Longitudinal Tension Variation in Collapsible Channels: A New Mechanism for the Breakdown of Steady Flow

1992 ◽  
Vol 114 (1) ◽  
pp. 60-67 ◽  
Author(s):  
T. J. Pedley
Keyword(s):  
Unsteady Motion ◽  
External Pressure ◽  
Collapsible Tube ◽  
Initial Tension ◽  
Viscous Shear Stress ◽  
Flow Reynolds Number ◽  
Viscous Shear ◽  
Upstream Part ◽  
Longitudinal Tension ◽  
Parameter Values

There are several mechanisms potentially involved in the breakdown of steady fluid flow in a collapsible tube under external pressure. Here we investigate one that has received little attention in the past: the fact that the longitudinal tension in the tube wall, T, decreases with distance downstream as a consequence of the viscous shear stress exerted by the fluid. If the tube is long enough, or the initial tension small enough, T may fall to zero before the end of the collapsible tube, and unsteady motion would presumably then ensue; this is what we mean by “breakdown.” We study the phenomenon theoretically, when the flow Reynolds number is of order one, using lubrication theory in a symmetric two-dimensional channel in which the collapsible tube is replaced by membranes occupying a segment of each wall. The resulting nonlinear ordinary differential equations are solved numerically for values of the dimensionless parameters that cover all the qualitatively different types of solution (e.g., in which the channel is distended over all its length, collapsed over all its length, or distended in the upstream part and collapsed downstream). Reducing the longitudinal tension has a marked effect on the shape of the collapsible segment, causing it to become much more deformed for the same flow rate and external pressure. Indeed, the wall slope is predicted to become very large when the downstream tension is very small, so the model is not self-consistent then. Nevertheless, the parameter values for which T becomes zero are mapped out and are expected to be qualitatively useful. The relationships between the values of T during flow and its value before the flow begins is also considered.

scholarly journals Multiple states for flow through a collapsible tube with discontinuities

2014 ◽  
Vol 761 ◽  
pp. 105-122 ◽  
Author(s):  
A. Siviglia ◽  
M. Toffolon
Keyword(s):  
Past History ◽  
Steady State Solution ◽  
External Pressure ◽  
The Other ◽  
Critical Conditions ◽  
Actual State ◽  
Collapsible Tube ◽  
Set Up ◽  
Parameter Values ◽  
Flow States

AbstractWe study the occurrence of the multiple steady states that flows in a collapsible tube can develop under the effect of: (i) geometrical alterations (e.g. stenosis), (ii) variations of the mechanical properties of the tube wall, or (iii) variations of the external pressure acting on the conduit. Specifically, if the approaching flow is supercritical, two steady flow states are possible in a restricted region of the parameter space: one of these flow states is wholly supercritical while the other produces an elastic jump that is located upstream of the variation. In the latter case the flow undergoes a transition through critical conditions in the modified segment of the conduit. Both states being possible, the actual state is determined by the past history of the system, and the parameter values show a hysteretic behaviour when shifting from one state to the other. First we set up the problem in a theoretical framework assuming stationary conditions, and then we analyse the dynamics numerically in a one-dimensional framework. Theoretical considerations suggest that the existence of multiple states is associated with non-uniqueness of the steady-state solution, which is confirmed by numerical simulations of the fully unsteady problem.

scholarly journals Shear models and parametric analysis of the PVC geomembrane-cushion interface in a high rock-fill dam

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245245
Author(s):  
Yun-Feng Liu ◽  
Ke Gu ◽  
Yi-Ming Shu ◽  
Xian-Lei Zhang ◽  
Xin-Xin Liu ◽  
...  
Keyword(s):  
Shear Stress ◽  
Friction Coefficient ◽  
Three Dimensional ◽  
Viscous Friction ◽  
Hydraulic Pressure ◽  
Viscous Shear Stress ◽  
Box Counting ◽  
Viscous Shear ◽  
The Stability ◽  
Hysteresis Friction

As a type of flexible impermeable material, a PVC geomembrane must be cooperatively used with cushion materials. The contact interface between a PVC geomembrane and cushion easily loses stability. In this present paper, we analyzed the shear models and parameters of the interface to study the stability. Two different cushion materials were used: the common extrusion sidewall and non-fines concrete. To simulate real working conditions, flexible silicone cushions were added under the loading plates to simulate hydraulic pressure loading, and the loading effect of flexible silicone cushions was demonstrated by measuring the actual contact areas under different normal pressures between the geomembrane and cushion using the thin-film pressure sensor. According to elastomer shear stress, there are two main types of shear stress between the PVC geomembrane and the cushion: viscous shear stress and hysteresis shear stress. The viscous shear stress between the geomembrane and the cement grout was measured using a dry, smooth concrete sample, then the precise formula parameters of the viscous shear stress and viscous friction coefficient were obtained. The hysteresis shear stress between the geomembrane and the cushion was calculated by subtracting the viscous shear stress from the total shear stress. The formula parameters of the hysteresis shear stress and hysteresis friction coefficient were calculated. The three-dimensional box-counting dimensions of the cushion surface were calculated, and the formula parameters of the hysteresis friction were positively correlated with the three-dimensional box dimensions.

scholarly journals Enhanced effects from tiny flexible in-wall blips and shear flow

2015 ◽  
Vol 772 ◽  
pp. 16-41 ◽  
Author(s):  
Luisa Pruessner ◽  
Frank Smith
Keyword(s):  
Boundary Layer ◽  
Interactive Effect ◽  
Fluid Motion ◽  
Unsteady Motion ◽  
Local Motion ◽  
Second Stage ◽  
Order Of Magnitude ◽  
High Reynolds ◽  
Parameter Values ◽  
Nonlinear Solutions

Fluid motion at high Reynolds number over a flexible in-wall blip (a compliant bump or dip in an otherwise fixed wall) is considered theoretically for a very short blip buried low inside a boundary layer. Only the near-wall shear of the oncoming flow affects the local motion past the tiny blip. Slowly evolving features are examined first to allow for variations in the incident flow. Linear and nonlinear solutions show that at certain parameter values (eigenvalues) intensifications occur in which the interactive effect on flow and blip shape is larger by an order of magnitude than at most parameter values. Similar findings apply to the boundary layer with several tiny blips present or to channel flows with blips of almost any length. These intensifications lead on to fully nonlinear unsteady motion as a second stage, after some delay, thus combining with finite-time breakups to form a distinct path into transition of the flow.

