scholarly journals Steady Stokes flow past dumbbell shaped axially symmetric body of revolution: An analytic approach

2012 ◽  
Vol 39 (3) ◽  
pp. 255-289
Author(s):  
Kumar Srivastava ◽  
Ram Yadav ◽  
Supriya Yadav
Keyword(s):  
Stokes Flow ◽  
Closed Form Expression ◽  
Body Of Revolution ◽  
Axially Symmetric ◽  
Moment Coefficient ◽  
Flow Past ◽  
Flow Situation ◽  
Axis Of Symmetry ◽  
Singularity Distribution ◽  
The Relationship

In this paper, the problem of steady Stokes flow past dumbbell-shaped axially symmetric isolated body of revolution about its axis of symmetry is considered by utilizing a method (Datta and Srivastava, 1999) based on body geometry under the restrictions of continuously turning tangent on the boundary. The relationship between drag and moment is established in transverse flow situation. The closed form expression of Stokes drag is then calculated for dumbbell-shaped body in terms of geometric parameters b, c, d and a with the aid of this linear relation and the formula of torque obtained by (Chwang and Wu, part 1, 1974) with the use of singularity distribution along axis of symmetry. Drag coefficient and moment coefficient are defined in various forms in terms of dumbbell parameters. Their numerical values are calculated and depicted in respective graphs and compared with some known values.

scholarly journals Axisymmertic Stokes flow images in spherical free surfaces with applications to rising bubbles

1983 ◽  
Vol 25 (2) ◽  
pp. 217-231 ◽  
Author(s):  
J. F. Harper
Keyword(s):  
Stokes Flow ◽  
Numerical Solutions ◽  
Free Boundaries ◽  
Rigid Surface ◽  
Axially Symmetric ◽  
Free Surfaces ◽  
Flow Past ◽  
Spherical Bubbles ◽  
Axis Of Symmetry ◽  
First Time

AbstractA theorem is derived for the hydrodynanuc image of an axially symmetric slow viscous (Stokes) flow in a sphere which is impermeable and free of shear stress. A second theorem establishes a sense in which such a flow past an arbitrary rigid surface or shear-free sphere becomes, on inversion in an arbitrary sphere with its centre on the axis of symmetry, a flow past the rigid or shear-free inverse of that surface or sphere.The theorems are used to simplify the proofs of a number of known results for images of point singularities in plane and spherical rigid and free boundaries, and for a pair of bubbles rising steadily in line in a viscous fluid. They also give for the first time accurate numerical solutions for the velocities of each of a larger number of spherical bubbles rising quasi-steadily in line. These enable one to assess the accuracy of simple approximations to those velocities.

Slow steady rotation of axially symmetric bodies in a viscous fluid

1961 ◽  
Vol 10 (1) ◽  
pp. 17-24 ◽  
Author(s):  
R. P. Kanwal
Keyword(s):  
Angular Velocity ◽  
Flow Field ◽  
Viscous Fluid ◽  
Stokes Flow ◽  
Flow Problem ◽  
Analytic Solutions ◽  
The Body ◽  
Axially Symmetric ◽  
Steady Rotation ◽  
Axis Of Symmetry

The Stokes flow problem is considered here for the case in which an axially symmetric body is uniformly rotating about its axis of symmetry. Analytic solutions are presented for the heretofore unsolved cases of a spindle, a torus, a lens, and various special configurations of a lens. Formulas are derived for the angular velocity of the flow field and for the couple experienced by the body in each case.

Axial and transverse Stokes flow past slender axisymmetric bodies

1970 ◽  
Vol 44 (3) ◽  
pp. 401-417 ◽  
Author(s):  
J. P. K. Tillett
Keyword(s):  
Stokes Flow ◽  
Body Shape ◽  
Slenderness Ratio ◽  
The Body ◽  
Axially Symmetric ◽  
Axis Of Symmetry ◽  
Linear Integral ◽  
Axisymmetric Bodies ◽  
Linear Integral Equations ◽  
Uniform Stream

This paper deals with Stokes flow due to a stationary axially symmetric slender body in a uniform stream, which may be either parallel or perpendicular to the axis of the body. The effect of the body is represented by distributions of singularities along a segment of its axis of symmetry. Systems of linear integral equations for these distributions are obtained, and the first few terms of uniformly valid (in the Stokes region) asymptotic expansions in the slenderness ratio are discussed. The leading terms yield the expected result that the drag on the body in a transverse stream is double that in an axial stream. The second approximation to the ratio of these two drags is also independent of the body shape.

