Analysis of Fully Developed Unsteady Viscous Flow in a Curved Elastic Tube Model to Provide Fluid Mechanical Data for Some Circulatory Path-Physiological Situations and Assist Devices

1979 ◽  
Vol 101 (2) ◽  
pp. 114-123 ◽  
Author(s):  
K. B. Chandran ◽  
R. R. Hosey ◽  
D. N. Ghista ◽  
V. W. Vayo
Keyword(s):  
Shear Stress ◽  
Unsteady Flow ◽  
Steady Flow ◽  
Pulsatile Flow ◽  
Flow Patterns ◽  
Elastic Tube ◽  
Flow Component ◽  
Flow Response ◽  
Elastic Tubes ◽  
Flow Components

The unsteady and steady flow components of pulsatile flow response, to an experimentally monitored representative pressure pulse, are computed to provide fluid mechanical data for the etiology of arteriosclerosis at arterial curvature sites and for the design analysis of some extracorporeal dialysis and oxygenatory systems. The unsteady flow component of pulsatile flow in curved elastic tubes is simulated by the superposition of the first six Fourier components of a derived oscillatory flow solution of a viscous, incompressible fluid through an elastic tube of small curvature. The computer flow patterns, wall shear stress and hoop and axial stresses in the wall, due to unsteady and steady flow components of pulsatile flow response, are compared and their implications are discussed. The results show that the unsteady component yields shear stress of an order of magnitude greater than the steady flow, but the steady flow component has a greater variation in the shear stress distribution over a cross section. The steady and unsteady flow patterns are presented for several values of the tube diameters and curvature parameters typical of major arteries in the human circulatory system. The flow pattern and the stress variations could also prove useful in the design of extracorporeal systems such as dialysis machines and oxygenators.

Vortex Generation in Pulsatile Flow Through Arterial Bifurcation Models Including the Human Carotid Artery

1988 ◽  
Vol 110 (3) ◽  
pp. 166-171 ◽  
Author(s):  
Takayoshi Fukushima ◽  
Tatsuji Homma ◽  
Kiyohito Harakawa ◽  
Noriyuki Sakata ◽  
Takehiko Azuma
Keyword(s):  
Steady Flow ◽  
Pulsatile Flow ◽  
Separation Bubble ◽  
Vortex Formation ◽  
Flow Distribution ◽  
Horseshoe Vortex ◽  
Helical Flow ◽  
Elastic Tube ◽  
Recirculating Flow ◽  
Flow Through

Visualization experiments were performed to elucidate the complicated flow pattern in pulsatile flow through arterial bifurcations. Human common carotid arteries, which were made transparent, and glass-models simulating Y- and T-shaped bifurcations were used. Pulsatile flow with wave forms similar to those of arterial flow was generated with a piston pump, elastic tube, airchamber, and valves controlling the outflow resistance. Helically recirculating flow with a pattern similar to that of the horseshoe vortex produced around wall-based protuberances in circular tubes was observed in pulsatile flow through all the bifurcations used in the present study. This flow type, which we shall refer to as the horseshoe vortex, has also been demonstrated to occur at the human common carotid bifurcation in steady flow with Reynolds numbers above 100. Time-varying flows also produced the horseshoe vortex mostly during the decelerating phase. Fluid particles of dye solution approaching the bifurcation apex diverged, divided into two directions perpendicularly, and then showed helical motion representing the horseshoe vortex formation. While this helical flow was produced, the stagnation points appeared on the wall upstream of the apex. Their position was dependent upon the flow distribution ratio between the branches in the individual arteries. The region affected by the horseshoe vortex was smaller during pulsatile flow than during steady flow. Lowering the Reynolds number together with the Womersley number weakened the intensity of helical flow. A separation bubble, resulting from the divergence or wall roughness, was observed at the outer or inner wall of the branch vessels and made the flow more complicated.

Differential effects of pulsatile versus steady flow on coronary endothelial membrane potential

2003 ◽  
Vol 285 (1) ◽  
pp. H341-H346 ◽  
Author(s):  
Wei-Ping Qiu ◽  
Qinghua Hu ◽  
Nazareno Paolocci ◽  
Roy C. Ziegelstein ◽  
David A. Kass
Keyword(s):  
Shear Stress ◽  
Membrane Potential ◽  
Steady Flow ◽  
Pulsatile Flow ◽  
Capillary Flow ◽  
Steady Shear ◽  
Glass Capillary ◽  
Differential Effects ◽  
Channel Inhibition ◽  
Pulsatile Shear Stress

Steady shear stress stimulates transient hyperpolarization coupled to calcium-sensitive potassium (KCa) channels and sustained depolarization linked to chloride-selective channels. Physiological flow is pulsatile not static, and whereas in vivo data suggest phasic shear stress may preferentially activate KCa channels, its differential effects on both currents remain largely unknown. To determine this interaction, coronary endothelial cells were cultured in glass capillary flow tubes, loaded with the voltage-sensitive dye bis-(1,3-dibutylbarbituric acid)trimethine oxonol, and exposed to constant or pulsatile shear stress. The latter was generated by a custom servoperfusion system employing physiological pressure and flow waveforms. Steady shear induced a sustained depolarization inhibited by the Cl- channel blocker DIDS. Even after exposure to steady flow, subsequent transition to pulsatile shear stress further stimulated DIDS-sensitive depolarization. DIDS pretreatment “unmasked” a pulsatile flow-induced hyperpolarization of which magnitude was further enhanced by nifedipine, which augments epoxygenase synthesis. Pulse-shear hyperpolarization was fully blocked by KCa channel inhibition (charybdotoxin + apamin), although these agents had no influence on membrane potential altered by steady flow. Thus KCa-dependent hyperpolarization is preferentially stimulated by pulsatile over steady flow, whereas both can stimulate Cl--dependent depolarization. This supports studies showing greater potency of pulsatile flow for triggering KCa-dependent vasorelaxation.

