Volume 15, Issue 12, December 2003
 LETTERS


Selfinduced oscillations in the shock wave flow pattern formed in a stationary supersonic flow over a double wedge
View Description Hide DescriptionNumerical simulations of a twodimensional supersonic flow of an inviscid perfect gas over a double wedge in the Mach numbers range revealed the existence of selfinduced oscillations in the shock wave flow pattern in a narrow range of geometrical parameters.
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 ARTICLES


Direct numerical simulation of turbulent channel flow with wall velocity disturbances
View Description Hide DescriptionThis paper considers the effect of applying nonzero velocity fluctuations along a flat smooth wall, mainly with the aim of understanding how conditions at the wall interact with the outer turbulent flow. Such a study is expected to be of use in formulating effective strategies for wall turbulence control. Three direct numerical simulations of a turbulent plane channel flow are carried out, starting with a flow field with noslip conditions. Each simulation evolves by imposing (on one wall) only one nonzero velocity component. When a nonzero longitudinal velocity fluctuation is applied, drag reduction occurs. With a nonzero spanwise velocity fluctuation the flow is very similar to that in an unperturbed channel. However, the use of a nonzero wallnormal velocity fluctuation results in structural changes similar to those observed in a direct numerical simulation of a turbulent flow over a rough surface. From the present simplified simulations, the inference is that the salient characteristics of rough wall flows reflect mainly the presence of a nonzero wallnormal normal velocity distribution at the interface between the roughness cavities and the external flow.

Effect of collisions on the dispersed phase fluctuation in a dilute tube flow: Experimental and theoretical analysis
View Description Hide DescriptionMeasurements of particle fluctuation in a fully developed pipe flow at moderate Reynolds number is performed in this study. The present data are obtained by using a twocomponent phase Doppler anemometer. The radial profiles are measured at a distance of 0.2 diameter downstream the exit of the tube. At this location, the core flow still carries all the properties of the tube turbulence. A low mass loading of partly responsive particles is considered. The Stokes number of these partly responsive particles is of order 3 when the integral turbulent time scale on the axis of the tube flow is used. The velocity statistics are analyzed up to the thirdorder moments and we show that the radial turbulenttransport of fluctuating kinetic energy is much higher for the particles than for the fluid. Radial balances of longitudinal and radial kinetic stresses of the particles are examined. Particle–particle collisions have a negligible direct effect on the evolution of the longitudinal fluctuating velocity. However, even at this low mass loading, we prove that particle–particle collisions and redistribution from the very large streamwise velocity variance to the radial velocity variance in the near wall region strongly influence the radial fluctuation of the particles. In the core region, a quadrant analysis enables the detection of low streamwise velocities focusing toward the axis and the corresponding quadrants are strongly dominant for the glass beads. We expect that the partly responsive particles, because of their inertia, keep some memory of the lower streamwise velocity existing in the near wall region while they fly across the tube. The collisions in the near wall region are, therefore, expected to have a strong indirect influence on the whole kineticenergy balance in the tube by partly driving the radial transport of the fluctuating kinetic energy of the particles. This effect should be particularly strong in this circular geometry because events from any azimuthal directions converge in the central region.

Spectral analysis of localized disturbances in boundary layer at subcritical Reynolds numbers
View Description Hide DescriptionA flat plate boundary layer disturbance in the form of a streak is excited by a vortex of limited spanwise extent generated upstream of the plate leading edge. Frequencywave spectral analysis of the streamwise velocity component of the streak is performed. The most part of energy in the spectrum is contained in lowfrequency waves with the angles of their wave vector inclination to streamwise direction more than 85°. Spanwise wave numbers, peculiarities of amplitude growth, as well as streamwise velocity profiles of the most powerful spectral components of the streak are in a good agreement with known theoretical data on linear transient growth. However, behavior of the total energy of the streak is not corresponding to that of theoretical “optimal” transient structures. We suspect that, to make the theoretical results concerning the streak energy valid, details of the receptivity process must be taken into consideration. As the frequency grows, dispersioncharacteristics and decrements of the spectral components approach results of stability theory for Tollmien–Schlichting waves.

