Stokes flow of a rotating sphere around the axis of a circular orifice or a circular disk

1995 ◽  
Vol 11 (4) ◽  
pp. 307-317 ◽  
Author(s):  
Feng Jianjun ◽  
Zhang Benzhao ◽  
Wu Wangyi
Keyword(s):  
Stokes Flow ◽  
Circular Disk ◽  
Rotating Sphere ◽  
Circular Orifice

Hydromagnetic Stokes flow past a rotating sphere

1978 ◽  
Vol 88 (4) ◽  
pp. 757-768 ◽  
Author(s):  
V. U. K. Sastry ◽  
K. V. Rama Rao
Keyword(s):  
Magnetic Field ◽  
Numerical Methods ◽  
Stokes Flow ◽  
Flow Reversal ◽  
Magnetic Pole ◽  
Rotating Sphere ◽  
Flow Past ◽  
Effects Of Rotation ◽  
The Magnetic Field

In the present investigation we consider hydromagnetic Stokes flow past a rotating sphere. The magnetic field is produced by a magnetic pole placed at the centre of the sphere. The problem is analysed by a combination of perturbation and numerical methods. It is seen that the flow reversal (due to rotation) at the rear portion of the sphere is enhanced as the strength of the magnetic field increases. In addition, we obtain the simultaneous effects of rotation and a magnetic field on the streamlines.

Approach to equilibrium of a rotating sphere in a Stokes flow

2011 ◽  
Vol 57 (2) ◽  
pp. 211-228 ◽  
Author(s):  
Guido Cavallaro ◽  
Carlo Marchioro ◽  
Tetsuro Tsuji
Keyword(s):  
Stokes Flow ◽  
Approach To Equilibrium ◽  
Rotating Sphere

Axisymmetric Stokes flow through a circular orifice in a tube

2005 ◽  
Vol 17 (5) ◽  
pp. 053602 ◽  
Author(s):  
Jae-Tack Jeong ◽  
Sung-Ryul Choi
Keyword(s):  
Stokes Flow ◽  
Circular Orifice ◽  
Flow Through

The separation of Stokes flows

1977 ◽  
Vol 80 (4) ◽  
pp. 785-794 ◽  
Author(s):  
D. H. Michael ◽  
M. E. O'Neill
Keyword(s):  
Global Solution ◽  
Stream Function ◽  
Stokes Flow ◽  
Axisymmetric Flow ◽  
Circular Disk ◽  
Dominant Mode ◽  
The Body ◽  
Spherical Lens ◽  
Local Boundary ◽  
Flow Past

A study is made of the extent to which local boundary geometry can influence separation in a two-dimensional or an axisymmetric Stokes flow. It is shown that a Stokes flow can separate from a point on a smooth body at an arbitrary angle, which can be determined only by reference to the global solution for the flow past the body, and the dominant mode in the stream function near a point of separation is O(r3) in the distance r from the separation point. When the body has a protruding cusped edge it is shown that separation can occur at an arbitrary inclination to the edge which must again be determined from the global solution. In this case the stream function is O(r3/2) near the edge. When the flow is locally within a wedge-shaped region of angle β, where β ≠ π or 2π, and β > 146·3°, it is shown that the dominant modes near the vertex of the wedge are non-separating modes. It follows that, in general, a Stokes flow around such a wedge cannot separate from the vertex. This conclusion is illustrated by reference to the global solution for uniform axisymmetric flow past a spherical lens, in which the structure of the flow near the rim is examined in detail. In the case of a body having a sharp edge of small but non-zero angle protruding into the flow, so that β is very close to 2π, it is shown that separation occurs exceedingly near to the edge. This happens, for example, in the flow past a thin concave-convex lens, for which separation occurs near the rim on the concave side. The analysis also suggests that a similar separation occurs very near the rim on the flatter side of a thin asymmetric biconvex lens. However, for the symmetric biconvex lens, and, as a special case, the circular disk, no separation occurs on either side near the rim. For β < 146·3·, streaming flow into the vertex of a wedge does not occur because of the presence of an infinite set of vortices, and the possibility of separation at the vertex in the sense discussed here does not arise.

Slow viscous flow past a rotating sphere

1971 ◽  
Vol 69 (2) ◽  
pp. 333-336 ◽  
Author(s):  
K. B. Ranger
Keyword(s):  
Stokes Flow ◽  
Rotating Fluid ◽  
Axially Symmetric ◽  
Asymmetric Flow ◽  
Symmetric Flow ◽  
Reversed Flow ◽  
Linear Superposition ◽  
Rotating Sphere ◽  
Flow Past ◽  
Uniform Stream

Keller and Rubinow(l) have considered the force on a spinning sphere which is moving through an incompressible viscous fluid by employing the method of matched asymptotic expansions to describe the asymmetric flow. Childress(2) has investigated the motion of a sphere moving through a rotating fluid and calculated a correction to the drag coefficient. Brenner(3) has also obtained some general results for the drag and couple on an obstacle which is moving through the fluid. The present paper is concerned with a similar problem, namely the axially symmetric flow past a rotating sphere due to a uniform stream of infinity. It is shown that leading terms for the flow consist of a linear superposition of a primary Stokes flow past a non-rotating sphere together with an antisymmetric secondary flow in the azimuthal plane induced by the spinning sphere. For a3n2 > 6Uv, where n is the angular velocity of the sphere, U the speed of the uniform stream, and a the radius of the sphere, there is in the azimuthal plane a region of reversed flow attached to the rear portion of the sphere. The structure of the vortex is described and is shown to be confined to the rear portion of the sphere. A similar phenomenon occurs for a sphere rotating about an axis oblique to the direction of the uniform stream but the analysis will be given in a separate paper.

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