摘要:

The time evolution of the Loitsianski integral at high‐Reynolds numbers is determined by computing an ensemble average of a large number of independent large‐eddy simulations of decaying isotropic turbulence. It is found that the Loitsianski integral becomes proportional tot&ggr;at large times and that &ggr; ≊0.25. The present simulations illustrate the efficient use of massively parallel computers for simulating large ensembles of turbulent flows.

ISSN:0899-8213    

DOI:10.1063/1.858773

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The dynamics of streamwise vorticity in axisymmetric jets is studied by direct numerical integration of the Navier–Stokes equations coupled with a passive scalar. Consistently with recent experiments and inviscid numerical simulations, the present viscous simulations show the appearance of pairs of axially counter‐rotating vortex filaments. After their formation the filaments move away from the jet, dragging the tracer into finger‐shaped structures. The three‐dimensional topology of the rings, filaments, and fingers is described, well beyond the time of filament formation. Finally, visualizations of the pressure gradient field are presented, which suggest that the filaments can be directly observed experimentally by seeding the flow with microbubbles.

ISSN:0899-8213    

DOI:10.1063/1.858774

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The rarefied flow of monatomic gas between an inner rotating cylinder and an outer stationary cylinder is simulated by the Monte Carlo direct simulation method. The flow is assumed to be axisymmetrical. A new idea to calculate the axisymmetrical flow is proposed. Simulations are performed for Knudsen numbers in the range 0.004<Kn<0.04 at a fixed rotation speed. The calculated torque coefficients show a very good agreement with experimental data not only for vortex free but also for vortical flow regimes. Once the Taylor vortices have developed, they cause a change of the circumferential velocity profile up to 35%. This is the first numerical simulation of Taylor vortices via solutions of the Boltzmann equation using the molecular approach.

ISSN:0899-8213    

DOI:10.1063/1.858775

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

This article presents a theoretical study of the deformation of a spherical liquid droplet impinging upon a flat surface. The study accounts for the presence of surface tension during the spreading process. The theoretical model is solved numerically utilizing deforming finite elements and grid generation to simulate accurately the large deformations, as well as the domain nonuniformities characteristic of the spreading process. The results document the effects of impact velocity, droplet diameter, surface tension, and material properties on the fluid dynamics of the deforming droplet. Two liquids with markedly different thermophysical properties, water and liquid tin, are utilized in the numerical simulations because of their relevance in the industrial processes of spray cooling and spray deposition, respectively. The occurrence of droplet recoiling and mass accumulation around the splat periphery are standout features of the numerical simulations and yield a nonmonotonic dependence of the maximum splat radius on time.

ISSN:0899-8213    

DOI:10.1063/1.858724

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Transient amplification of a particular set of favorably configured forcing functions in the stochastically driven Navier–Stokes equations linearized about a mean shear flow is shown to produce high levels of variance concentrated in a distinct set of response functions. The dominant forcing functions are found as solutions of a Lyapunov equation and the response functions are found as the distinct solutions of a related Lyapunov equation. Neither the forcing nor the response functions can be identified with the normal modes of the linearized dynamical operator. High variance levels are sustained in these systems under stochastic forcing, largely by transfer of energy from the mean flow to the perturbation field, despite the exponential stability of all normal modes of the system. From the perspective of modal analysis the explanation for this amplification of variance can be traced to the non‐normality of the linearized dynamical operator. The great amplification of perturbation variance found for Couette and Poiseuille flow implies a mechanism for producing and sustaining high levels of variance in shear flows from relatively small intrinsic or extrinsic forcing disturbances.

ISSN:0899-8213    

DOI:10.1063/1.858894

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

For many materials processing techniques, the meniscus of liquid bridging the crystal to the melt is critical in determining the properties of the solidified crystal. It is standard practice for existing theoretical models to use equilibrium meniscus shapes with specified contact angle to represent the behavior of the meniscus. It is shown here that with such boundary conditions, multiple solutions exist to the axisymmetric form of the Laplace–Young equation. Furthermore, these possible meniscus profiles may, depending on the interaction of Bond number, pressurization, aspect ratio and contact angle, correspond to minima, maxima or nonextrema points, as far as energy is concerned. The implications of this observation on meniscus stability are explored. The effect of direction of pulling in relation to gravity is also investigated. It appears that for tall menisci, commonly adopted equilibrium shapes may be unstable and the consequent dynamic behavior must be considered. Quasiequilibrium dynamics of the meniscus is simulated using a simplified hysteresis model for the contact angle at the top of the meniscus. A variety of behavior is found to arise, which is not fully captured by relations governing meniscus behavior used hitherto in many theoretical simulations.