Stability of a sheared particle suspension
View Description Hide DescriptionA stability analysis is carried out for a gas–particle suspension in which the energy dissipation occurs due to the viscous drag force exerted on the particles. The flow is driven by two types of energy sources, an imposed mean shear and fluid velocity fluctuations, in the limit where the time between collisions is small compared to the viscousrelaxation time so that the dissipation of energy between collisions is small compared to the energy of a particle. Constitutive relations from the kinetic theory of dense gases are used when the flow is driven by the mean shear. The effect of fluid velocity fluctuations is incorporated using an additional diffusive term in the Boltzmann equation for the particle velocity distribution, and this leads to an additional “diffusion” stress. For a suspension driven by fluid velocity fluctuations, it is found that perturbations are always stable. For a suspension driven by mean shear, the viscousrelaxation time is large compared to the collision time for where is the mean strain rate. The rate of diffusion of energy is small compared to the rate of dissipation for where is the wave number scaled by the mean free path. In this regime, it is found that density perturbations are unstable in all three directions in the limit of low volume fraction, but become stable when the volume fraction is increased beyond a critical value. For the rate of diffusion of energy is large compared to the rate of dissipation, and it is found that perturbations are always stable. The transition between these two regimes is obtained numerically in the dilute limit, and the neutral stability curves for the density perturbations are obtained. It is found that in the gradientvorticity plane, the transition wave number is proportional to in the limit

Computing granular avalanches and landslides
View Description Hide DescriptionGeophysical mass flows—debris flows, volcanic avalanches, landslides—are often initiated by volcanic activity. These flows can contain or more of material, typically soil and rock fragments that might range from centimeters to meters in size, are typically deep, and can run out over distances of tens of kilometers. This vast range of scales, the rheology of the geological material under consideration, and the presence of interstitial fluid in the moving mass, all make for a complicated modeling and computing problem. Although we lack a full understanding of how mass flows are initiated, there is a growing body of computational and modeling research whose goal is to understand the flow processes, once the motion of a geologic mass of material is initiated. This paper describes one effort to develop a tool set for simulations of geophysical mass flows. We present a computing environment that incorporates topographical data in order to generate a numerical grid on which a parallel, adaptive mesh Godunov solver can simulate model systems of equations that contain no interstitial fluid. The computational solver is flexible, and can be changed to allow for more complex materialmodels, as warranted.

Global destabilization of flow over a backwardfacing step
View Description Hide DescriptionGlobal destabilization of twodimensional flow over a backwardfacing step embedded in a channel, i.e., flow in a plane channel with a sudden expansion, is investigated by numerical simulations using a spectral element method. In the low Reynolds number regime where the twodimensional flow is steady without manipulation, selfexcited oscillations of the entire flow are induced by appropriate simultaneous suction at the step face and blowing at the wall adjacent to the step. The boundary between steady and timedependent (destabilized) flow is determined as a function of the streamwise extent of the blowing region and its position relative to the step, for an expansion ratio of approximately two, a Reynolds number fixed at and equal suction and blowing mass flow rates. The computed periodic, globally synchronized flow regimes are characterized using instantaneous streamline patterns, time traces of physical quantities, and proper orthogonal decomposition of the velocity fields. The global flow behavior is also related to the absolute instability properties of the local streamwise velocity profiles. Preliminary threedimensional simulations finally suggest that the 2D unsteady flows obtained in the present study are, in general, susceptible to threedimensional secondary instabilities. Nevertheless, the first experiments suggest that the 2D analysis provides a qualitatively correct description of the flow transitions and that practical applications of this wallblowing and suction scheme, such as mixing enhancement, may be feasible.

