Index of content:
Volume 9, Issue 12, December 1997

Inverse modeling for largeeddy simulation
View Description Hide DescriptionApproximate higher order polynomial inversion of the tophat filter is developed with which the turbulent stress tensor in largeeddy simulation can be consistently represented using the filtered field. Generalized (mixed) similarity models are proposed which improved the agreement with the kinetic energy transfer to small scales. These similarity models are analyzed for random periodic signals and the ensemble averaged spectra of the turbulent stress tensor and the corresponding models are compared.

Viscosity scaling in suspensions of nonBrownian rodlike particles
View Description Hide DescriptionA systematic experimental study of the settling of a spherical ball in a fiber suspension for different particle aspect ratios and a wide range of volume concentrations is presented. The situation where the ball size is much greater than the fiber length is considered. First, it has been observed that, even at very low concentration, the flow induced by the sphere drastically modifies the orientation distribution of the particles. It was found that, in the dilute and semidilute regime, the viscosity inferred from the sphere falling velocity scales with the excluded volume and compares well with existing shear measurements. Moreover, the viscosity was found to be almost independent of the initial orientation distribution of the fibers, indicating that the rheological response of the suspension was dominated by the configuration induced by the sphere displacement.

Symmetry and reversibility in mixing fluids
View Description Hide DescriptionA notion of reversibility in misciblefluid flow, that does not depend on the amount of molecular diffusion, is introduced. This notion relies on a reciprocity relation for hydrodynamicdispersion which is derived and discussed. Using these results, an experimental technique for the measurement of hydrodynamic reversibility is investigated by means of numerical simulations employing a lattice Boltzmannmodel. Results demonstrate the sensitivity of the technique as well as potential biological applications.

Radial segregation of granular mixtures in rotating cylinders
View Description Hide DescriptionSimultaneous mixing and segregation of granular materials is of considerable practical importance; the interplay among both processes is, however, poorly understood from a fundamental viewpoint. The focus of this work is radial segregation—core formation—due to density in a rotating cylinder. The flow regime considered is the cascading or continuous flow regime where a thin layer of solids flows along a nearly flat free surface, while the remaining particles rotate as a fixed bed along with the cylinder. The essence of the formation of a central segregated core of the more dense particles lies in the flow,mixing, and segregation in the cascading layer. The work involves experiments and analysis. A constitutive model for the segregation flux in cascading layers is proposed and validated by particle dynamics and Monte Carlo simulations for steady flow down an inclined plane. The model contains a single parameter, the dimensionless segregation velocity (β), which is treated as a fitting parameter here. Experimental results for the equilibrium segregation of steel balls and glass beads are presented for different fractions and different extents of filling. There is a good match between theoretical predictions and all experimental results when the value of dimensionless segregation velocity is taken to be β=2. The extent of segregation is found to increase with increase in the dimensionless segregation velocity and dimensionless diffusivity but is independent of the level of filling. Lagrangian simulations based on the theory and experiments demonstrate the competition between segregation and mixing. In the case of slow mixing, the intensity of segregation monotonically decreases to an equilibrium value; for fast mixing, however, there exists an optimal mixing time at which the best mixing is obtained.

Convection related phenomena in granular dynamics simulations of vibrated beds
View Description Hide DescriptionThreedimensional discrete element simulations are carried out to investigate the behavior of a shallow bed of inelastic, frictional spheres (of uniform diameter ), which are energized by vertical sinusoidal oscillations of a plane floor at amplitude and frequency We investigate the longterm and instantaneous velocity fields as well as the evolution of the pressuretensor. Results show that the onset of convection reported in the literature is not only determined by the floor acceleration, but also the ratio In a wide bed narrow persistent vortices appear near vertical sidewalls, while no distinct pattern is found within the central region. A large sphere within the bed is convected upward to the surface and either “segregates” itself from the bulk, or becomes reentrained, depending on the width of the downward velocity field near the wall relative to the sphere size. An inspection of the bed microstructure reveals internal vortexlike cells spanning its width giving rise to arching observed in recent experiments and other simulations. Computations of the potential constituent of the pressuretensor revealed high values in collisiondominated regions of the bed and a trend that repeated every two oscillations of the floor.

