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.

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.

Small amplitude oscillations of a thin beam immersed in a viscous fluid near a solid surface

2005 ◽  
Vol 17 (7) ◽  
pp. 073102 ◽  
Author(s):  
Christopher P. Green ◽  
John E. Sader
Keyword(s):  
Viscous Fluid ◽  
Solid Surface ◽  
Small Amplitude ◽  
Thin Beam

Flow in a channel with pulsating walls

1978 ◽  
Vol 88 (2) ◽  
pp. 273-288 ◽  
Author(s):  
T. W. Secomb
Keyword(s):  
Small Amplitude ◽  
Wall Motion ◽  
Pressure Fluctuations ◽  
External Pressure ◽  
Two Dimensional ◽  
Large Mammals ◽  
Steady Streaming ◽  
Amplitude Parameter ◽  
Preceding Work ◽  
Two Dimensional Flow

In this paper calculations are made of the two-dimensional flow field of an incompressible viscous fluid in a long parallel-sided channel whose walls pulsate in a prescribed way. The study covers all values of the unsteadiness parameter α and the steady-streaming Reynolds number. The wall motion is, in general, assumed to be of small amplitude and sinusoidal. Particular attention is given to the steady component of the flow at second order in the amplitude parameter ε. The results for the corresponding problem in axisymmetric geometry are given in an appendix.Next the following problem is considered: the calculation of the wall motion which will result, in response to prescribed unsteady pressures imposed at the ends of the channel and outside its walls, if the walls are assumed to respond elastically to variations in transmural pressure. It is found that the system has a natural frequency of oscillation, and that resonance will occur if this frequency is close to a multiple of the frequency of the external pressure fluctuations. Finally the preceding work is applied in a discussion of blood flow in the coronary arteries of large mammals.

Sign in / Sign up

Export Citation Format

Share Document