Pulsatile Blood Flow in a Channel of Small Exponential Divergence—Part II: Steady Streaming Due to the Interaction of Viscous Effects With Convected Inertia

1976 ◽  
Vol 98 (4) ◽  
pp. 707-713 ◽  
Author(s):  
D. J. Schneck ◽  
F. J. Walburn
Keyword(s):  
Viscous Incompressible Fluid ◽  
Exponential Rate ◽  
Inertial Effects ◽  
Pulsatile Blood Flow ◽  
Viscous Effects ◽  
Flow Phenomenon ◽  
Steady Streaming ◽  
Self Consistent ◽  
Downstream Flow ◽  
Streaming Motion

This paper describes a secondary streaming motion that appears during the pulsatile flow of a viscous, incompressible fluid through rigid circular channels having walls which diverge at a slow exponential rate. Arising primarily from the interaction of viscous effects with convected inertial effects, this steady streaming motion acts to continuously retard downstream flow near the wall surface and enhance such flow nearer midstream. The secondary flow phenomenon is shown to be directly proportional to mean Reynolds Number, inversely proportional to the unsteadiness parameter of the flow, and to attenuate with decreasing rates of channel divergence. These effects are all self-consistent and interdependent.

Pulsatile Blood Flow in a Channel of Small Exponential Divergence—I. The Linear Approximation for Low Mean Reynolds Number

1975 ◽  
Vol 97 (3) ◽  
pp. 353-360 ◽  
Author(s):  
D. J. Schneck ◽  
Simon Ostrach
Keyword(s):  
Reynolds Number ◽  
Vascular Endothelium ◽  
Coronary Circulation ◽  
Viscous Incompressible Fluid ◽  
Axial Direction ◽  
Reynolds Numbers ◽  
Pulsatile Blood Flow ◽  
Viscous Effects ◽  
Radial Velocity Component ◽  
Phase Lags

The pulsating flow of a viscous, incompressible fluid through rigid circular channels having walls which diverge at a slow exponential rate is examined analytically. Linearized solutions for low mean Reynolds numbers reveal that viscous effects lead to radially dependent phase shifts between different layers of fluid oscillating in the axial direction, and characteristic phase lags between flow and pressure curves. When the Reynolds number and channel divergence are each small, the flow does not separate, but there is a downstream attenuation of both flow and pressure, together with the appearance of a finite radial velocity component. Utilizing data relevant to basal conditions existing in the major blood vessels of the human coronary circulation, it is found (in the absence of any persistent flow anomalies) that the shear stress at the wall is at least one to two orders of magnitude lower than values reported to be damaging to vascular endothelium.

scholarly journals Strong-field spherical dynamos

2016 ◽  
Vol 789 ◽  
pp. 500-513 ◽  
Author(s):  
Emmanuel Dormy
Keyword(s):  
Strong Field ◽  
Numerical Models ◽  
Weak Field ◽  
Force Balance ◽  
Inertial Effects ◽  
Viscous Effects ◽  
Field Limit ◽  
Magnetic Prandtl Number ◽  
Number Ratio ◽  
Magnetic Diffusivity

Numerical models of the geodynamo are usually classified into two categories: dipolar modes, observed when the inertial term is small enough; and multipolar fluctuating dynamos, for stronger forcing. We show that a third dynamo branch corresponding to a dominant force balance between the Coriolis force and the Lorentz force can be produced numerically. This force balance is usually referred to as the strong-field limit. This solution coexists with the often described viscous branch. Direct numerical simulations exhibit a transition from a weak-field dynamo branch, in which viscous effects set the dominant length scale, and the strong-field branch, in which viscous and inertial effects are largely negligible. These results indicate that a distinguished limit needs to be sought to produce numerical models relevant to the geodynamo and that the usual approach of minimising the magnetic Prandtl number (ratio of the fluid kinematic viscosity to its magnetic diffusivity) at a given Ekman number is misleading.

An experimental investigation of high Reynolds number steady streaming generated by oscillating cylinders

1974 ◽  
Vol 64 (3) ◽  
pp. 589-598 ◽  
Author(s):  
Arnold F. Bertelsen
Keyword(s):  
Boundary Layer ◽  
Experimental Investigation ◽  
Reynolds Number ◽  
Incompressible Fluid ◽  
High Reynolds Number ◽  
Viscous Incompressible Fluid ◽  
Steady Streaming ◽  
Harmonic Motion ◽  
High Reynolds ◽  
Good Agreement

The steady streaming generated in the boundary layer on a cylinder performing simple harmonic motion in a viscous incompressible fluid which is otherwise at rest is investigated in the case where the Reynolds numberRsassociated with this streaming is large. Comparison is made between experimental results obtained here and the theories of Riley (1965) and Stuart (1966). This comparison shows good agreement between the theories and the experiment close to the cylinder, but away from the cylinder significant discrepancies are observed. Possible reasons for these discrepancies are discussed.