Stokes flow past a slender body of revolution

1976 ◽  
Vol 78 (3) ◽  
pp. 577-600 ◽  
Author(s):  
James Geer
Keyword(s):  
Stokes Flow ◽  
Slenderness Ratio ◽  
Slip Boundary Condition ◽  
The Body ◽  
Slender Body ◽  
Total Force ◽  
Body Of Revolution ◽  
Flow Past ◽  
Special Cases ◽  
Slender Body Of Revolution

The complete uniform asymptotic expansion of the velocity and pressure fields for Stokes flow past a slender body of revolution is obtained with respect to the slenderness ratio ε of the body. A completely general incident Stokes flow is assumed and hence these results extend the special cases treated by Tillett (1970) and Cox (1970). The part of the flow due to the presence of the body is represented as a superposition of the flows produced by three types of singularity distributed with unknown densities along a portion of the axis of the body and lying entirely inside the body. The no-slip boundary condition on the body then leads to a system of three coupled, linear, integral equations for the densities of the singularities. The complete expansion for these densities is then found as a series in powers of ε and ε log ε. It is found that the extent of these distributions of singularities inside the body is the same for all the singular flows and depends only upon the geometry of the body. The total force, drag and torque experienced by the body are computed.

scholarly journals Shear-free boundary in Stokes flow

1996 ◽  
Vol 19 (1) ◽  
pp. 145-150 ◽  
Author(s):  
D. Palaniappan ◽  
S. D. Nigam ◽  
T. Amaranath
Keyword(s):  
Free Boundary ◽  
Stokes Flow ◽  
Axially Symmetric ◽  
Symmetric Flow ◽  
Stream Surface ◽  
Flow Past ◽  
Flow Past A Sphere

A theorem of Harper for axially symmetric flow past a sphere which is a stream surface, and is also shear-free, is extended to flow past a doubly-body𝔅consisting of two unequal, orthogonally intersecting spheres. Several illustrative examples are given. An analogue of Faxen's law for a double-body is observed.

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.

The Stokes flow problem for a class of axially symmetric bodies

1960 ◽  
Vol 7 (4) ◽  
pp. 529-549 ◽  
Author(s):  
L. E. Payne ◽  
W. H. Pell
Keyword(s):  
Stream Function ◽  
Stokes Flow ◽  
Flow Problem ◽  
Fluid Motion ◽  
Explicit Calculation ◽  
Axially Symmetric ◽  
Flow Problems ◽  
Fundamental Operator ◽  
Axis Of Symmetry

The Stokes flow problem is concerned with fluid motion about an obstacle when the motion is such that inertial effects can be neglected. This problem is considered here for the case in which the obstacle (or configuration of obstacles) has an axis of symmetry, and the flow at distant points is uniform and parallel to this axis. The differential equation for the stream function ψ then assumes the form L2−1ψ = 0, where L−1 is the operator which occurs in axiallysymmetric flows of the incompressible ideal fluid. This is a particular case of the fundamental operator of A. Weinstein's generalized axially symmetric potential theory. Using the results of this theory and theorems regarding representations of the solutions of repeated operator equations, the authors (1) give a general expression for the drag of an axially symmetric configuration in Stokes flow, and (2) indicate a procedure for the determination of the stream function. The stream function is found for the particular case of the lens-shaped body.Explicit calculation of the drag is difficult for the general lens, without recourse to numerical procedures, but is relatively easy in the case of the hemispherical cup. As examples illustrative of their procedures, the authors briefly consider three Stokes flow problems whose solutions have been given previously.

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