Timedependent equations governing the shape of a twodimensional liquid curtain, Part 1: Theory
View Description Hide DescriptionApproximate equations have been derived that govern the timedependent response of a twodimensional liquid curtain falling under the influence of gravity and subjected to ambient pressure disturbances. Starting with the assumptions of potential flow and constant surface tension, and using the approximation that the curtain is long and thin, a steadystate base flow is first determined. In agreement with previous literature results, the analysis reveals that the curtain flow is essentially in free fall, where the velocity profile is only slightly curved across the curtain thickness. Then, by assuming that the disturbances to the curtain are small, the timedependent equations are linearized about the approximated base flow. The approximate nature of the base flow necessitates a careful ordering of terms to assure that the linearization is valid. Two equations governing the curtain shape are derived: the first governs the deflection of the curtain centerline, and the second governs the thickness variations. Previous literature results regarding wave propagation and steady curtain deflections can be predicted via the derived equations. It is also found that to lowest order, pressure disturbances induce a deflection of the curtain centerline while preserving the local thickness associated with the undisturbed curtain.

Timedependent equations governing the shape of a twodimensional liquid curtain, Part 2: Experiment
View Description Hide DescriptionIn Part I of this paper, two governing equations have been derived that describe the shape of a falling liquid sheet (a curtain) subjected to ambient pressure disturbances. These equations are termed varicose and sinuous. The varicose equation governs thickness variations in the curtain, for which the two air–liquid interfaces move exactly out of phase. The sinuous equation governs the deflection of the curtain centreline, i.e., the two air–liquid interfaces move in phase such that the local thickness of the liquid is preserved. To the order of the approximations used, the theory presented in Part 1 indicates that pressure disturbances invoke a sinuous curtain deflection with no varicose contribution. In Part 2 of this paper, the sinuous equation is verified by means of a localised pressure disturbance induced by an electrostatic field. After initiation, the propagation of this disturbance is followed and the shape of the air liquid interface is measured using a laser reflection technique. Both the generation and detection of the disturbance are noncontacting and therefore allow a precise verification of the equation.

Linear stability analysis of an insoluble surfactant monolayer spreading on a thin liquid film
View Description Hide DescriptionRecent experiments by several groups have uncovered a novel fingering instability in the spreading of surface active material on a thin liquid film. The mechanism responsible for this instability is yet to be determined. In an effort to understand this phenomenon and isolate a possible mechanism, we have investigated the linear stability of a coupled set of equations describing the Marangoni spreading of a surfactantmonolayer on a thin liquid support. The unperturbed flows, which exhibit simple linear behavior in the film thickness and surfactant concentration, are selfsimilar solutions of the first kind for spreading in a rectilinear geometry. The solution of the disturbance equations determines that the rectilinear base flows are linearly stable. An energy analysis reveals why these base flows can successfully heal perturbations of all wavenumbers. The details of this analysis suggest, however, a mechanism by which the spreading can be destabilized. We propose how the inclusion of additional forces acting on the surfactant coated spreading film might give rise to regions of adverse mobility gradients known to produce fingering instabilities in other fluid flows.

Drop formation from a vibrating orifice generator driven by modulated electrical signals
View Description Hide DescriptionThe recently introduced technique of amplitudemodulated (AM) excitation of laminar liquid jets to produce drops by controlled Rayleightype jet disintegration is extended to frequency modulation(FM) and investigated in detail to quantify the available ranges of excitation wavenumbers and modulation depths for various jet velocities and liquids. The AM and FM techniques are compared regarding the achievable ratios of carrier and modulation frequencies. The modulated excitation is applied to a vibrating orifice drop generator (TSI Inc.). Four different drop formation processes are observed for different wavenumber domains. Experiments with three different Newtonian liquids and a dimensional analysis yield a generalized representation of the parameter windows of the technique in terms of excitation wavenumber and jet velocity for a wide range of liquidviscosity and surface tension.