Axisymmetric slosh frequencies of a liquid mass in a circular cylinder
View Description Hide DescriptionSpectraleigenvalue methods along with some lowerdimensional techniques are used to determine the natural frequencies of a liquid slug in a circular tube. The contact lines are either pinned or governed by a slip coefficient assumed small. Corresponding physical experiments are conducted for a borosilicate glass tube and a treated water slug. Gravitational and viscous effects are neglected for the analyses. The spectral results agree well with a simple spherical end cap approximation (zero dimensional) for large aspect ratio slugs and with a membrane approximation (one dimensional) for small aspect ratios. The experimental observations for different aspect ratios agree well with the predictions, although the gravity, viscosity and/or slip are neglected in the analyses.

Topographic effects on establishment of selective withdrawal
View Description Hide DescriptionThis study is concerned with evolution of selective withdrawal of a linearly stratified fluid through a line sink at the base of a reservoir with bottom topography in the form of a sill of small height. The problem is investigated theoretically in the linear, inviscid limit using a perturbation technique. The induced flow due to motion of the first few shear waves is studied. It is shown that the effect of a sill on the flow field is confined mostly to the withdrawal layer in the vicinity of the sill. Equations are proposed for the steady withdrawal layer thickness and the critical Froude number in the presence of a sill.

A multilevelbased dynamic approach for subgridscale modeling in largeeddy simulation
View Description Hide DescriptionIn this paper we present a new dynamic methodology to compute the value of the numerical coefficient present in numbers of subgrid models, by mean of a multilevel approach. It is based on the assumption of a power law for the spectral density of kinetic energy in the range of the highest resolved wave numbers. It is shown that this assumption also allows us to define an equivalent law for the subgrid dissipation, and to obtain a reliable estimation for it through the introduction of a threelevel flow decomposition. The model coefficient is then simply tuned dynamically during the simulation to ensure the proper amount of subgrid dissipation. This new dynamic procedure has been assessed here in inviscid homogeneous isotropic turbulence and plane channel flow simulations (with skinfriction Reynolds numbers up to 2000).

Schlieren measurements and analysis of concentration field in selfexcited helium jets
View Description Hide DescriptionA lowdensity gas jet injected into a highdensity ambient gas is known to exhibit selfexcited global oscillations accompanied by large vortical structures interacting with the flow field. In this study, the formation and evolution of vortices and scalar structure of the flow field are investigated in buoyant helium jets discharged from a vertical tube into quiescent air. This is accomplished by applying the quantitative rainbow schlieren deflectometry technique to optically measure the local helium mole percentage across the whole field. Data were acquired over downstream locations extending from tube exit to about or 19.1 mm is the jet tube inside diameter) at spatial resolution of 0.14 mm and temporal resolution of 16.7 ms. Oscillations at identical frequency were observed throughout the flow field. The evolving flow structure is described by helium mole percentage contours during an oscillation cycle. Instantaneous, mean, and rms concentration profiles are presented to describe interactions of the vortex with the jet flow. Oscillations in a narrow wake region near the jet exit are shown to spread through the jet core near the downstream location of the vortex formation. The effects of jet Richardson number on characteristics of vortex and flow field are investigated and discussed.

The evolution of corotating vortices in a canonical boundary layer with inclined jets
View Description Hide DescriptionThe evolution of corotating streamwise vortices in a canonical flat plate turbulent boundary layer (thickness of the boundary layer is studied. The vortices are produced by an array of inclined jets (diameter with the same orientation (skew angle β and pitch angle α of 45°). The focus of the investigation is on the immediate vicinity of the jet exit and downstream locations up to 40 D. The Reynolds number based on the diameter of the jet nozzle ranges from 9700 to 29 000, at various jet speed ratios. The main method of investigation is laser Doppler anemometry. Both mean and statistic data are collected and analyzed. The streamwise vortices are a product of complex fluid flow process, featuring horseshoe vortices in front of the nozzle exit, recirculating flow to the lee side of the nozzle, contrarotating vortices from the rolling up of vortex sheet around the jet, strong and induced spanwise flow. Two types of streamwise vortices are produced: (a) weak vortices at a jet speed ratio λ of 0.5 located close to the wall and featuring diametrically opposed, secondary, nearwall flows in between the vortices, (b) strong vortices at higher jet speed ratio featuring significant spanwise movement. The vortices are accompanied by high levels of turbulence, with distinct normal and shear stress distributions. Both turbulence production and convection play important roles in defining the normal stress but only the turbulence production is important in determining the shear stress.