Quasi-steady vortical structures in vertically vibrating soap films

1998 ◽  
Vol 372 ◽  
pp. 213-230 ◽  
Author(s):  
JOSÉ M. VEGA ◽  
F. J. HIGUERA ◽  
P. D. WEIDMAN
Keyword(s):  
Numerical Simulations ◽  
Liquid Flow ◽  
Excitation Frequency ◽  
Soap Film ◽  
Soap Films ◽  
Vortical Structures ◽  
Steady Streaming ◽  
Streaming Motion

An analysis of the quasi-steady streaming of the liquid in a vertically vibrated horizontal soap film is reported. The air around the soap film is seen to play a variety of roles: it transmits normal and tangential oscillatory stresses to the film, damps out Marangoni waves, and forces non-oscillatory deflection of the film and tangential motion of the liquid. Non-oscillatory volume forcing originating inside the liquid is also analysed. This forcing dominates the quasi-steady streaming when the excitation frequency is close to the eigenfrequency of a Marangoni mode of the soap film, while both volume forcing in the liquid and surface forcing of the gas on the liquid are important when no Marangoni mode resonates. Different manners by which the combined forcings can induce quasi-steady streaming motion are discussed and some numerical simulations of the quasi-steady liquid flow are presented.

Pulsatile Blood Flow in a Channel of Small Exponential Divergence—III. Unsteady Flow Separation

1977 ◽  
Vol 99 (2) ◽  
pp. 333-338 ◽  
Author(s):  
Daniel J. Schneck
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Steady State ◽  
Flow Separation ◽  
Reynolds Numbers ◽  
Critical Value ◽  
Flow Oscillation ◽  
Pulsatile Blood Flow ◽  
Steady Streaming ◽  
Flow Through

Analysis of pulsatile flow through exponentially diverging channels reveals the existence of critical mean Reynolds numbers for which the flow separates at a downstream axial station. These Reynolds numbers vary directly with the frequency of flow oscillation and inversely with the rate of channel divergence. Increasing the Reynolds number above its critical value results in a rapid upstream displacement of the point of separation. For a tube of fixed geometry, periodic unsteadiness causes flow separation to occur at lower Reynolds numbers and upstream of a corresponding steady-state situation. The point of separation moves progressively downstream, however, towards its steady-state location, as the frequency of oscillation increases. These results are discussed as consequences of the nonlinear steady streaming phenomenon described in an earlier paper.

Boundary-layer flow around a submerged circular cylinder induced by free-surface travelling waves

1996 ◽  
Vol 316 ◽  
pp. 241-257 ◽  
Author(s):  
B. Yan ◽  
N. Riley
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Wave Amplitude ◽  
Perturbation Methods ◽  
Travelling Waves ◽  
Inviscid Flow ◽  
Steady Streaming ◽  
Viscous Forces ◽  
Layer Flow ◽  
Streaming Motion

We consider the fluid flow induced when free-surface travelling waves pass over a submerged circular cylinder. The wave amplitude is assumed to be small, and a suitably defined Reynolds number large, so that perturbation methods may be employed. Particular attention is focused on the steady streaming motion, which induces circulation about the cylinder. The viscous forces acting on the cylinder are calculated and compared with the pressure forces which are solely responsible for the loading on the cylinder in a purely inviscid flow.

scholarly journals Steady streaming around a cylinder pair

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160522 ◽  
Author(s):  
W. Coenen
Keyword(s):  
Reynolds Number ◽  
Oscillatory Flow ◽  
Circular Cylinders ◽  
Flow Topology ◽  
Order Unity ◽  
Steady Streaming ◽  
Stokes Layer ◽  
Streaming Velocity ◽  
Gap Width ◽  
Streaming Motion

The steady streaming motion that appears around a pair of circular cylinders placed in a small-amplitude oscillatory flow is considered. Attention is focused on the case where the Stokes layer thickness at the surface of the cylinders is much smaller than the cylinder radius, and the streaming Reynolds number is of order unity or larger. In that case, the steady streaming velocity that persists at the edge of the Stokes layer can be imposed as a boundary condition to numerically solve the outer streaming motion that it drives in the bulk of the fluid. It is investigated how the gap width between the cylinders and the streaming Reynolds number affect the flow topology. The results are compared against experimental observations.

Analysis and Test of a Robust Sector Thrust Bearing for a Cryogenic Turboalternator

2001 ◽  
Vol 123 (4) ◽  
pp. 768-776
Author(s):  
G. F. Nellis ◽  
M. V. Zagarola ◽  
H. Sixsmith
Keyword(s):  
Thrust Bearing ◽  
Large Temperature ◽  
Cryogenic Temperatures ◽  
Inertial Effects ◽  
Test Results ◽  
Viscous Effects ◽  
Reliable Operation ◽  
Restoring Force ◽  
Thrust Bearings ◽  
Leakage Flows

The miniature turboalternator associated with a reverse-Brayton cryocooler requires geometrically simple, self-acting thrust bearings capable of reliable operation over a large temperature range and insensitive to secondary leakage flows. In order to meet this need, a robust sector thrust bearing has been developed. This thrust bearing is different from a classic stepped sector thrust bearing in that the restoring force at cryogenic temperatures originates primarily from inertial effects while at higher temperatures its restoring force is related primarily to viscous effects. This paper describes the analysis and initial test results for a prototypical robust sector thrust bearing.

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