Volume 14, Issue 7, July 2002
 ARTICLES


Mechanical imperfections effect on the minimum volume stability limit of liquid bridges
View Description Hide DescriptionThe bifurcation to unstable equilibrium shapes in the neighborhood of the minimum volume stability limit of liquid bridges has been described by using the Lyapunov–Schmidt technique. Prior to the bifurcation analysis, the stability limits of axisymmetric liquid bridges (both that of maximum and that of minimum volume) have been analytically calculated when the liquid bridge supports are two circular, coaxial disks. The interface shapes have been parametrically described and the parameters corresponding to the marginally stable shapes have been determined in terms of elliptic variables. Bifurcation equations have been obtained analytically describing the behavior near the critical points previously calculated and the effect of small axisymmetric imperfections has been considered. The considered imperfections are inequality in the diameter of the supporting disks, small body forces due to an axial gravity, and liquid bridge rotation as a solid body.

Dynamic wall modeling for largeeddy simulation of complex turbulent flows
View Description Hide DescriptionThe efficacy of largeeddy simulation(LES) with wall modeling for complex turbulent flows is assessed by considering turbulent boundarylayer flows past an asymmetric trailingedge. Wall models based on turbulent boundarylayer equations and their simpler variants are employed to compute the instantaneous wall shear stress, which is used as approximate boundary conditions for the LES. It is demonstrated that, as first noted by Cabot and Moin [Flow Turb. Combust. 63, 269 (2000)], when a Reynoldsaveraged Navier–Stokes type eddyviscosity is used in the walllayer equations with nonlinear convective terms, its value must be reduced to account for only the unresolved part of the Reynolds stress. A dynamically adjusted mixinglength eddyviscosity is used in the turbulent boundarylayer equationmodel, which is shown to be considerably more accurate than the simpler wall models based on the instantaneous log law. This method predicts loworder velocity statistics in good agreement with those from the full LES with resolved walllayers, at a small fraction of the original computational cost. In particular, the unsteady separation near the trailingedge is captured correctly, and the prediction of surface pressure fluctuations also shows promise.

Miscible displacements in capillary tubes: Influence of Korteweg stresses and divergence effects
View Description Hide DescriptionThe question is addressed as to whether Korteweg stresses and/or divergence effects can potentially account for discrepancies observed between conventional Stokes flow simulations (Chen and Meiburg) and experiments (Petitjeans and Maxworthy) for miscible flows in capillary tubes. An estimate of the vorticity and stream function fields induced by the Korteweg stresses is presented, which shows these stresses to result in the formation of a vortex ring structure near the tip of the concentration front. Through this mechanism the propagation velocity of the concentration front is reduced, in agreement with the experimental observations. Divergence effects, on the other hand, are seen to be very small, and they have a negligible influence on the tip velocity. As a result, we can conclude that they are not responsible for the discrepancies between experiments and conventional Stokes simulations.

Thermomagnetic convection of magnetic fluids in a cylindrical geometry
View Description Hide DescriptionThe thermomagnetic convection of magnetic fluids in a cylindrical geometry subjected to a homogeneous magnetic field is studied. The study is motivated by a novel thermal instability [W. Luo et al., Phys. Rev. Lett. 82, 4134 (1999)]. As model system a composite cylinder with inner heating is considered which reflects the symmetry of the experimentally setup. The general condition for the existence of a potentially unstable stratification in the magnetic fluid is derived. Within a linear stability analysis the critical external induction for the onset of thermomagnetic convection is determined for dilute and nondilute magnetic fluids. The difference between both thresholds allows to test experimentally whether a test sample is a dilute fluid or not.

Some characteristics of entrainment at a cylindrical turbulence boundary
View Description Hide DescriptionOver the last 30 years, turbulent entrainment has come to be viewed as a largescale process, directed by coherent structures, and described as engulfing. With turbulence simulations, we examined the process of entrainment directly, as growth of vorticity and concentration along fluid particle pathlines which were computed simultaneously. Our results indicate that the process is more often small scale. Growth occurs close to the turbulence boundary, within small radial displacements, and in times which are smaller than local largescale times. These observations can be cast into a model to show that overall rates can be predicted by largescale quantities even though the process occurs at small scales; the only requirement is a fixed relationship across scales as in fully developed turbulent flows. So it is not inconsistent that engulfment can be a successful, and accepted, model for fully developed flows even if it is not the more frequent process.

