摘要:

Direct numerical simulations are used to analyze the evolution of a temporally growing two‐dimensional shear layer seeded with dilute concentrations of bubbles under gravity. The bubble concentrations are dilute enough so that bubble–bubble interactions can be neglected, but are large enough for cumulative effects of bubbles to influence the flow. The evolution of the bubble field is determined by tracking many individual bubbles, and the flow field is advanced by using the Navier–Stokes equations with a coupling term representing the effect of the bubbles on the flow. The results are interpreted in terms of the vorticity, density, and pressure fields relative to the one‐way coupled or passive case. For the coupled case, a reduction in the magnitude of the vorticity and pressure gradients near the vortex center is observed. In addition to modification of the flow, it is observed that the accumulation of bubbles is smaller and the location of the equilibrium points are shifted farther from the vortex center as a result of the coupling. It is explored how these changes are modified by different Froude numbers and bubble sizes. The differences between passive and coupled cases usually increase due to larger accumulations as larger bubbles are considered. However, for certain Froude numbers an optimum coupling is observed at intermediate bubble sizes due to the absence of equilibrium points for large bubbles.

ISSN:1070-6631    

DOI:10.1063/1.868155

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A new phenomenon of successive branching of a liquid jet emanating from a nozzle into the atmosphere has been reported [Phys. Fluids A3, 241 (1991)]. It was observed that an intact jet can be made to bifurcate successively into a two‐, three‐, and multiple‐pronged jet by oscillating the nozzle along its axis at a successively higher frequency. It is shown here that the observed multiple‐pronged jet was actually multiple streams of droplets after the jet breakup generated by the lateral component of the nozzle oscillation, which was induced at the free end when the piezoelectric nozzle was axially vibrated. A plausible theoretical explanation of the formation of the multiple streams is given.

ISSN:1070-6631    

DOI:10.1063/1.868156

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A one‐dimensional analysis of slender axisymmetric viscous liquid jets is considered. A set of one‐dimensional models is derived by substituting a truncated Taylor series in the radial coordinate into the Navier–Stokes equations and boundary conditions at the interface. The relative error, defined as the order of magnitude of the neglected terms divided by the order of the retained ones, is small if the dimensionless wave numberkis small enough. The Lee slice model is generalized to take into account viscosity, the relative error beingk2. A new model having a parabolic radial dependence for the axial velocity is developed, with a relative errork4. The Cosserat model comes from the introduction of the mean axial velocity into the previous one, but an inconsistency arises from neglecting some viscous terms of the same order as those retained. A new model for the mean axial velocity is derived. It conserves the same inertial contribution but avoids the above‐mentioned problem by estimating the involved terms instead of neglecting them. Therefore the relative error isk4for any value of viscosity. Linear stability analysis is performed for the infinite jet. Results are compared with the exact linear solution given by Lord Rayleigh. The main features predicted in the derivation of the one‐dimensional models manifest themselves in the linear case.

ISSN:1070-6631    

DOI:10.1063/1.868157

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Previous experimental studies indicate that the steady two‐dimensional flow in a lid‐driven cavity becomes unstable and goes through a sequence of transitions before becoming turbulent. In this study, an analysis of this instability is undertaken. The two‐dimensional base flow is computed numerically over a range of Reynolds numbers and is perturbed with three‐dimensional disturbances. The partial differential equations governing the evolution of these perturbations are then obtained using linear stability analysis and normal mode analysis. Using a finite difference discretization, a generalized eigenvalue problem is formulated from these equations whose solution gives the dispersion relation between complex growth rate and wave number. An eigenvalue solver using simultaneous iteration is employed to identify the dominant eigenvalue which is indicative of the growth rate of these perturbations and the associated eigenfunction which characterizes the secondary state. This paper presents stability curves to identify the critical Reynolds number and the critical wavelength of the neutral mode and discusses the mechanism of instability through energy calculations. This paper finds that the loss of stability of the base flow is due to a long wavelength mode at a critical Reynolds number (Re) of 594. The mechanism is analyzed through a novel application of the Reynolds–Orr equations and shown to be due to a Goertler type instability. The stability curves are relatively flat indicating that this state will be challenged by many shorter wavelength modes at a slightly higher Reynolds number. In fact, a second competing mode with a wavelength close to the cavity width was found to be unstable at Re=730. The present results of the reconstructed flow based on these eigenfunctions at the neutral state, show striking similarities to the experimental observations.

ISSN:1070-6631    

DOI:10.1063/1.868158

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The flow field inside a cylindrical container induced by the rotation of the top and bottom end walls with a fixed sidewall is described. For this problem, this paper shows that stagnation points occur along the axis of rotation between the midplane of symmetry and the rotating end walls for appropriate values of the characteristic parameters, viz., the Reynolds number and the aspect ratio of the container. Aspect ratios of 0.5, 0.8, 1.0, and 1.5 were examined over a range of Reynolds numbers from 100 to 2000. As the Reynolds number increased beyond a critical value a recirculation zone surrounding a columnar vortex core in the meridional‐plane flow pattern is predicted to occur near the midplane. This toroidal vortex is different from the type B vortex breakdown phenomenon that occurs in cylindrical containers with only one end wall rotating.