On binary impacts of small liquidfilled shells
View Description Hide DescriptionWe report the peculiar impact properties of small spherical shells filled with a viscousliquid. Upon collisions of two identical liquidfilled shells, the fluid is progressively set in rotation by the shell spin induced by tangential impact forces. An analysis of the corresponding fluid motion predicts a collision outcome unlike that of solid spheres where angular velocity is uniform. Observations of colliding vitaminE pills reveal that the point of contact is rarely involved in gross slip. In the direction of the line of centers, collisions are adequately described by a kinematic restitution coefficient. In the perpendicular direction, they generally exhibit rolling contact.

Twophase flow structure of sheet cavitation
View Description Hide DescriptionAn experimental study of flow within sheetcavities is performed in a cavitation tunnel equipped with a Venturitype test section. The flow is investigated by means of a double optical probe allowing void fraction, velocity, and chord length of the vapor structures to be measured. Laser velocimetery, wall pressure measurements, and visualization techniques are also used to characterize the liquid flow around the cavity. The consistency of the experimental results was checked though mass and momentum balances. The effects of Reynolds and cavitation numbers are analyzed. Special attention is given to the dynamic behavior of the flow, and to the vapor flow rate within the cavities. The measurements show a complex twophase flow characterized by the presence of an extended reversed flow occurring along the solid surface and a regular decrease in void fraction along the cavity. The phase transitions seem to be mainly restricted by the dynamic of the bubbles and thermodynamic effects.

Hydrodynamic stability of flow between rotating porous cylinders with radial and axial flow
View Description Hide DescriptionA linear stabilityanalysis was carried out for axial flow between a rotating porous inner cylinder and a concentric, stationary, porous outer cylinder when radial flow is present for several radius ratios. The radial Reynolds number, based on the radial velocity at the inner cylinder and the inner radius, was varied from to 15, and the axial Reynolds number based on the mean axial velocity and the annular gap was varied from 0 to 10. Linear stabilityanalysis for axisymmetric perturbations results in an eigenvalue problem that was solved using a numerical technique based on the Runge–Kutta method combined with a shooting procedure. At a given radius ratio, the critical Taylor number at which Taylor vortices first appear for radial outflow decreases slightly for small positive radial Reynolds numbers and then increases as the radial Reynolds number becomes more positive. For radial inflow, the critical Taylor number increases as the radial Reynolds number becomes more negative. For a given radial Reynolds number, increasing the axial Reynolds number increases the critical Taylor number for transition very slightly. The critical wave velocity decreases slightly for small positive radial Reynolds numbers, but increases for larger positive and all negative radial Reynolds numbers. The perturbed velocities are very similar to those for no axial flow.

On the evolution of unsteady disturbances in continuous strip casting processes
View Description Hide DescriptionContinuous solidification processes in thin layers of molten metal are of central importance in many fields of modern metallurgical engineering. This paper deals with unsteady disturbances possibly emerging at the free surface or the phase boundary within the solidification zone of a horizontal strip casting process. Assuming that the wave lengths of the disturbances are large compared to the characteristic depth of the melt, we can apply governing equations for onedimensional flow. Furthermore, we assume the amplitudes of the disturbances to be so small that their evolution can be regarded as weakly nonlinear. Since unsteady wave propagation phenomena can arise from temperature variations as well as from the excitation of waves at the free surface or the solidification front, both mechanisms will be studied in the following. In the latter case the disturbances at the surface are found to be governed by the inviscid Burgers equations with varying coefficients and will then, in general, develop shock discontinuities.

Stability of a liquidmetal layer between gas streams with and without a magnetic field
View Description Hide DescriptionThe linear stability of a plane liquidsheet of metal flowing between parallel gas streams having different velocities is considered. The presence of a magnetic field only slightly modifies the neutral stability curves obtained in the hydrodynamic regime where Kelvin–Helmholtz instabilities are the dominant mechanism in the destabilization of the sheet. The most unstable wavelength is found to scale with where We is the Weber number. As expected, the growth rate of the instabilities is decreased when a transverse magnetic field is applied. However, the growth rate is increased when the applied magnetic field is parallel to the direction of the velocities. A possible explanation of this unusual phenomenon is presented. In an experimental airblast atomizer with water and nitrogen, particle size and velocity measurements have been made with a laserdoppler analyzer. The results agree with the theoretical predictions for zero magnetic flux density and are also consistent with predictions based on a more global breakup mechanism.