Optimal rotary control of the cylinder wake in the laminar regime
View Description Hide DescriptionIn this paper we develop the Optimal Control Approach to the rotary control of the cylinder wake. We minimize the functional which represents the sum of the work needed to resist the drag force and the work needed to control the flow, where the rotation rate is the control variable. Sensitivity of the functional to control is determined using the adjoint equations. We solve them in the “vorticity” form, which is a novel approach and leads to computational advantages. Simulations performed at and reveal systematic decrease of the total power and drag achieved using a very small amount of control effort. We investigate the effect of the optimization horizon on the performance of the algorithm and the correlation of the optimal controls with the changes of the flow pattern. The algorithm was also applied to the control of the subcritical flow at however, no drag reduction was achieved in this case. Based on this, limits of the performance of the algorithm are discussed.

Numerical investigations of smallamplitude disturbances in a boundary layer with impinging shock wave at
View Description Hide DescriptionThe stability behavior of a laminar boundary layer with shock boundary layerinteraction and small amplitude disturbances is investigated by linear stabilitytheory and direct numerical simulation. By a complex interaction of several physical properties, the impinging shock wave locally influences stability behavior of the boundary layer, dependent on its shock strength, applied disturbance frequency, and disturbance propagation angle with respect to the flow direction (obliqueness angle). Due to the displacement of the boundary layer near shock impingement and the according Reynolds numbereffect in this area, the boundary layer is locally destabilized. The displacement of the boundary layer also produces an increase of the thickness of local regions of relative supersonic speed, which promotes second mode instability. For the results obtained by direct numerical simulation nonparallel effects could be identified and quantified. Taking these nonparallel effects into account, linear stabilitytheory is able to represent the stability behavior of wall distant disturbance amplitude maxima having small obliqueness angles for the cases investigated here. For larger obliqueness angles and disturbance amplitudes at or close to the wall the agreement between linear stabilitytheory and direct numerical simulation declines considerably.

The effect of weak inertia on the emptying of a tube
View Description Hide DescriptionWe present an extension of the classical axisymmetric Bretherton theory giving the thickness of the liquid film left on the walls of a drained tube, treating the case of weak inertia by a regular perturbation method. The results obtained by numerical integration fit Taylor’s [J. Fluid Mech. 10, 161 (1961)] experiments, obtained with viscous fluids (glycerine and strong sucrose solutions), and Aussillous and Quéré’s [Phys. Fluids 12, 2367 (2000)] experiments with low viscosity liquids (hexamethyldisiloxane and water) when inertia becomes important. The discrepancies observed between the theory and high Reynolds numbers experiments (Re>1000) are commented on.

On the phase velocity effect of nonlinear interactions between surface gravity waves
View Description Hide DescriptionThe change of phase velocity of a train of surface gravity waves due to nonlinear interaction with another train of surface gravity waves is investigated. Three different expressions for the change of phase velocity have been derived from Zakharovtype equations, and it is confirmed that all these expressions are equivalent with each other, as well as with the classical result of LonguetHiggins and Phillips. The theory for the interaction between two wave trains is also extended naively to that among component waves in a continuous energy spectrum, and the validity of this extension is assessed by comparing with direct numerical simulations based on the primitive equations.

Unsteady mixed convection in a horizontal channel with protruding heated blocks and a rectangular vortex promoter
View Description Hide DescriptionThe objective of this research is to study the resonance oscillatory flow in a channel and the resulting effect on thermal transport, leading to cooling enhancement in electronic systems. The unsteady mixed convection through a horizontal channel with two isolated protruding blocks on the bottom wall has been studied numerically. For this geometry, at moderate Reynolds numbers, the flow is found to separate at the leading edge of the first block, and then reattach at the top surface of the second block. At a given Grashof number, when Re exceeds a critical value, vortex is shed only from the second block, and rolls over the bottom wall with its size decaying, while one or two recirculating cells are trapped in the groove. The base vortex shedding frequency is dependent on the buoyancy level The critical value of Re is much lower when perturbation is introduced by a rectangular or square promoter in the channel. The frequency and amplitude of perturbation are changed by adjusting the geometry of the promoter. An improved fluid exchange between the main flow and the recirculating cell occurs when the promoter is employed. The effects of frequency and perturbation amplitude on the flow and on the heat transfer are investigated. The study consists of three parts. The first studies the developing flow in the grooved channel; the second investigates the vortex shedding from a rectangular promoter confined in a smooth channel; and the last studies the effect of resonance by tuning the frequency of vortex shedding.

