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.

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.

Cylindrical tank of fluid oscillating about a state of steady rotation

1970 ◽  
Vol 41 (3) ◽  
pp. 581-592 ◽  
Author(s):  
Chang-Yi Wang
Keyword(s):  
Boundary Layer ◽  
Angular Velocity ◽  
Flow Field ◽  
Boundary Layers ◽  
Experimental Measurements ◽  
Centrifugal Forces ◽  
Cylindrical Tank ◽  
Side Walls ◽  
Steady Rotation ◽  
Axis Of Symmetry

A cylindrical tank, full of fluid, is oscillating with frequency ω and rotating with angular velocity Ω about its axis of symmetry. It is assumed that the amplitude of oscillation, δ, is small and the viscosity is low such that boundary layers exist. Analysis shows that the unsteady boundary layer is of thickness [ε/(1 − 2Ω/ω)]½ on the top and bottom plates and of thickness ε½ on the side walls, where ε = ν/2ω. The interior unsteady flow shows source-like behaviour at the corners. The steady flow field is caused by the steady component of the non-linear centrifugal forces coupled with an induced steady rotation of the interior. This rotation, of order δ2ω, is prograde when Ω/ω < 0·118 and retrograde otherwise. Maximum retrograde rotation occurs at Ω/ω = 0·5. A steady boundary layer of thickness [ε/(1 − 2Ω/ω)]½ exists on the top and bottom plates, and of thicknesses \[ \epsilon^{\frac{1}{2}},\quad (\nu/L^2\Omega)^{\frac{1}{3}},\quad (\nu/L^2\Omega)^{\frac{1}{4}} \] on the side walls. Experimental measurements of the interior induced steady rotation compare well with theory.

Flow due to a point source of momentum in a viscous fluid contained in a sphere

1967 ◽  
Vol 63 (1) ◽  
pp. 249-256
Author(s):  
K. B. Ranger
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Stokes Flow ◽  
Fluid Motion ◽  
Perturbation Expansion ◽  
General Term ◽  
Axially Symmetric ◽  
Order Of Magnitude ◽  
Self Consistency ◽  
Viscous Fluid Motion

AbstractIt is argued that the zero Reynolds limit of the steady incompressible axially symmetric viscous fluid motion interior to a sphere due to a Landau source at the centre is a Stokes flow. The first three terms of the perturbation expansion are determined and the order of magnitude of the general term not derivable from the Landau source is established. Comparison of the convection terms with the diffusion terms for each order of the Reynolds number demonstrates self consistency at each stage of the expansion.

scholarly journals Конвективный теплообмен во вращающемся полом цилиндре с торцевой стенкой

2020 ◽  
Vol 46 (14) ◽  
pp. 29
Author(s):  
В.А. Архипов ◽  
О.В. Матвиенко ◽  
А.С. Жуков ◽  
Н.Н. Золоторёв
Keyword(s):  
Heat Transfer ◽  
Angular Velocity ◽  
Flow Field ◽  
Convective Heat Transfer ◽  
Hollow Cylinder ◽  
Convective Heat ◽  
Axis Of Symmetry ◽  
End Wall

The method and results of calculating the flow field and convective heat transfer in a hollow cylinder with end wall rotating around the axis of symmetry with varying angular velocity and height of the cylinder are presented

The forces on a body moving through a viscous fluid

1992 ◽  
Vol 437 (1899) ◽  
pp. 185-193 ◽  
Keyword(s):  
Flow Field ◽  
Viscous Fluid ◽  
Arbitrary Shape ◽  
Stokes Equations ◽  
The Body ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Explicit Formulae ◽  
Approximate Equations

The forces on a body moving through a viscous fluid are related to the asymptotic flow field at large distances from the body and can be deduced therefrom. Explicit formulae are derived for the force and couple in terms of the parameters defining the asymptotic flow field. The form of these results remains unchanged for a body of arbitrary shape moving in two or three dimensions, and for a body rotating as well as translating, provided the flow is steady relative to an appropriate set of axes. They are also applicable when the Navier–Stokes equations are replaced by approximate equations, as in the work of Stokes and Oseen.

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.

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