摘要:

We derive an infinite set of invariants for two-dimensional Stokes flow with a free surface, driven by a point sink, in the case that surface tension effects are negligible. The complex variable methods used are closely related to those used for certain Hele–Shaw flows, which likewise have infinitely many conserved quantities. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869207

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Dispersion at short times is studied using a PFG-NMR (pulsed field gradient NMR) technique inside a fixed bed of nonconsolidated spherical beads saturated with water flowing at a constant velocity. This allows measurement of the probability distribution of the displacement of water molecules along the magnetic field gradient during a preset measurement time&Dgr;: the mean displacement of the water molecules is varied between 0.1 and 7.3 times the bead diameter by varying&Dgr;between 20 and 100 ms and the bead diameter between 800 and 81&mgr;m. At short times, the displacement of the molecules is small enough so that the local displacement is proportional to the local velocity component along the magnetic field gradient. At mean displacements larger than 5 bead diameters, the displacement distribution is Gaussian and centered about the mean displacement; the width of the distribution corresponds to the macroscopic dispersion coefficient as measured by other techniques. At intermediate displacements, this distribution displays two peaks corresponding to a combination of the two processes. The main features of this transition can be reproduced by a simple Monte-Carlo simulation modeling the porous medium as a set of finite length tubes with random orientations. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869208

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Dynamical simulations of bulk sedimentation have been carried out, using up to 32 000 solid particles. There is no evidence that the long-range hydrodynamic interactions are screened by changes in the pair correlation function at large distances. Instead the velocity fluctuations and diffusion coefficients diverge linearly with the width of the container, consistent with the random long-range microstructures observed in the simulations. Our data suggest that other mechanisms must be uncovered to account for experimental observations. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869212

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

This paper presents an experimental investigation of the hydrodynamic instabilities inside a self-excited fluidized bed. Pressure fluctuation and bed height measurements have been reported. In the slugging regime (above a critical gas flow rate), the bulk is found to exhibit a regular and periodic macroscopic pattern (large numbers of particles moving collectively in a seemingly organized manner). This state is characterized by nearly signoidal pressure fluctuations and regular bed height oscillations. As the gas flow increases the bulk motion tends toward large oscillations with intermittent smaller ones. The pressure fluctuations above the bed surface and the bed height oscillations are found to be intimately correlated. We report experimental evidence that the pressure fluctuations observed in a fluidized bed under and above its surface are caused by the oscillations of the bed height. The pressure wave initiates at the surface of the bed and propagates both upward and downward. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869214

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

We focus in this paper on the effect of natural convection in thermodiffusion coefficients measurements in liquid metal alloys both for normal and microgravity conditions. Our previous experimental results are briefly recalled, with a special emphasis on the data recently obtained from the EURECA space mission. With respect to the ground based values, it is seen that the solutal separation is always significantly higher in microgravity, even in systems where solutal stabilization of the flow has an effect. Simple scaling analysis arguments show that the error induced by additional convective transport scales with the square of the fluid velocity. Such a result compares favorably with existing three dimensional (3D) numerical data. The theory also accounts qualitatively for the reduced separation observed experimentally in ground based set-ups. We conclude that it is in principle possible to perform accurate measurements in space, but that the size of the capillaries used in the experiments should always be limited to roughly two millimeters. On Earth on the other hand, the risk of convective interference cannot be avoided. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869215

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

In this work, the boundary element method combined with the fourth order Runge–Kutta scheme as time integrator is used to simulate the dynamics of an acoustically levitated axisymmetric liquid drop. For a given set of dimensionless parameters—wavenumber, Bond number, and acoustic Bond number—the drop dynamics in an acoustic field is studied in terms of the shape oscillation and the translational motion of the drop. The shape oscillation of the drop is characterized by using the equatorial radius and its rate of change as two phase variables. Fixed points on this phase plane represent the static equilibrium shapes. The translational motion is characterized by using the position and the velocity of the drop centroid as two phase variables. The fixed points on this phase plane represent the equilibrium positions of the drop in the acoustic field. It is found that fixed points corresponding to both translational and shape oscillations undergo saddle-node bifurcations with the acoustic Bond number as a parameter. These saddle-node bifurcations define an upper and a lower limit on the acoustic Bond number that can be used in acoustic levitation. We also investigate the coupling effect between the translational oscillation and the shape oscillation. It is found that owing to the order-of-magnitude difference between the period of translational oscillation and that of shape oscillation the coupling effect is only significant at the boundary of the trapping region. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869216