ISSN:0899-8213    

DOI:10.1063/1.858725

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A thin liquid film on a horizontal solid surface undergoing radiative heat transfer with an external heat source and the surrounding environment is considered. Thermal gradients along the free surface give rise to a thermocapillary flow in the liquid that is opposed by a hydrostatic pressure gradient within the film. Transient and steady‐state solutions are obtained for the interfacial shape and temperature and the velocity field. These results are compared with those from another model, in which a temperature distribution is imposed on the free surface of the film. At a critical value of the dynamic Bond number, a cusp in the form of a free‐surface slope discontinuity appears in this fixed free‐surface temperature model, but not in the radiation model. When the Bond number is less than this critical value, the time required to thin the film by a significant fraction of its original thickness is much larger with the radiation model. It is shown how the thermal boundary conditions used in the models directly cause these differences.

ISSN:0899-8213    

DOI:10.1063/1.858726

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The heat and salt fluxes produced by salt fingering at a density interface are studied with a numerical and an analytical model. Specifically, the issue concerning the value of the heat‐to‐salt flux ratio is addressed. The numerical modeling based on direct numerical computation of the nonlinear governing equations obtains values around 0.5. This value is approximately the average of widely varying experimental values reported in the literature. The large difference between the theoretical flux ratio predicted based on the buoyancy maximization hypothesis and the experimentally derived flux ratio is examined with an analytical model, which includes both effects of salt stratification in the interface and salt discontinuity at the edges of the interface. Combined with the numerical model results, the analysis shows that the disagreement can be traced to the flux maximization hypothesis itself. An alternative hypothesis that maximizes convective velocity amplitude is presented which gives flux‐ratio predictions consistent with the measurements. Discussion of the finger width scale and the magnitude of the salt flux is also given as well as comparison of the salt flux with laboratory measurements.

ISSN:0899-8213    

DOI:10.1063/1.858727

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The nonlinear evolution of the interface between two miscible fluids of different densities and viscosities is simulated numerically for flow in a two‐dimensional porous medium in which gravity is directed at various angles to the interface. Global velocities tangential to the interface are included in the analysis in addition to a normal displacing velocity. In unstable configurations, the viscous fingers that result translate as they amplify when nonzero tangential velocities are present. The increased stabilization by tangential shearing velocities reported in [A. Rogerson and E. Meiburg, Phys. Fluids A5, 1344 (1993)] affects the growth and wavelength selection of the emerging fingers. Tangential shearing also breaks the symmetry in the shape and concentration distribution of emerging fingers. In addition to the fingering mechanisms reported in previous studies, new mechanisms of diagonal fingering, trailing‐lobe detachment, and secondary side‐finger instability, resulting from the presence of gravity and tangential velocities, have been identified. These phenomena are reflected in one‐dimensional averaged profiles of the concentration field. Also, how different density–concentration relations influence the interfacial evolution is investigated. When the dependence of viscosity and density on the concentration has different functional forms, the region of instability may be localized. The nature of the interfacial development is altered by varying the density relation and thereby changing the region of instability, suggesting that careful modeling of the density and viscosity relations is warranted.

ISSN:0899-8213    

DOI:10.1063/1.858728

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The flow past a semicircular cylinder at the bottom of a channel is considered. The channel is of finite vertical extent and of infinite horizontal extent. The fluid consists of two layers of constant densities. Both viscosity and surface tension are neglected. It is assumed that the flow is symmetric with respect to a vertical line through the center of the circular cross section and uniform in each layer at infinity. An integrodifferential equation for the unknown shape of the interface is derived, discretized, and solved numerically using Newton’s method. It is shown that there are flows that are perturbations of uniform streams and others that are perturbations of solitary waves. Progression along the various branches of solutions produce two different types of limiting configurations. One is characterized by an infinite broadening in the horizontal direction and the other by overhanging interfacial profiles.

ISSN:0899-8213    

DOI:10.1063/1.858729

出版商:AIP    

年代:1993

数据来源: AIP