摘要:

A hysteresis phenomenon has been revealed through experiments conducted with large‐amplitude forced oscillations of pendant drops in air. Under strong excitation, the frequency response of a drop forced at constant amplitude exhibits jump behavior; a larger peak response amplitude &egr;↓appears at a lower frequency &ohgr;↓during a downward (↓) variation of forcing frequency than during an upward (↑) variation, viz. &egr;↓≳&egr;↑and &ohgr;↓<&ohgr;↑. Similar results are obtained when forcing amplitude is varied at constant frequency. This behavior is characteristic of a system with a soft nonlinearity. These findings indicate that oscillating pendant drops constitute a convenient system for studying nonlinear dynamics. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868576

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

A liquid being ejected from a nozzle emanates from it as discrete, uniformly sized drops when the flow rate is sufficiently low. In this paper, an experimental study is presented of the dynamics of a viscous liquid drop that is being formed directly at the tip of a vertical tube into ambient air. The evolution in time of the drop shape and volume is monitored with a time resolution of 1/12 to 1 ms. Following the detachment of the previous drop, the profile of the new growing drop at first changes from spherical to pear‐shaped. As time advances, the throat of the pear‐shaped drop takes on the appearance of a liquid thread that connects the bottom portion of the drop that is about to detach to the rest of the liquid that is pendant from the tube. The focus here is on probing the effects of physical and geometric parameters on the universal features of drop formation, paying special attention to the development, extension, and breakup of the liquid thread and the satellite drops that are formed subsequent to its breakup. The role of surfactants in modifying the dynamics of drop formation is also studied. The effects of finite inertial, capillary, viscous, and gravitational forces are all accounted for to classify drastically different formation dynamics and to elucidate the fate of satellite drops following thread rupture. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868577

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Bifurcation diagrams of nonaxisymmetric liquid bridges subject to a lateral gravitational force and to both lateral and axial gravitational forces are found by solving the Young–Laplace equation for the interface by a finite difference method. The potential energy of the equilibrium shapes is also calculated. The results obtained show that the slenderness of the bridge determines whether the breaking of the liquid bridge subject to a lateral gravitational force leads to equal or unequal drops. The stability limits calculated are compared with the ones obtained using asymptotic techniques around the cylinder, the agreement being extremely good for a wide range of the parameters. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868578

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The spreading of a thin, planar drop of fluid that completely wets a solid surface is described, from an initial state in which the drop has a compact shape through its final approach to an infinitesimally thin film extending to infinity. Because the slope of the drop surface is everywhere small, the lubrication approximation can be used, and the effects of capillarity, viscosity, and intermolecular forces are all included. It is shown that a simple model for the intermolecular forces allows a mathematically acceptable solution to be found, without the need to invoke a large‐distance cutoff and without violating the small‐slope requirement of lubrication theory. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868579

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The thickness of the film entrained by a fiberquicklywithdrawn out of a bath of wetting liquid is of interest. For velocities larger than a threshold (usually of the order of 1 m/s), inertia can no longer be neglected and must be incorporated in a generalized form of the classical Landau–Levich–Deryaguin model. It is shown here that the effect of inertia is to make the film thicker, which agrees with recent observations. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868580

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The unsteady streamlined motion of a constant property fluid in the unobstructed space between a pair of disks corotating at angular velocity &OHgr; in a fixed cylindrical enclosure is investigated numerically. Two‐dimensional (axisymmetric) and three‐dimensional calculations are performed using a second‐order accurate time‐explicit algorithm. The flow configuration corresponds to that investigated experimentally by Schuleretal. [Phys. Fluids A2, 1760 (1990)]. The steady flow solutions are characterized by a symmetrical pair of counter‐rotating toroidal vortices in the cross‐stream (r‐z) plane. This secondary motion is driven by the radial imbalance between the outward‐directed centrifugal force and the inward‐directed pressure gradient force. Axisymmetric calculations predict a flow that is steady for Re<22 200, where Re is the Reynolds number based on the disk radius, the tip speed of the disks, and the kinematic viscosity of the fluid. Above this value the motion is unsteady periodic and, while the features of the cross‐stream flow pattern are broadly preserved, the symmetry of the motion about the midplane is broken by alternating periodic crossings of the toroidal vortices.This instability is maintained through an interaction that arises between outward‐directed fluid in the disk Ekman layers and inward‐directed fluid in the return core flow. Three‐dimensional calculations at Re=22 200 and 44 400 show that the toroidal vortices acquire a time‐varying sinuous shape in the circumferential direction. These calculations reveal circumferentially periodic reversals of the axial velocity component in the cross‐stream plane, including the detached shear layer separating the region of motion in solid‐body rotation near the hub from the potential core, in agreement with the flow visualization observations of Humphrey and Gor [Phys. Fluids A5, 2438 (1993)]. The wavelength of this oscillation is shown to be twice that of the circumferential velocity component which is responsible for the nodal distribution of axial vorticity. When plotted on the interdisk midplane, the axial component of vorticity manifests itself as an even integer number, 2n(n=1,2,...), of circumferentially periodic foci. Experiments show that the number of foci decreases in a stepwise manner with increasing Reynolds number. For the conditions of this study, the calculated dimensionless angular velocity of the foci, &OHgr;F/&OHgr;, ranges from 0.55 at Re=22 200 to 0.44 at Re=44 400. These values are close to the present experimental estimate &OHgr;F/&OHgr;=0.5. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868753

