scholarly journals UNSTEADY MHD POISEUILLE FLOW THROUGH A POROUS CHANNEL UNDER AN OSCILLATING PRESSURE GRADIENT AND UNIFORM SUCTION/INJECTION

2020 ◽  
Author(s):  
Judith Balkissoon ◽  
Sreedhara Gunakala ◽  
Victor Job
Keyword(s):  
Pressure Gradient ◽  
Poiseuille Flow ◽  
Porous Channel ◽  
Uniform Suction ◽  
Flow Through

Hemodynamic Method to Predict Whether Hunterian Ligation of the Basilar Artery Will Lead to Thrombosis of Basilar Bifurcation Aneurysms

Neurosurgery ◽  
1987 ◽  
Vol 20 (2) ◽  
pp. 249-253 ◽  
Author(s):  
Jack Chang ◽  
Margot R. Roach
Keyword(s):  
Pressure Gradient ◽  
Basilar Artery ◽  
Diameter Ratio ◽  
Phase Lag ◽  
Maximal Width ◽  
Before And After ◽  
Simple Measurement ◽  
Flow Through ◽  
Stop Flow

Abstract In some cases, basilar artery aneurysms cannot be repaired surgically and the basilar artery is occluded near the neck of the aneurysm to stop flow into the aneurysm. After the operation, the aneurysm can fill only by flow through the posterior communicating arteries (PCoAs). Hemodynamically, if the flow were the same in both PCoAs and there were no phase lag in the pressures, there would be no pressure gradient for flow to go across the neck of the aneurysm and therefore the aneurysm would thrombose. We have assumed that the diameter of the artery is roughly proportional to the flow that goes through it chronically. We measured the diameters of the PCoAs in 25 patients who had hunterian ligation of the basilar artery. We also measured the maximal width, height, and depth of the aneurysms on angiograms obtained before and after operation. Eleven aneurysms thrombosed completely and had a diameter ratio of > 0.6; 10 aneurysms thrombosed partially and had a diameter ratio of 0.46 ˜ 1.0; 4 aneurysms did not change and had a diameter ratio of <0.45. The ratio of the sizes of the PCoAs pre- and postoperatively was comparable in most cases, so we believe that it is possible to predict reasonably accurately from this simple measurement whether the aneurysm is likely to thrombose if the basilar artery is ligated.

A Topological Study of the Genesis of a Horseshoe Vortex in the Symmetry Plane Due to an Adverse Pressure Gradient

2001 ◽  
Author(s):  
Martijn A. van den Berg ◽  
Michael M. J. Proot ◽  
Peter G. Bakker
Keyword(s):  
Pressure Gradient ◽  
Bifurcation Theory ◽  
Nonlinear Differential Equations ◽  
Nonlinear Dynamical System ◽  
Symmetry Plane ◽  
Adverse Pressure Gradient ◽  
Horseshoe Vortex ◽  
Nonlinear Dynamical ◽  
Separating Flow ◽  
Flow Through

Abstract The present paper describes the genesis of a horseshoe vortex in the symmetry plane in front of a juncture. In contrast to a previous topological investigation, the presence of the obstacle is no longer physically modelled. Instead, the pressure gradient, induced by the obstacle, has been used to represent its influence. Consequently, the results of this investigation can be applied to any symmetrical flow above a flat plate. The genesis of the vortical structure is analysed by using the theory of nonlinear differential equations and the bifurcation theory. In particular, the genesis of a horseshoe vortex can be described by the unfolding of the degenerate singularity resulting from a Jordan Normal Form with three vanishing eigenvalues and one linear term which is related to the adverse pressure gradient. The examination of this nonlinear dynamical system reveals that a horseshoe vortex emanates from a non-separating flow through two subsequent saddle-node bifurcations in different directions and the transition of a node into a focus located in the flow field.

scholarly journals Modal and non-modal linear stability of Poiseuille flow through a channel with a porous substrate

2019 ◽  
Vol 75 ◽  
pp. 29-43 ◽  
Author(s):  
Souvik Ghosh ◽  
Jean-Christophe Loiseau ◽  
Wim-Paul Breugem ◽  
Luca Brandt
Keyword(s):  
Linear Stability ◽  
Poiseuille Flow ◽  
Porous Substrate ◽  
Flow Through

scholarly journals The temporal evolution of neutral modes in the impulsively started flow through a circular pipe and their connection to the nonlinear stability of Hagen–Poiseuille flow

2002 ◽  
Vol 457 ◽  
pp. 339-376 ◽  
Author(s):  
ANDREW G. WALTON
Keyword(s):  
Poiseuille Flow ◽  
Multiple Scales ◽  
Stability Boundary ◽  
Circular Cross Section ◽  
Flow Characteristics ◽  
Internal Flow ◽  
Bypass Transition ◽  
Flow Through ◽  
High Reynolds ◽  
Wave Limit

The linear stability of the impulsively started flow through a pipe of circular cross-section is studied at high Reynolds number R. A crucial non-dimensional time of O(R7/9) is identified at which the disturbance acquires internal flow characteristics. It is shown that even if the disturbance amplitude at this time is as small as O(R−22/27) the subsequent evolution of the perturbation is nonlinear, although it can still be followed analytically using a multiple-scales approach. The amplitude and wave speed of the nonlinear disturbance are calculated as functions of time and we show that as t → ∞, the disturbance evolves into the long-wave limit of the neutral mode structure found by Smith & Bodonyi in the fully developed Hagen–Poiseuille flow, into which our basic flow ultimately evolves. It is proposed that the critical amplitude found here forms a stability boundary between the decay of linear disturbances and ‘bypass’ transition, in which the fully developed state is never attained.

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