimental conditions considered in this work, the densimetric Froude number, Fr=rhojU<sub>j</sub><sup>2</sup>/[(rho0−rhoj)gD], which represents the ratio between the jet momentum and the buoyancy forces, emerges as the most relevant parameter characterizing the dynamics of the flow. Two different flow regimes have been observed depending on the Froude number: for sufficiently small Fr, the vortex ring generated initially is pushed radially away by gravity forces before it has time to detach from the shear layer originating at the orifice. On the other hand, when the Froude number is larger than a critical value, Fr>Frc~1, the vortex ring detaches from the injection orifice and propagates downstream into the stagnant ambient followed by a trailing jet until it eventually reaches a maximum penetration depth. In order to clarify the mechanisms leading to the transition between the two regimes, and to gain physical understanding of the formation dynamics of negatively buoyant starting jets, the total and the vortex circulation, as well as the trajectory of the vortex center, have been measured and compared to the case of neutrally buoyant jets. Finally, based on the experimental measurements and on the results of the numerical computations, a kinematic model that successfully describes the evolution of both total circulation and vortex trajectory is proposed.
Show PACS
47.15.Uv, 47.32.cf, 47.32.Ef, 47.11.-j
back to top

COMMENTS

FREE

Comment on “Heat transfer in vacuum packaged microelectromechanical system devices” [Phys. Fluids 20, 017103 (2008)]

Yoshio Sone

Phys. Fluids 21, 119101 (2009) (2 pages)

Online Publication Date: 18 November 2009

Full Text: PDF (50 kB)

Show Abstract
It is pointed out that the solution of a free molecular gas in a bounded domain proposed as speculation in Sec. II of Cai [Phys. Fluids 20, 017103 (2008)] and in Sec. II of Cai and Liu [Phys. Fluids 20, 067105 (2008)] and its result of the vanishing of flow velocity were rigorously derived under a more general situation and boundary condition more than 20 years ago.
Show PACS
47.27.te, 47.61.Fg

Copyright © American Institute of Physics