ISSN:0899-8213    

DOI:10.1063/1.3480469

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Evolution equations are derived for the density function of a suspension sedimenting above a plane. The equations are in the form of a nonlinear conservation law and the solutions might develop jump discontinuities in a finite time. The analysis starts on a local microscopic level, and the averaged equations are obtained via explicit calculations of particle–particle and particle–wall interactions.

ISSN:0899-8213    

DOI:10.1063/1.857690

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

A theory is presented to describe the momentum transport properties of suspensions containing randomly placed, slender fibers. The theory is based on a diagrammatic representation of the multiple scattering expansion for the averaged Green’s function as developed in the authors’ previous work on the heat and mass transfer properties of fiber dispersions [Phys. Fluids A1, 3 (1989)]. The ‘‘best one‐body approximation’’ is used to calculate the wavenumber‐dependent, ensemble‐averaged stress for both aligned and isotropically oriented fiber dispersions. Both the dilute and semidilute concentration regimes are considered. The effective viscosity is calculated as a limit unit of the previously obtained wavenumber‐dependent properties. In the semidilute concentration regime the scaling form originally suggested by Batchelor [J. Fluid Mech.46, 813 (1971)] is recovered forbothorientation distributions and its relation to short range ‘‘screening’’ is discussed. Corrections to this result in a ‘‘semidilute expansion’’ for small volume fraction are calculated and the dependence of these corrections on orientation distribution and particle shape is demonstrated.

ISSN:0899-8213    

DOI:10.1063/1.857683

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

In this paper a derivation of the Faxe´n theorem for a circular cylinder moving unsteadily through a compressible fluid in arbitrary motion with arbitrary slip is presented. This theorem is a generalization of the Faxe´n formula for incompressible flow and the no‐slip condition, derived by Varley and Zhou [Physica A127, 363 (1984)].

ISSN:0899-8213    

DOI:10.1063/1.857688

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

A model that can approximately describe a non‐Newtonian fluid such as paint and fluid mud is a Bingham plastic with a yield stress. To facilitate the study of slow but transient spreading of a thin sheet of fluid mud, we need the approximate equations governing the nonlinear motion. Beginning with a modified Bingham model with two viscosities, the approximate equations are derived by a systematic perturbation analysis. The controlling parameters are found to be the Reynolds numberR, the shallowness ratioh¯/L¯=&dgr;1/2, and the ratio of viscosities &bgr;=&ngr;/&ngr;1[as defined in (45)]. Results valid forR,&bgr;,&dgr;≪1 but &dgr;/&bgr;2≤O(1) are obtained. In the special case when &dgr;/&bgr;2≪1, the limits can also be obtained by heuristic arguments similar to those in the lubrication theory. Two examples are discussed.

ISSN:0899-8213    

DOI:10.1063/1.857821

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Linear stability theory is used to discriminate between the possible convective structures (axisymmetric rolls, axially independent columns, and general three‐dimensional patterns) in the case of unipolar injection between coaxial cylinders of arbitrary radii. The cases of weak, strong, and arbitrary finite injection, either from the inner or outer cylinder, are considered. In all cases three‐dimensional modes are found to be the least stable. Physical mechanisms involved are discussed thoroughly.

ISSN:0899-8213    

DOI:10.1063/1.857689

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Flow fields within spatially periodic arrays of cylinders arranged in square and hexagonal lattices are calculated, with microscale Reynolds number ranging between zero and 200, employing a finite element numerical scheme. The terminology of an ‘‘apparent permeability’’ is introduced to establish a relationship existing between mean velocity and macroscopic pressure gradient characterized by a finite Reynolds number flow. In contrast with the low Reynolds number ‘‘true ’’ permeability, the apparent permeability is shown here to generally depend upon the direction of the applied pressure gradient, owing to nonlinearities existing within the local fluid motion. The orientation‐dependent permeabilities of both square and hexagonal monodisperse arrays are observed to diminish with increasing Reynolds number. Similar behavior is also observed for a bidisperse square array, though the apparent permeability of the latter is shown less sensitive to Darcy velocity orientation at large Reynolds numbers in comparison to the corresponding monodisperse square array, for all cylinder concentrations examined.

ISSN:0899-8213    

DOI:10.1063/1.857691

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The steady flow on a curved bed of large radius of curvature is perturbed by fixed‐frequency waves. The frequency is small, commensurate with the magnitude of the curvature of the bed and the perturbations are of the long‐wave type. A streamwise growth rate is calculated and several examples are given showing that the flow is theoretically unstable even for very small Reynolds numbers, in contrast to the classical theories of Benjamin [J. Fluid Mech.2, 554 (1957)] and Yih [Phys. Fluids8, 812 (1965)] for plane inclined beds.

ISSN:0899-8213    

DOI:10.1063/1.857692

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Detailed numerical simulation has been carried out for fully developed laminar flow through a circular straight pipe with radiusa, which is rotating with constant speed &OHgr; about an axis perpendicular to its own axis. The flow is symmetric about a plane containing the pipe axis with its normal parallel to the rotation axis. There are four types of flow regime that result from the various effects of the secondary flow on the main stream via the convection and Coriolis term. WhenR&OHgr;≤10 andR&OHgr;G≤100, the axial velocity profile is essentially axisymmetric and parabolic. HereR&OHgr;=&OHgr;a2/&ngr; andG=G*a3/(&rgr;&ngr;2), whereG* is the reduced axial pressure gradient driving the flow, &rgr; is the fluid density, and &ngr; is the kinematic viscosity. WhenR&OHgr;<0.85(R&OHgr;G)1/3andR&OHgr;G>100, the axial velocity profile is skewed toward the pressure side with one maximum occurring on the symmetric plane. WhenR&OHgr;>1.26(R&OHgr;G)2/5andR&OHgr;>10, the axial velocity shows a dumbell‐like profile with the ‘‘dumbell’’ center coinciding with the pipe axis and the ‘‘dumbell’’ axis perpendicular to the symmetric plane. When 0.85(R&OHgr;G)1/3≤R&OHgr;≤1.26(R&OHgr;G)2/5andR&OHgr;G>100, the axial velocity profile is skewed toward the pressure size but with two maxima, occurring symmetrically on both sides of the symmetric plane. The present calculation bridges most of the previous asymptotic analyses and provides a correlation formula for the friction factor ratio between the rotating and stationary pipe flow for most of the laminar regime of engineering interest.

ISSN:0899-8213    

DOI:10.1063/1.857693

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The three‐dimensional (3‐D) instability of a two‐dimensional (2‐D) flow with elliptical streamlines has been proposed as a generic mechanism for the breakdown of many 2‐D flows. A physical interpretation for the mechanism is presented together with an analytical treatment of the problem. It is shown that the stability of an elliptical flow is governed by an Ince equation. An analytical representation for a localized solution is given and establishes a direct link with previous computations and experiments.

ISSN:0899-8213    

DOI:10.1063/1.857682

出版商:AIP    

年代:1990

数据来源: AIP