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The dispersion and settling of small, heavy, spherical particles in a temporally evolving two‐dimensional mixing layer under gravity is investigated. The dilute limit is assumed, in which both the effect of the particles on the fluid flow and the interaction among the particles is negligible. The particle dynamics is quantified as a function of the dimensionless Stokes and Froude numbers, St and Fr, which express the ratios of the three time scales related to (i) the fluid flow, (ii) the particles’ inertia, and (iii) their settling velocity, respectively. For horizontal flow in which the upper stream is the seeded one, the mixing layer accelerates the settling of particles with small St, whereas particles with large St are slowed down in their settling motion. At intermediate St and for moderate settling velocities, root‐mean‐square (RMS) data for the particle concentration field demonstrate the generation of strong inhomogeneities by the mixing layer. These regions of high particle concentration have the form of bands in the initially unseeded stream. Scaling laws for their angles and the distance between them are given. Furthermore, analytical results for linearized flow fields are derived that demonstrate the optimal efficiency of the dispersion and settling process at intermediate St. The numerical simulations show the existence of different parameter regimes, in which the particle motion is dominated by the coherent vortices and by gravity, respectively. Scaling laws are derived for the particle dispersion and settling for both of these regimes, which show reasonable quantitative agreement with the simulation data. Flows that exhibit a vortex pairing process show a reduced tendency of the particles toward suspension. For vertically upward flow in which the faster stream is seeded, is observed a sharp maximum in the particle dispersion measures for intermediate St and settling velocities equal to one‐half the difference between the free‐stream velocities. Under these conditions, the cross‐stream fluid velocity components become optimally efficient in ejecting particles into the unseeded stream. ©1995 American Institute of Physics. 

ISSN:1070-6631    

DOI:10.1063/1.868581

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

The structure of the flow around an oblate ellipsoidal bubble of fixed shape is studied by means of direct numerical simulation for Reynolds numbers Re up to 103. In agreement with a previous study by Dandy and Leal [Phys. Fluids29, 1360 (1986)] the computations demonstrate that if the bubble aspect ratio &khgr; is high enough a standing eddy can exist at the rear of the bubble in an intermediate range of Re. This eddy disappears beyond a certain Reynolds number and it is shown that its existence is governed by the competition between accumulation and evacuation of the vorticity in the flow. The range of Re where the eddy exists increases very rapidly with &khgr; meaning that this structure is certainly present in many experimental situations. The evolution of the drag coefficient with Re reveals that the oblateness has a dramatic influence on the minimum value of Re beyond which Moore’s theory [J. Fluid Mech.23, 749 (1965)] can be used to predict the rise velocity of a bubble of fixed shape. In contrast, owing to the shape of the vorticity distribution at the surface of the bubble, no noticeable influence of the standing eddy on the drag is found. A quantitative comparison between the present results and those of previous authors shows that the computational description of the boundary layer around curved free surfaces is not a trivial matter since a strong influence of the numerical method is observed. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868515

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

Mean velocity and Reynolds‐stress profiles were measured in the incompressible turbulent boundary layer with zero pressure gradient on the aerodynamically smooth sidewall of the German–Dutch windtunnel. Data were taken at Reynolds numbers Re&dgr;2, based on momentum thickness &dgr;2of 2×104, 4×104, and 6×104by means of four different types of hot‐wire probes (three‐wire probes, X wire, and normal‐wire probes). There are also measurements of skin friction and of spectra. The data compare well with the few available other measurements, and all profiles show independence of Reynolds number in the outer region of the boundary layer when plotted againsty/&Dgr;, where &Dgr; is the Rotta–Clauser length. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868516

出版商:AIP    

年代:1995

数据来源: AIP

摘要:

In an attempt to elucidate the laminar/turbulent transition mechanism in a Blasius boundary‐layer flow, a nonsemisimple resonance of phase‐locked secondary instability modes is investigated. Thelocalnonlinear behavior is described by means of a center manifold reduction. The numerically computed normal form is of the symmetric Takens–Bogdanov type and predicts a homoclinic orbit which is possibly related to a physical bursting process. Aglobalcontinuation procedure for equilibrated three‐dimensional (3‐D) waves in the full Navier–Stokes system validates some of the local predictions and very closely outlines the experimentally observed skin friction domain including subcritical transition. ©1995 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868517

出版商:AIP    

年代:1995

数据来源: AIP