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.

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.

A Lagrangian Reactive Transport Simulator with Successive Paths and Stationary-States: Concepts, Implementation and Verification

1989 ◽  
Vol 176 ◽  
Author(s):  
R. B. Knapp
Keyword(s):  
Reference Frame ◽  
Peclet Number ◽  
Software Package ◽  
Reactive Transport ◽  
Quantitative Agreement ◽  
Stationary States ◽  
Good Quantitative Agreement ◽  
Analytical Results ◽  
Single Path ◽  
Aqueous Species

ABSTRACTA geochemical software package which models static, single-path kinetic water-rock interactions, EQ3/6, has been modified to incorporate successive-paths and stationary states under high Peclet number transport conditions in a Lagrangian reference frame. These modifications permit calculation of reactive transport with reasonable computational requirements. Results from the new option in EQ3/6 have been compared with analytical results for the simple HC1 - SiO2 system; excellent agreements were achieved. Results have also been compared with published results for a portion of the A12O3 - HCI - K2O - SiO2 system. The results are in good qualitative and, in some cases, good quantitative agreement. However, the values of some variables differ substantially; these differences can be attributed to use of a different set of Al and Si aqueous species.

Evolution of Matt Surface Topography in Aluminium Pack Rolling

2005 ◽  
Author(s):  
Hiroshi Utsunomiya ◽  
Michael P. F. Sutcliffe ◽  
Hugh R. Shercliff ◽  
Pete S. Bate ◽  
Dan B. Miller
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Surface Topography ◽  
Material Properties ◽  
Quantitative Agreement ◽  
Aluminium Foil ◽  
The Finite Element Method ◽  
Good Quantitative Agreement ◽  
Pack Rolling ◽  
Element Method

Roughening of the matt surface of pack rolled aluminium foil has been modelled. The model is based on the finite element method using isotropic plasticity. A distribution in material properties has been used to simulate the distribution of orientations through the material. The predictions of roughness show good quantitative agreement with the experiments.

Steady streaming induced by a cylinder performing transverse and torsional oscillations

1991 ◽  
Vol 3 (5) ◽  
pp. 782-792 ◽  
Author(s):  
A. A. Panagopoulos ◽  
Z. M. Psillakis ◽  
G. T. Karahalios
Keyword(s):  
Torsional Oscillations ◽  
Steady Streaming

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.

Visualization and Measurement of Steady Streaming Induced in Oscillating Flow

2004 ◽  
Author(s):  
Hideyuki Nakayama ◽  
Haruhiko Mori ◽  
Jun Shimizu ◽  
Takahiro Ito ◽  
Hideo Nakamura ◽  
...  
Keyword(s):  
Excitation Frequency ◽  
Oscillating Flow ◽  
Stagnation Region ◽  
Piv Measurements ◽  
Steady Streaming ◽  
Driving Mechanisms ◽  
Interface Wave ◽  
Order Of Magnitude ◽  
Zero Time ◽  
Streaming Flow

Non-zero time averaged flows can be induced in fluctuating flows. Shimizu et al. found such time-averaged streaming to occur in stratified fluids excited in a vertical, stationary cylinder at a frequency close to the natural frequency of the axisymmetric interface wave [1]. PIV measurements have revealed intermittent formation of a stagnation region close the fluid-fluid interface that enables a jet-like flow departing from the center of the interface to be sustained over cycles. The jet-like flow induces a recirculating streaming flow that extends several diameters away from the interface. Difficulty still remains in quantifying experimentally the detailed flow structure and defining the driving mechanisms, since the streaming is more than one order of magnitude smaller than the forced oscillating flow. The present paper presents PIV data that show temporal evolution of the flow in each cycle, the effect of fluid viscosities and the excitation frequency and amplitude.

scholarly journals Capillary bridges between a plane and a cylindrical wall

2015 ◽  
Vol 773 ◽  
Author(s):  
Etienne Reyssat
Keyword(s):  
Numerical Solution ◽  
Quantitative Agreement ◽  
Horizontal Cylinder ◽  
Numerical Results ◽  
Planar Boundary ◽  
Cylindrical Wall ◽  
Good Quantitative Agreement ◽  
Capillary Bridges

We report experimental, theoretical and numerical results on the shapes of liquid menisci connecting a planar boundary and the surface of a horizontal cylinder placed above. The gradient of confinement traps the wetting drops in the most confined regions, which promotes their elongation along the line of smallest gap between the walls. The experimental shapes of these stretched capillary bridges are shown to be in good quantitative agreement with the numerical solution of the equation describing their contour. In particular, we show that the measured shapes are better described when taking into account the correction resulting from the coupling of in-plane and transverse interfacial curvatures calculated by Park & Homsy (J. Fluid Mech., vol. 139, 1984, pp. 291–308) over thirty years ago.

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