A flow in the depth of infinite annular cylindrical cavity

Shtern, V. N.

doi:10.1017/jfm.2012.429

Cited by 10 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For this reason, the discovery of a chain of eddies in a slow flow between two inclined planes (Moffatt 1964) has attracted much attention and initiated numerous studies of creeping cellular motions. In steady planar or axisymmetric flows, similar eddies have been found in a plane cavity (Moffatt 1964;Shankar & Deshpande 2000), cone (Wakiya 1976), cylinder (Blake 1979;Hills 2001), in cavities with oppositely moving walls (Gürcan et al 2003;Wilson, Gaskell & Savage 2005), between concentric cones (Hall, Hills & Gilbert 2007) and coaxial cylinders (Shtern 2012a).…”

supporting

confidence: 56%

Patterns of a creeping water-spout flow

Herrada

Shtern²

2014

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

This paper explains a mechanism of eddy formation in a slow air-water motion, driven by the rotating top disk, in a vertical sealed cylinder. The numerical simulations reveal nine changes in the flow topology as water volume fraction H w varies from 0 to 1. At H w around 0.8, there are two large regions of the clockwise meridional circulation, one in air and one in water. These regions are separated by two small cells of the anticlockwise circulation adjacent to the interface near the sidewall in water and near the axis in air. The air cell is a thin layer and topologically is a bubble-ring for 0.745 < H w < 0.785. Alterations of this flow pattern are explored as (i) pressure increases, (ii) the bottom disk co-rotates and (iii) the top-disk rotation speeds up. This paper provides the physical reasoning behind the flow transformations; the results are of fundamental interest and can be utilized in bioreactors.

show abstract

supporting

confidence: 56%

Patterns of a creeping water-spout flow

Herrada

Shtern²

2014

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Eddies disappear as the angle between the planes enlarges and passes a threshold. Similar cellular flow patterns have been found in in a plane cavity [1,2], cone [3], cylinder [4,5], between concentric cones [6] and coaxial cylinders [7].…”

Section: Introductionsupporting

confidence: 77%

Patterns of a slow air–water flow in a semispherical container

Balci

Brøns

Herrada

et al. 2016

European Journal of Mechanics - B/Fluids

View full text Add to dashboard Cite

“…Finally, considering that the impermeability boundary condi tion, vz = 0, is uniform along the liquid surface, which means that = 0, the previous boundary condition (18) can be turned into a Dirichlet condition for the nonprimitive variable, This last boundary condition must be revised in case of uniform contamination along the liquid surface (Appendix A). C. Solutions for the ve,oo,f problems Forcing terms of Eqs.…”

Section: B Boundary Conditions As W Ritten In Term S Of Mixed Variablesmentioning

confidence: 99%

“…Most existing studies on annular channel flows have been performed numerically or experimentally [13,[15][16][17], quite often with the aim of investigating the impact of physicochemical contamination along the upper liquid surface. To our knowledge, except for the recent analytical modeling performed by Shtern [18,19] for an annular cavity considered as semi-infinite along the vertical direction, all existing analytical studies devoted to this configuration only focus on the azimuthal flow either when the liquid surface is free of contamination [20] or when it is contaminated [21,22],…”

Section: Introductionmentioning

confidence: 99%

Low-to-moderate Reynolds number swirling flow in an annular channel with a rotating end wall

2015

View full text Add to dashboard Cite

This paper presents a new method for solving analytically the axisymmetric swirling flow generated in a finite annular channel from a rotating end wall, with no-slip boundary conditions along stationary side walls and a slip condition along the free surface opposite the rotating floor. In this case, the end-driven swirling flow can be described from the coupling between an azimuthal shear flow and a two-dimensional meridional flow driven by the centrifugal force along the rotating floor. A regular asymptotic expansion based on a small but finite Reynolds number is used to calculate centrifugation-induced first-order correction to the azimuthal Stokes flow obtained as the solution at leading order. For solving the first-order problem, the use of an integral boundary condition for the vorticity is found to be a convenient way to attribute boundary conditions in excess for the stream function to the vorticity. The annular geometry is characterized by both vertical and horizontal aspect ratios, whose respective influences on flow patterns are investigated. The vertical aspect ratio is found to involve nontrivial changes in flow patterns essentially due to the role of corner eddies located on the left and right sides of the rotating floor. The present analytical method can be ultimately extended to cylindrical geometries, irrespective of the surface opposite the rotating floor: a wall or a free surface. It can also serve as an analytical tool for monitoring confined rotating flows in applications related to surface viscosimetry or crystal growth from the melt.

show abstract

A flow in the depth of infinite annular cylindrical cavity

Cited by 10 publications

References 15 publications

Patterns of a creeping water-spout flow

Patterns of a creeping water-spout flow

Patterns of a slow air–water flow in a semispherical container

Low-to-moderate Reynolds number swirling flow in an annular channel with a rotating end wall

Contact Info

Product

Resources

About