Similarity law for the streamwise turbulence intensity in zeropressuregradient turbulent boundary layers
View Description Hide DescriptionA similarity relationship is proposed to describe the streamwise broadbandturbulence intensity in a zeropressuregradient boundary layer. The formulation is applicable to the entire region of the flow beyond the viscous buffer zone and is based on the attached eddy hypothesis, the Reynoldsnumbersimilarity hypothesis and the assumed existence of Kolmogorov eddies with a universal inertial subrange. Experimental data of the authors and those from various published works covering a large Reynolds number range are investigated in light of this formulation.

Disturbances produced by motion of an actuator
View Description Hide DescriptionLaminar flowcontrol methods employ some device to act on the flow. These devices, termed actuators, vary from blowingsuction holes, to heating strips, to walldeflected membranes. We use computer simulations to optimize membrane actuators to generate singlemode disturbances which develop in an unstable laminar boundary layer. We compare how varied actuator dimensions and motions reproduce the disturbance velocity profiles of naturally occurring disturbances. Finally, we use an analytical technique to support numerical simulations which determine actuator dimensions that generate the largest streamwise velocity disturbances downstream of the actuator.

Reversal in spreading of a tabbed circular jet under controlled excitation
View Description Hide DescriptionDetailed flow field measurements have been carried out for a turbulent circular jet perturbed by tabs and artificial excitation. Two “delta tabs” were placed at the nozzle exit at diametrically opposite locations. The excitation condition involved subharmonic resonance that manifested in a periodic vortex pairing in the near flow field. While the excitation and the tabs independently increased jet spreading, a combination of the two diminished the effect. The jet spreading was most pronounced with the tabs but was reduced when excitation was applied to the tabbed jet. The tabs generated streamwise vortex pairs that caused a lateral spreading of the jet in a direction perpendicular to the plane containing the tabs. The excitation, on the other hand, organized the azimuthal vorticity into coherent ring structures whose evolution and pairing also increased entrainment by the jet. In the tabbed case, the excitation produced coherent azimuthal structures that were distorted and asymmetric in shape. The selfinduction of these structures produced an effect that opposed the tendency for the lateral spreading of the streamwise vortex pairs. The passage of the distorted vortices, and their pairing, also had a cancellation effect on the timeaveraged streamwise vorticity field. These led to the reduction in jet spreading.

Behavior of naturally unstable and periodically forced axisymmetric buoyant plumes of helium and helium–air mixtures
View Description Hide DescriptionEffects of forcing on the behavior of naturally unstable buoyant plumes of helium and helium/air mixtures are investigated experimentally. Axisymmetric buoyant plumes originating from a 10 cm diam nozzle are perturbed in a periodic manner by an upstream loudspeaker introducing a sinusoidal streamwise velocity oscillation with a peaktopeak velocity magnitude of about 3% of the mean velocity at the nozzle exit. The experimental conditions in this study corresponded to Richardson number, of 42. Video images of the naturally unstable plumes as well as the forced plumes were analyzed to study the features of the resulting flow oscillations and the vortical structures. It was found that the plume responds readily to the imposed oscillations with the toroidal vortices forming at the forcing frequency. Plume images indicate a more complicated and turbulent state of the flow within the largescale toroidal vortices as they convect downstream. These vortical structures have lateral dimensions of the order of the nozzle diameter at low oscillation frequencies, but the vortex length scales become smaller at higher forcing frequencies. Additionally, mushroomshaped smallerscale vortex pairs appear in the very early part of the forced plumes that are absent in the unforced case. Frequency spectrum of the plume centerline velocity fluctuations, detected by two total pressure probes located at onehalf and two diameter heights above the nozzle exit, show that the plume predominantly responds to the imposed flow excitation. However, as the flow evolves downstream, frequency spectra exhibit a broader range of frequencies some of which do not coincide with the imposed one and its harmonics. The streamwise convection velocities of the largescale vortical structures are not influenced by the imposed oscillation frequency. As the excitation frequency approaches that of the natural frequency of the flow, a more chaotic behavior of the largescale vortices is observed in terms of their convection velocity. This is in contrast to the behavior of momentum dominated shear flows (jets and mixing layers), where a large degree of spatial and temporal coherence of the flow is attained when the flow is excited at its natural frequency. To complement these experiments and probe into the nature of the axisymmetric plume instabilities, we also visualized the transitional behavior of these buoyant plumes from their initially nonoscillatory state to the final periodic state. This is important as far as identifying the nature of the instability as either absolute or convective. Our findings show that the experiments exhibit features that point toward a convectivetype instability.