Mean drift induced by free and forced dilational waves
View Description Hide DescriptionThe mean drift velocity induced by longitudinal dilational waves in an elastic film is studied theoretically on the basis of a Lagrangian description of motion. The film is horizontal and situated at the interface between two viscous fluids. For timedamped dilational waves we let the film (i) move freely with the mean fluid velocity at the interface, and (ii) be kept fixed, i.e., having no mean motion. In the latter case the mean Lagrangian drift velocity in both fluids becomes oppositely directed to the wave propagation direction after a very short time. This is due to the fact that a fixed film initially generates a strong source of negative Eulerian second order mean momentum at the interface. This effect becomes even more pronounced when we consider forced dilational waves in a fixed film. Now a suitably arranged shear stress in the upper fluid prevents wave amplitude decay in the film. Accordingly, the negative mean Eulerian momentum at the interface becomes independent of time, and the backward drift will propagate deeper and deeper into the lower fluid. For a noslip bottom at finite depth we may have a stationary drift solution with negative Lagrangian drift velocity everywhere in the fluid.

Polygonal vortex arrays: A Stuart model
View Description Hide DescriptionA class of exact planar solutions of the Euler equations representing stationary polygonal arrays of vortices are found. The solutions are parametrized by two parameters and denotes the number of vorticity extrema surrounding the origin; denotes the extremal value of this vorticity. Except for a point vortex at the origin, the solutions have everywheresmooth vorticity distributions and are generalizations of the classic exact solution of Stuart [J. Fluid Mech. 29, 417 (1967)] for an infinite row of smooth vortices. In the limit the solutions reduce to the pure point vortex problem considered by Morikawa and Swenson [Phys. Fluids 14, 1058 (1971)]. The new solutions can be understood as “smoothedout” counterparts to this point vortex problem.

Particle image velocimetry study on the pattern formation in a vertically vibrated granular bed
View Description Hide DescriptionIn this paper, a twodimensional particle image velocimetry(PIV)system was used to examine the stripe patternforming in a vertically vibrated granular layer. Since the PIV sampling frequency does not match with the vibrating frequency, a special identificationcoupling method was adopted to combine the images taken in different cycles to offer the information in one complete cycle. The measuredvelocity vectors showed exactly the particle motions at various stages of a motion cycle, illustrating the alternating peaks and valleys on the layer top. Furthermore, quantitative results on the temporal evolution of velocity profiles were obtained and some other interesting phenomena were observed, such as the appearance of local structures (e.g., dualphase layer structure) and the moving feature of the “standing point.” The mechanism accounting for the occurrence of stripes on the surface is discussed.

