STEADY STREAMING DUE TO SMALL-AMPLITUDE TORSIONAL OSCILLATIONS OF A SPHERE IN A VISCOUS FLUID

1993 ◽  
Vol 46 (3) ◽  
pp. 501-520 ◽  
Author(s):  
ASHOK GOPINATH
Keyword(s):  
Viscous Fluid ◽  
Small Amplitude ◽  
Torsional Oscillations ◽  
Steady Streaming

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

Steady streaming within a periodically rotating sphere

2008 ◽  
Vol 608 ◽  
pp. 71-80 ◽  
Author(s):  
RODOLFO REPETTO ◽  
JENNIFER H. SIGGERS ◽  
ALESSANDRO STOCCHINO
Keyword(s):  
Series Expansion ◽  
Oscillation Frequency ◽  
Small Amplitude ◽  
Quantitative Agreement ◽  
Torsional Oscillations ◽  
Rotating Sphere ◽  
Good Quantitative Agreement ◽  
Steady Streaming ◽  
Theory And Experiments ◽  
Streaming Flow

We consider the flow in a spherical chamber undergoing periodic torsional oscillations about an axis through its centre, and analyse it both theoretically and experimentally. We calculate the flow in the limit of small-amplitude oscillations in the form of a series expansion in powers of the amplitude, finding that at second order, a steady streaming flow develops consisting of two toroidal cells. This streaming behaviour is also observed in our experiments. We find good quantitative agreement between theory and experiments, and we discuss the dependence of the steady streaming behaviour as both the oscillation frequency and amplitude are varied.

The flow induced by the torsional oscillations of an elliptic cylinder

1995 ◽  
Vol 290 ◽  
pp. 279-298 ◽  
Author(s):  
N. Riley ◽  
M. F. Wybrow
Keyword(s):  
Small Amplitude ◽  
Fluid Motion ◽  
Fluid Flows ◽  
Elliptic Cylinder ◽  
Minor Axis ◽  
Oscillatory Motion ◽  
Torsional Oscillations ◽  
Steady Streaming ◽  
Axis Parallel ◽  
Streaming Flow

We consider the fluid motion induced when an elliptic cylinder performs small-amplitude torsional oscillations about an axis parallel to a generator which passes through either the centre or a point on the major or minor axis of the ellipse. In common with other fluid flows dominated by oscillatory motion, a time-independent, or steady streaming flow develops. This steady streaming exhibits several unusual and unexpected features, which are confirmed by experiment.

Lateral Vibrations of a Rotating Shaft in a Viscous Fluid

1969 ◽  
Vol 36 (4) ◽  
pp. 682-686 ◽  
Author(s):  
Chang-Yi Wang
Keyword(s):  
Viscous Fluid ◽  
Small Amplitude ◽  
Normal Force ◽  
Rotating Shaft ◽  
Steady Streaming ◽  
Fast Rotation ◽  
Lateral Vibrations ◽  
Cylindrical Shaft

A rigid rotating cylindrical shaft is vibrating along a diameter in a viscous fluid. Two different cases are investigated through the method of inner and outer expansions. The case of small amplitude vibrations is characterized by the diffusion of vorticity. The coupling of rotation with vibration introduces a normal force, of both inviscid and viscous origins, perpendicular to the direction of oscillation. As rotation increases, the induced steady streaming becomes more skewed and weaker. The case of fast rotation is characterized by the transport of vorticity. Rotation affects both the drag and normal force. The steady torque is increased due to the induction of a steady secondary rotary flow.

The flow induced by torsional oscillations of infinite planes

1969 ◽  
Vol 37 (2) ◽  
pp. 337-347 ◽  
Author(s):  
A. F. Jones ◽  
S. Rosenblat
Keyword(s):  
Viscous Fluid ◽  
Boundary Layers ◽  
High Frequency ◽  
Small Amplitude ◽  
Second Order ◽  
Torsional Oscillations ◽  
Common Axis ◽  
High Frequency Oscillations

A viscous fluid is confined between two parallel, infinite planes which perform torsional oscillations of small amplitude about a common axis. The resulting flow is studied for the case of high-frequency oscillations, when boundary layers form adjacent to moving surfaces. Particular analysis is made of the second-order, steady, radial-axial streaming. It is shown that in certain circumstances viscosity may be effective throughout the domain of flow, while in others there is a region in which viscosity is negligible.

On the Torsional Oscillations of a Solid Sphere in a Viscous Fluid

1956 ◽  
Vol 23 (4) ◽  
pp. 601-605
Author(s):  
G. F. Carrier ◽  
R. C. Di Prima
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Angular Displacement ◽  
Solid Sphere ◽  
Circumferential Velocity ◽  
Torsional Oscillations ◽  
Viscosity Measurements ◽  
First Approximation ◽  
Viscous Torque ◽  
Solid Bodies

Abstract Most treatments of the torsional oscillations of solid bodies assume that the velocity field is circumferential. In this paper the motion in planes containing the axis of oscillation is also considered. An expansion in terms of the angular displacement ϵ (assumed small) is made. The first approximation to the circumferential velocity is computed, and then used in computing the first approximation to the pumping motion. This is used to compute the correction to the circumferential velocity and, in particular, the correction to the viscous torque. For the range of parameters considered it is found that the correction to the torque is of the order of 0.04ϵ2|N0|, where N0 is the classical viscous torque. This problem is of interest in practical viscosity measurements.

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