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Fluid flowing down an inclined plane commonly exhibits a fingering instability in which the contact line corrugates. We show that below a critical inclination angle the base state before the instability is linearly stable. Several recent experiments explore inclination angles below this critical angle, yet all clearly show the fingering instability. We explain this paradox by showing that regardless of the long time linear stability of the front, microscopic scale perturbations at the contact line grow on a transient time scale to a size comparable with the macroscopic structure of the front. This amplification is sufficient to excite nonlinearities and thus initiate finger formation. The amplification is a result of the well-known singular dependence of the macroscopic profiles on the microscopic length scale near the contact line. Implications for other types of forced contact lines are discussed. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869217

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A method is presented for modeling the cavity formation and collapse induced by high-speed impact and penetration of a rigid projectile into water. The approach proposes thathigh-speedwater-entry is characterized by a cavity that experiences adeepclosure prior to closure at the surface. This sequence in the physical events of the induced cavity dynamics is suggested by the most recent high-speed water-entry experimental data, by results from numerical experiments using a hydrocode, and by an understanding of the fundamental physics of the processes that govern surface closure. The analytical model, which specifies the energy transfer for cavity production as equivalent to the energy dissipated by velocity-dependent drag on the projectile, provides accurate estimates for variables that are important in characterizing the cavity dynamics, and reveals useful knowledge regarding magnitudes and trends. In particular, it is found that the time of deep closure is essentially constant and independent of the impact velocity for a given projectile size, while the location of deep closure has a weak dependence on impact velocity. Comparison of these analytical results with experimental results from the literature and with results from numerical simulations verifies the analytical solutions. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869472

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Reduced dynamical models are derived for transitional flow and heat transfer in a periodically grooved channel. The full governing partial differential equations are solved by a spectral element method. Spontaneously oscillatory solutions are computed for Reynolds number Re⩾300 and proper orthogonal decomposition is used to extract the empirical eigenfunctions at Re=430, 750, 1050, and Pr=0.71. In each case, the organized spatio-temporal structures of the thermofluid system are identified, and their dependence on Reynolds number is discussed. Low-dimensional models are obtained for Re=430, 750, and 1050 using the computed empirical eigenfunctions as basis functions and applying Galerkin’s method. At least four eigenmodes for each field variable are required to predict stable, self-sustained oscillations of correct amplitude at “design” conditions. Retaining more than six eigenmodes may reduce the accuracy of the low-order models due to noise introduced by the low-energy high order eigenmodes. The low-order models successfully describe the dynamical characteristics of the flow for Re close to the design conditions. Far from the design conditions, the reduced models predict quasi-periodic or period-doubling routes to chaos as Re is increased. The case Pr=7.1 is briefly discussed. ©1997 American Institute of Physics. 

ISSN:1070-6631    

DOI:10.1063/1.869218

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Flow visualization of two highly elastic, nonshear-thinning polyisobutylene/polybutene fluids in the gap between concentric cylinders was performed over a range of shear rates and choices of relative cylinder rotations. The observed secondary flows are discussed in terms of destabilizing elastic and centrifugal forces. In the more viscous, more elastic fluid, instabilities are found to be independent of the choice of rotating cylinder and due entirely to elasticity. At the lowest shear rates examined, the first detectable secondary flows are steady counter-rotating vortices forming after a shearing time more than five orders of magnitude greater than the characteristic relaxation time of the fluid. At somewhat higher shear rates, a much more rapidly appearing oscillatory flow is observed to evolve into the steady vortex structure. In the less elastic fluid, the structure first detectable at the lowest shear rates is again steady vortices regardless of the choice of driving cylinder. At all shear rates examined, only elastic stationary vortices are observed in the absence of centrifugal destabilization (outer cylinder rotating). Secondary flows are significantly stronger in the presence of the centrifugal destabilization due to a rotating inner cylinder. Interaction of elasticity and centrifugal forces is found to generate a number of axially translating vortex structures, many of which are described here for the first time. At a shear rate more than five times the critical, another family of instability is observed which closely resembles a purely elastic instability observed by Baumert and Muller (1995). These experimental results are expected to provide a challenging test of numerical simulations of these viscoelastic flows. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869209

出版商:AIP    

年代:1997

数据来源: AIP