Simultaneous measurements of all three components of velocity and vorticity vectors in a lobed jet flow by means of dualplane stereoscopic particle image velocimetry
View Description Hide DescriptionResults from an advanced particle imagevelocimetry(PIV) technique, named as dualplane stereoscopic PIV technique, for making simultaneous measurements of all three components of velocity and vorticity vectors are presented for a lobed jet flow. The dualplane stereoscopic PIV technique uses polarization conservation characteristic of Mie scattering to achieve simultaneous stereoscopic PIVmeasurements at two spatially separated planes. Unlike “classical” PIV systems or conventional stereoscopic PIV systems, which can only get one component of vorticity vectors, the present dualplane stereoscopic PIV system can provide all three components of velocity and vorticity distributions in fluid flows instantaneously and simultaneously. The evolution and interaction characteristics of the largescale streamwise vortices and azimuthal Kelvin–Helmholtz vortices in the lobed jet flow are revealed very clearly and quantitatively from the simultaneous measurement results of the dualplane stereoscopic PIV system. A discussion about the satisfaction of the measurement results of the present dualplane stereoscopic PIV system to mass conservation equation is also conducted in the present paper to evaluate the error levels of the measurement results.

Statistical mechanics of strong and weak point vortices in a cylinder
View Description Hide DescriptionThe motion of 100 point vortices in a circular cylinder is simulated numerically and compared with theoretical predictions based on statistical mechanics. The novel aspect considered here is that the vortices have greatly different circulation strengths. Specifically, there are 4 strong vortices and 96 weak vortices, the net circulation in either group is zero, and the strong circulations are five times larger than the weak circulations. As envisaged by Onsager [Nuovo Cimento, Suppl. 6, 279 (1949)], such an arrangement leads to a substantial amplification of statistical trends such as the preferred clustering of the strong vortices in either samesigned or oppositely signed pairs, depending on the overall energy level. To prepare the ground, this behavior is illustrated here first by a simple toy model with exactly solvable statistics. A microcanonical ensemble based on the conserved total energy E and angular momentumM for the whole vortex system is then used, in which the few strong vortices are treated as a subsystem in contact with a reservoir composed of the many weak vortices. It is shown that allowing for the finite size of this reservoir is essential in order to predict the statistics of the strong vortices accurately. Notably, this goes beyond the standard canonical ensemble with positive or negative temperature. A certain approximation is then shown to allow a single random sample of uniformly distributed vortex configurations to be used to predict the strong vortex statistics for all possible values of E and M. Detailed predictions for the energy, twovortex, and radial distribution functions of the strong vortices are then made for comparison with three simulated cases of nearzero M and low, neutral, or high E. It is found that the statistical mechanics predictions compare remarkably well with the numerical results, including a prediction of vortex accumulation at the cylinder wall for low values of E.

Selforganization of quasitwodimensional turbulence in stratified fluids in square and circular containers
View Description Hide DescriptionLaboratory experiments on decaying quasi2D (twodimensional) turbulence have been performed in stratified fluids in both square and circular containers. The turbulence was generated by towing an array of vertical cylinders through the container, which was filled with either a twolayer or a linearly stratified fluid. By varying the grid configuration a different amount of angular momentum could be added to the initial flow. The evolution of the flow was visualized by 2D particle tracking velocimetry. The observed decay scenario has been investigated with emphasis on the evolution of the kinetic energy and the enstrophy of the horizontal flow, vortex statistics and the angular momentum of the flow. In particular it is shown that the experiments in both the square and the circular container support the observations from numerical simulations of decaying 2D turbulence in bounded domains with noslip walls. Two striking examples are the experimental observation of the spontaneous spinup phenomenon (in the squarecontainer experiments) and the confirmation that the angular momentum of the flow in the circularcontainer experiment is better conserved than the total kinetic energy of the flow. The role of the initial nonzero net angular momentum on the decay of quasi2D turbulence is investigated for both geometries and indications for an acceleration of the selforganization process are presented.