ISSN:1070-6631    

DOI:10.1063/1.868159

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The von Ka´rma´n vortex street behind a circular cylinder in a laminar homogeneous jet core is experimentally investigated. The Strouhal–Reynolds number relationships are measured for various shear‐layer thicknesses and aspect ratios. The experimental Strouhal number values are found to collapse with the discrete vortex shedding modes, which were observed for boundary‐layer end conditions. The results indicate that the shedding modes are independent from the end conditions, but are an intrinsic feature of the shedding process of an infinitely long cylinder. The experimentally assumed shedding mode, however, is strongly dependent of the geometric parameters, like the shear‐layer thickness and the aspect ratio. The observed tendencies can be made physically plausible.

ISSN:1070-6631    

DOI:10.1063/1.868160

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The modeling of the pressure strain rate terms is an important issue in the improvement of the generality of closure models for the Reynolds stress transport (RST) equations. A part of these efforts is to provide accurate experimental information on the pressure–strain rate tensor, which in turn requires equally accurate information on the dissipation and the diffusion tensors. Here the far wake of a cylinder was studied in order to enable the required balances of the RST equations. The experimental results indicate a nonisotropic dissipation tensor, and show the energy redistribution between the different components as described by the pressure–strain rate correlations. Comparisons are made between the experimentally determined pressure–strain rate distributions and the corresponding distributions predicted by closure models.

ISSN:1070-6631    

DOI:10.1063/1.868161

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

In this study the stability characteristics of uniformly elongating plastic jets exposed to axial electric currents are investigated. The objective of this study is to expand the results of previous analyses by Littlefield [‘‘The effect of electromagnetic fields on the stability of a uniformly elongating plastic jet,’’ Phys. Fluids A2, 2240 (1990); ‘‘Finite conductivity effects on the MHD instabilities in uniformly elongating plastic jets,’’ibid.3, 166 (1991); ‘‘Enhancement of stability in uniformly elongating plastic jets with electromagnetic fields,’’ibid.3, 2927 (1991)] to include high levels of electric current, where thermal energy effects must be included. Coupling of the magnetohydrodynamic and thermal characteristics of the flow is accomplished through the variation of mechanical, thermal, and electrical properties with temperature. Phase change effects are also considered. The jet is assumed incompressible and perfectly plastic, with the Levy–von Mises criterion imposed to limit the effective stress. Solutions to the appropriate base flow are subjected to small axisymmetric disturbances, and linear perturbation theory is employed to determine the time evolution of these disturbances. Perturbations that grow the fastest in magnitude as time progresses are identified as the most unstable. Results of the analysis indicate that thermal effects can dramatically alter both the base and perturbed flow fields, as well as the growth rate of perturbations.

ISSN:1070-6631    

DOI:10.1063/1.868162

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The topological description of flows in the vicinity of a solid boundary, that is familiar from the aerodynamics literature, has recently been extended to the case of flow at a liquid–gas interface or a free surface by Lugt [Phys. Fluids30, 3647 (1987)]. Lugt’s work is revisited in a more general setting, including nonconstant curvature of the interface and gradients of surface tension, using tools of modern nonlinear dynamics. Bifurcations of the flow pattern occur at degenerate configurations. Using the theory of unfolding, this paper gives a complete description of the bifurcations that depend on terms up to the second order. The general theory of this paper is applied to the topology of streamlines during the breaking of a wave and to the flow below a stagnant surface film.

ISSN:1070-6631    

DOI:10.1063/1.868163

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A new ‘‘vorticity confinement’’ method is described which involves adding a term to the momentum conservation equations of fluid dynamics. This term depends only on local variables and is zero outside vortical regions. The partial differential equations with this extra term admit solutions that consist of Lagrangian‐like confined vortical regions, orcovons, in the shape of two‐dimensional (2‐D) vortex ‘‘blobs’’ and three‐dimensional (3‐D) vortex filaments, which convect in a constant external velocity field with a fixed internal structure, without spreading, even if the equations contain diffusive terms. Solutions of the discretized equations on a fixed Eulerian grid show the same behavior, in spite of numerical diffusion. Effectively, the new term, together with diffusive terms, constitute a new type of regularization of the inviscid equations which appears to be very useful in the numerical solution of flow problems involving thin vortical regions. The discretized Euler equations with the extra term can be solved on fairly coarse, Eulerian computational grids with simple low‐order (first‐ or second‐) accurate numerical methods, but will still yield concentrated vortices which convect without spreading due to numerical diffusion. Since only a fixed grid is used with local variables, the vorticity confinement method is quite general and can automatically accommodate changes in vortex topology, such as merging. Applications are presented for incompressible flow in 3D, where pairs of thin vortex rings interact and, in some cases, merge.

ISSN:1070-6631    

DOI:10.1063/1.868164

出版商:AIP    

年代:1994

数据来源: AIP