Vortexaccelerated secondary baroclinic vorticity deposition and lateintermediate time dynamics of a twodimensional Richtmyer–Meshkov interface
View Description Hide DescriptionWe study the vortexaccelerated secondary baroclinic vorticity deposition (VAVD) at lateintermediate times, and dynamics of sinusoidal singlemode Richtmyer–Meshkov interfaces in two dimensions. Euler simulations using a piecewise parabolic method are conducted for three postshock Atwood numbers 0.2, 0.635, and 0.9, with Mach number (M) of 1.3. We initialize the sinusoidal interface with a slightly “diffuse” or smallbutfinite thickness interfacial transition layer to facilitate comparison with experiment and avoid illposed phenomena associated with evolutions of an inviscid vortex sheet. The thickness of the interface is chosen so that there are no secondary structures along the interface prior to the multivalue time which is defined as the time when the extracted medial axis of an interfacial layer first becomes multivalued. For an interval of beyond the simulations reveal nearly monotonic strong growth of both positive and negative baroclinic circulation in a vortex bilayer pattern inside the complex rollup region. The circulations grow and secondary baroclinic circulation dominates at intermediate times, especially for higher This vorticity deposition is due to misalignment of density gradient across the interface and vortexcentripetal acceleration (secondary baroclinic), and enhanced by the intensification of interfacial density gradient arising from the vortexinduced strain. Our simulation results for agree with the recent air–sulfur hexafluoride experiment of Jacobs and Krivets [Proceedings of the 23rd International Symposium on Shock Waves, Fort Worth, Texas, (2001)], including several largescale features of the evolving mushroom structure: The usual interface spikebubble amplitude growth rate and the dimensions of the spike rollup cavity. VAVD plays an important role in the intermediate time dynamics of the interfaces. Our amplitude growth rate disagrees with the result of Sadot et al. [Phys. Rev. Lett. 80, 1654 (1998)]. Instead, it approaches a constant which increases with An adjusting periodic single point vortexmodel which uses the calculated net circulation magnitude and its location, gives excellent results for the amplitude growth rates to lateintermediate times at low Atwood numbers The evolution of enstrophy, vorticity skewness, and flatness are quantified for the entire run duration, and onedimensional averaged kineticenergy spectra are presented at several times.

Numerical analysis of thermalslip and diffusionslip flows of a binary mixture of hardsphere molecular gases
View Description Hide DescriptionThe thermalslip (thermalcreep) and the diffusionslip problems for a binary mixture of gases are investigated on the basis of the linearized Boltzmann equation for hardsphere molecules with the diffuse reflection boundary condition. The problems are analyzed numerically by the finitedifference method incorporated with the numerical kernel method, which was first proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)] for a singlecomponent gas. As a result, the behavior of the mixture is clarified accurately not only at the level of the macroscopic variables but also at the level of the velocity distribution function. In addition, accurate formulas of the thermalslip and the diffusionslip coefficients for arbitrary values of the concentration of a component gas are constructed by the use of the Chebyshev polynomial approximation.

Relative equilibria of singly periodic point vortex arrays
View Description Hide DescriptionThis paper presents a systematic investigation of singly periodic discrete vortex configurations that move uniformly without change of shape or size. The general condition for existence of such equilibria is that where is the net circulation within a single period and is (the complex conjugate of) the vortex velocity. Those configurations that satisfy this condition are determined for two and three vortices per period.

Vortexmerger statisticalmechanics model for the late time selfsimilar evolution of the Kelvin–Helmholtz instability
View Description Hide DescriptionThe nonlinear growth, of the multimode incompressible Kelvin–Helmholtz shear flow instability at all density ratios is treated by a largescale statisticalmechanics eddypairing model that is based on the behavior of a single eddy and on the two eddy pairing process. From the model, a linear time growth of the mixing zone is obtained and the linear growth coefficient is derived for several density ratios. Furthermore, the asymptotic eddy size distribution and the average eddy life time probability are calculated. Very good agreement with experimental results and full numerical simulations is achieved.

Effectiveness of a drag reducing polymer: Relation to molecular weight distribution and structuring
View Description Hide DescriptionSolutions of partially hydrolyzed polyacrylamide were degraded by intermittent circulation through a large pump in a turbulent flow loop. Measurements of pressure drop, fluid turbulence, molecular weight distribution, and viscosity were made. Rheooptical studies were also carried out to explore the propensity of solutions to form structures under simple shear flow. Degradation was not accompanied by significant changes in the molecular weight distributions. This observation suggests that, for the system studied, clusters or aggregates of polymers have a more important effect on the turbulence than individual molecules. Therefore, degradation occurs by the destruction of these clusters. This result is consistent with the observation that larger drag reductions are realized by the injection of concentrated polymer solutions into a water flow.