Conditionally filtered scalar dissipation, scalar diffusion, and velocity in a turbulent jet
View Description Hide DescriptionConditionally filtered conserved scalar (temperature) dissipation (CFD),diffusion, and conditionally filtered velocity are studied experimentally in the fully developed region of a turbulent jet with a jet Reynolds number of 40 000. These variables are the unclosed terms in the transport equation of the conserved scalar filtered density function. Onedimensional box filters of widths Δ ranging from 30 to 496 scalar dissipation scales as well as a twodimensional box filter which consists of three discrete sensors are used to obtain filtered variables. Taylor’s hypothesis is used to perform the streamwise filtering. The means of these conditionally filtered variables conditional on the resolvablescale scalar fluctuations and the subgridscale (SGS) variance indicate two regimes of the SGS scalar mixing. For large SGS variance the SGS scalar exhibits similarities to scalars in initially binary mixing at early times, suggesting existence of diffusionlayerlike structure and nonequilibrium SGS scalar. The nonequilibrium is further evidenced by the observed large SGS mechanicaltoscalar time scale ratio and large SGS variance productiontodissipation ratio. These characteristics have not been previously observed in fully developed flows. For small SGS variance the conditionally filtered variables indicate wellmixed SGS scalar. The results also show that the SGS advection is only significant at large SGS variance. Our measurements also suggest that the dependence of the scalar dissipation (and the filtered dissipation) on largescale scalar fluctuations is caused primarily by the fluctuations in the spectral transfer and that the conditional CFD is directly affected mostly by scales near the filter scale. The present study suggests that the nonequilibrium effects related to sheetlike structures are important for modeling the conditionally filtered variables.

Effects of subgridscale modeling on time correlations in large eddy simulation
View Description Hide DescriptionThe effects of the unresolved subgridscale (SGS) motions on the energy balance of the resolved scales in large eddy simulation(LES) have been investigated actively because modeling the energy transfer between the resolved and unresolved scales is crucial to constructing accurate SGS models. But the subgrid scales not only modify the energy balance, they also contribute to temporal decorrelation of the resolved scales. The importance of this effect in applications including the predictability problem and the evaluation of sound radiation by turbulent flows motivates the present study of the effect of SGS modeling on turbulent time correlations. This paper compares the twopoint, twotime Eulerian velocity correlation in isotropic homogeneous turbulence evaluated by direct numerical simulation (DNS) with the correlations evaluated by LES using a standard spectral eddy viscosity. It proves convenient to express the twopoint correlations in terms of spatial Fourier decomposition of the velocity field. The LES fields are more coherent than the DNS fields: their time correlations decay more slowly at all resolved scales of motion and both their integral scales and microscales are larger than those of the DNS field. Filtering alone is not responsible for this effect: in the Fourier representation, the time correlations of the filtered DNS field are identical to those of the DNS field itself. The possibility of modeling the decorrelating effects of the unresolved scales of motion by including a random force in the model is briefly discussed. The results could have applications to the problem of computing sound sources in isotropic homogeneous turbulence by LES.

Measurement of an unexpectedly large shearinduced selfdiffusivity in a dilute suspension of spheres
View Description Hide DescriptionWe report the measurement of unexpectedly large shearinduced diffusivities for various sized tracers in a dilute suspension of noncolloidal spheres in simple shear. The suspension was sheared in a narrow gap Couette device at low Reynolds number, and the tracer diffusivities parallel to the velocity gradient D were obtained using an orbittime technique. It is shown that the presence of even a dilute concentration φ of particles renders an otherwise smooth tracer trajectory strongly stochastic and the resulting diffusivity is linear in φ in this limit, indicating irreversible displacements at the pair interaction level. The measured values of the diffusivity, however, are at least an order of magnitude larger than that predicted by current theories. In a previous study, Beimfohr et al. [Proc. DOE/NSF Workshop, Ithaca, NY (1993)] likewise obtained values for D larger than that predicted by theory, but the discrepancy was attributed to the large eccentricity (average aspect of the particles used. In the present study, very nearly spherical ground acrylic particles were used, yet diffusivities of the same order of magnitude as that obtained by Beimfohr et al. were measured. Various possible causes for this anomalous diffusivity were explored and tested in the course of our investigation, including the effect of inertial lift and possible nonNewtonian properties of the base fluid, but none proved sufficiently large to account for the observed behavior.