Threedimensional, unsteady, acousticshear flow dynamics in a cylinder with sidewall mass addition
View Description Hide DescriptionThreedimensional internal flowdynamics are studied in a cylinder with mass injection from the sidewall. A timedependent, harmonic, nonaxisymmetric axial velocity disturbance is imposed on the endwall of the cylinder to create a nonaxisymmetric velocity field. An asymptotic analysis is used to reduce the NavierStokes equations to more elementary forms in two regions adjacent to the endwall with distinct physical characteristics: an incompressible, inviscid and irrotational core near the endwall, and an incompressible viscous boundary layer containing all three components of vorticity adjacent to the sidewall. Solutions to these equations for disturbance frequencies associated with the lowest order axial acoustic modes show that the nonaxisymmetric nature of the flow is confined to the core region adjacent to the endwall with a characteristic axial dimension on the order of the cylinder radius. Within the region, axial, radial, and azimuthal velocities exist. These nonaxisymmetric effects decay exponentially fast so that only axisymmetric acoustic modes exist further downstream. These results are valid for driving frequencies below the “cutoff” value that one would find in a duct.

Multidimensional stability analysis of overdriven gaseous detonations
View Description Hide DescriptionMultidimensional instabilities of planar detonations that lead to cellular structures are addressed by use of a distinguished limit in which the propagation Mach number is large and the difference between the specific heats at constant pressure and at constant volume is small. In this limit, the Neumannstate Mach number is small, and the fractional variations of the pressure change after the Neumann state also are small for the overdriven conditions that are considered, under which the heat release is comparable in magnitude with the thermal enthalpy at the Neumann state. The resulting postshock flow is quasiisobaric in the first approximation. For all linear modes the analysis provides a dispersion relation expressing the frequency and the linear growth rate in terms of the transverse wavelength. The analysis serves to demonstrate how the interactions among the entropy waves, the varying rate of heat release and the transverse flow induced by the large density change across the wrinkled shock result in the multidimensional instability. The instabilities have a large transverse length but oscillate and evolve on a short time, comparable with the transit time of a fluid particle through the detonation. The coupling with the acoustic waves is a stabilizing factor, dominant at short wavelengths for assuring a suitably large ratio of transverse wavelength to detonation thickness for instability. Even when the detonation is stable to planar disturbances, so that there is a range of stability at long wavelengths, it is shown that there always exists an intermediate range of wavelengths for which the detonation is unstable. This is true even when heatrelease rates are entirely independent of temperature, corresponding to detonations that are very stable to planar disturbances. A sufficiently large temperature sensitivity modifies the multidimensional instability. The general chemical kinetics adopted, having different temperature sensitivities for induction and for heat release, the former possibly large, is of the same character as that previously developed by the first authors for describing the planar stability and nonlinear oscillations of galloping detonations but differs from onestep activationenergy asymptotics, which produces nonphysical, spurious instability under all conditions. From the present extension to multiple dimensions with moderate overdrive, inferences are drawn concerning differences that arise for strong overdrive and when Chapman–Jouguet conditions are approached.