PIV Experiments to Measure the Velocity Field Just Downstream of an Oscillating Collapsible Tube

2007 ◽  
Author(s):  
Christopher D. Bertram ◽  
Nicholas K. Truong ◽  
Stephen D. Hall
Keyword(s):  
Cardiac Output ◽  
Cross Section ◽  
Venous Return ◽  
Circular Cross Section ◽  
External Pressure ◽  
Forced Expiration ◽  
Collapsible Tube ◽  
Pulmonary Capillaries ◽  
Pulmonary Airways ◽  
Almost All

Almost all vascular conduits in the human body, being flexible, collapse elastically to a non-circular cross-section when the external pressure sufficiently exceeds the internal. Examples include the brachial artery (sphygmomanometry), veins (everyday manoeuvres), pulmonary airways (forced expiration), pulmonary capillaries (zones 1 and 2), and the urethra (micturition). Venous collapse is involved in regulation of venous return, which in turn regulates cardiac output.

scholarly journals Winds and feedback from supermassive black holes accreting at low rates: hydrodynamical treatment

2020 ◽  
Vol 492 (2) ◽  
pp. 2553-2571 ◽  
Author(s):  
Ivan Almeida ◽  
Rodrigo Nemmen
Keyword(s):  
Black Holes ◽  
Initial Conditions ◽  
Rest Mass ◽  
Host Galaxy ◽  
Feedback Effects ◽  
Accretion Flows ◽  
Viscous Shear Stress ◽  
Viscous Shear ◽  
Thermally Driven ◽  
Hydrodynamical Simulations

ABSTRACT Outflows produced by a supermassive black hole (SMBH) can have important feedback effects in its host galaxy. An unresolved question is the nature and properties of winds from SMBHs accreting at low rates in low-luminosity active galactic nuclei (LLAGNs). We performed two-dimensional numerical, hydrodynamical simulations of radiatively inefficient accretion flows on to non-spinning black holes. We explored a diversity of initial conditions in terms of rotation curves and viscous shear stress prescriptions, and evolved our models for very long durations of up to 8 × 105GM/c3. Our models resulted in powerful subrelativistic, thermally driven winds originated from the corona of the accretion flow at distances 10−100 GM/c2 from the SMBH. The winds reached velocities of up to 0.01c with kinetic powers corresponding to $0.1\!-\!1 {\,{\rm per\, cent}}$ of the rest-mass energy associated with inflowing gas at large distances, in good agreement with models of the ‘radio mode’ of AGN feedback. The properties of our simulated outflows are in broad agreement with observations of winds in quiescent galaxies that host LLAGNs, which are capable of heating ambient gas and suppressing star formation.

On the radial structure of planetary rings

1984 ◽  
Vol 75 ◽  
pp. 431-437 ◽  
Author(s):  
A.W. Harris ◽  
W.R. Ward
Keyword(s):  
Shear Stress ◽  
Optical Depth ◽  
Orbital Velocity ◽  
Planetary Rings ◽  
Radial Gradient ◽  
Viscous Shear Stress ◽  
Viscous Shear ◽  
Radial Structure ◽  
Uniform Ring ◽  
Increasing Function

ABSTRACTA ring of particles in orbit about a planet experiences a viscous shear stress due to the radial gradient of orbital velocity. This stress tends to spread the ring with time. At low optical depth (τ ≲ 0.5), and again at high optical depth (τ ≳ 2), the shear stress is an increasing function of optical depth. In the intermediate range (0.5 ≲ x ≲ 2), stress may decrease with increasing τ, leading to a diffusive instability which will tend to break an Initially uniform ring into ringlets of high and low optical depths.

The Yield Stress for an Electrorheological Fluid in Squeeze

2001 ◽  
Author(s):  
Ali K. El Wahed ◽  
John L. Sproston
Keyword(s):  
Yield Stress ◽  
Electrorheological Fluid ◽  
Strain Characteristic ◽  
Viscous Shear Stress ◽  
Viscous Shear ◽  
Direction Dependence ◽  
Force Velocity ◽  
Displacement Force ◽  
Er Fluid

Abstract This paper is concerned with an experimental and theoretical determination of the rheological performance of an electrorhcological (ER) fluid when subjected to time-dependent applied loads. The experimental facility was built as a squeeze cell in which the fluid is sandwiched between two electrodes, one fixed and the other moving, which permits the instantaneous measurement of the mechanical and electrical responses of the fluid. The transient rheological characteristics of the fluid were assessed for various mechanical force levels and for constant voltage excitation of the fluid. Input and output stress levels across the fluid were monitored enabling the dynamic response of the fluid to be determined using a combination of displacement, force, velocity and acceleration transducers. The experimental results were compared with the results from a modified theoretical analysis, which employs a bi-viscous shear stress/shear strain characteristic of the electrically stressed fluid together with a fluid yield stress, which has a strain-direction dependence on the electrical field.

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