Transient coating flow of a thin nonNewtonian fluid film
View Description Hide DescriptionThe interplay between nonNewtonian effects, gravity, and substrate topography is examined in this theoretical study for the transient twodimensional flow of a thin nonNewtonian film. The study is a continuation of the previous work by Khayat and Welke [Phys. Fluids 13, 355 (2001)], which focused on the influence of inertia on a Newtonian film. The fluid emerges from a channel and is driven by a pressure gradient maintained inside the channel. The substrate is assumed to be stationary and of arbitrary shape. The flow is dictated by the thinfilmequations of the “boundary layer” type, which are solved by expanding the flow field in terms of orthonormal modes in the transverse direction and using the Galerkin projection, combined with a timestepping implicit scheme, and integration along the flow direction. Gravity and substrate topography can have a significant effect on transient behavior, but this effect varies significantly, depending on whether the fluid is Newtonian, shear thinning or shear thickening. Wave formation and propagation, as well as steady film flow are examined. It is found that shearthickening fluids tend to accumulate near the channel exit, exhibiting a standing wave that grows with time. This behavior clearly illustrates the difficulty faced with coating shearthickening fluids at any level of inertia. The influence of the substrate topography has been explored in the case of undulated substrate.

Shape stability of unsteadily translating bubbles
View Description Hide DescriptionIn this paper the problem of shape stability is considered, for a bubble with timedependent radius, translating unsteadily in a flow. This situation can be brought about, for example, by forcing with an acoustic traveling wave. The equation governing translation was derived in a previous work [Reddy and Szeri (unpublished)]. Here, the equations governing the amplitudes of shape modes are derived using domain perturbation theory, following a classical paper by Plesset. Contrary perhaps to intuition, results show that driving at the natural frequency of volume oscillations is not necessarily the ideal forcing to engender a shape instability. Moreover, severe radial oscillations can have a stabilizing effect on shape oscillations. The results suggest the possibility of destroying bubbles selectively by size.

Fourthorder nonlinear evolution equations for counterpropagating capillarygravity wave packets on the surface of water of infinite depth
View Description Hide DescriptionAsymptotically exact nonlocal fourthorder nonlinear evolution equations are derived for two counterpropagating capillarygravity wave packets on the surface of water of infinite depth. On the basis of these equations a stability analysis is made for a uniform standing capillarygravity wave for longitudinal perturbation. The instability conditions and an expression for the maximum growth rate of instability are obtained. Significant deviations are noticed between the results obtained from thirdorder and fourthorder nonlinear evolution equations.

Ergodic theory and experimental visualization of invariant sets in chaotically advected flows
View Description Hide DescriptionWe analyze a recently proposed experimental technique for constructing Poincaré maps in flows exhibiting chaotic advection and develop the theoretical framework that explains the reasons for the success of this approach. The technique is nonintrusive and, thus, simple to implement. Planar laserinduced fluorescence is employed to collect a sufficiently long sequence of instantaneous light intensity fields on the plane of section of the Poincaré map (defined by the laser sheet). The invariant sets of the flow are visualized by timeaveraging the instantaneous images and plotting isocontours of the so resulting mean light intensity field. By linking the Eulerian time averages of light intensity at fixed points in space with the Lagrangian time averages along particle paths passing through these points, we show that ergodic theory concepts can be used to show that this procedure will indeed visualize invariant sets of the Poincaré map. As the technique is based on timeaveraging, we discuss the rates of convergence and show that inside regular islands the convergence is fast. An example is presented from the application of this technique to visualize the intricate web of regular islands within a steady, threedimensional vortex breakdown bubble.