Investigation of the Effects of Dynamic Change in Curvature and Torsion on Pulsatile Flow in a Helical Tube

2012 ◽  
Vol 134 (7) ◽  
Author(s):  
N. K. C. Selvarasu ◽  
Danesh K. Tafti
Keyword(s):  
Shear Stress ◽  
Coronary Artery ◽  
Wall Shear Stress ◽  
Secondary Flow ◽  
Pulsatile Flow ◽  
Flow Patterns ◽  
Shear Stresses ◽  
Wall Shear ◽  
Vorticity Flux ◽  
Curvature And Torsion

Cardiovascular diseases are the number one cause of death in the world, making the understanding of hemodynamics and the development of treatment options imperative. The effect of motion of the coronary artery due to the motion of the myocardium is not extensively studied. In this work, we focus our investigation on the localized hemodynamic effects of dynamic changes in curvature and torsion. It is our objective to understand and reveal the mechanism by which changes in curvature and torsion contribute towards the observed wall shear stress distribution. Such adverse hemodynamic conditions could have an effect on circumferential intimal thickening. Three-dimensional spatiotemporally resolved computational fluid dynamics (CFD) simulations of pulsatile flow with moving wall boundaries were carried out for a simplified coronary artery with physiologically relevant flow parameters. A model with stationary walls is used as the baseline control case. In order to study the effect of curvature and torsion variation on local hemodynamics, this baseline model is compared to models where the curvature, torsion, and both curvature and torsion change. The simulations provided detailed information regarding the secondary flow dynamics. The results suggest that changes in curvature and torsion cause critical changes in local hemodynamics, namely, altering the local pressure and velocity gradients and secondary flow patterns. The wall shear stress (WSS) varies by a maximum of 22% when the curvature changes, by 3% when the torsion changes, and by 26% when both the curvature and torsion change. The oscillatory shear stress (OSI) varies by a maximum of 24% when the curvature changes, by 4% when the torsion changes, and by 28% when both the curvature and torsion change. We demonstrate that these changes are attributed to the physical mechanism associating the secondary flow patterns to the production of vorticity (vorticity flux) due to the wall movement. The secondary flow patterns and augmented vorticity flux affect the wall shear stresses. As a result, this work reveals how changes in curvature and torsion act to modify the near wall hemodynamics of arteries.

Comparison of Steady and Pulsatile Flow Near the Ventral and Dorsal Walls of Casts of Human Aortic Bifurcations

1984 ◽  
Vol 106 (1) ◽  
pp. 79-82 ◽  
Author(s):  
O. J. Deters ◽  
F. F. Mark ◽  
C. B. Bargeron ◽  
M. H. Friedman ◽  
G. M. Hutchins
Keyword(s):  
Secondary Flow ◽  
Steady Flow ◽  
Pulsatile Flow ◽  
Flow Direction ◽  
Flow Patterns ◽  
Laser Doppler Anemometer ◽  
Common Features ◽  
Fluid Velocities ◽  
Pulsatile Flows ◽  
The Common

Steady and pulsatile flows were passed through casts of human aortic bifurcations and, by means of a laser Doppler anemometer, fluid velocities were measured at selected sites near the ventral and dorsal walls. At these sites, in the vicinity of the bifurcation, the influence of secondary flow is significant and therefore an appreciation of the phasic variation of secondary flow patterns is important. Results are presented comparing the flow direction in both steady and pulsatile flow at sites in three casts. The common features of the flow at these sites were the persistence of the flow direction during the accelerating and decelerating phases of the pulsatile cycle, and the consistently smaller angle (measured from the inlet centerline) of the pulsatile flow direction as compared to the angle of the flow direction in steady flow.

Unsteady flow in a branch

1976 ◽  
Vol 75 (2) ◽  
pp. 315-336 ◽  
Author(s):  
V. O'Brien ◽  
L. W. Ehrlich ◽  
M. H. Friedman
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Atherosclerotic Plaque ◽  
Pulsatile Flow ◽  
Flow Dynamics ◽  
Spatial Distributions ◽  
Two Dimensional ◽  
Wave Shape ◽  
Preliminary Information ◽  
Temporal And Spatial

This study was motivated by the focal tendency of atherosclerotic plaque to appear near arterial junctions. A two-dimensional bifurcation was selected to provide preliminary information on branch flow dynamics. Superseding previous steady flow estimates in similar branches, digital solutions for two flux waves have been obtained to reveal temporal and spatial distributions of shear and separation in pulsatile flow. Marked differences from steady flow are illustrated as well as variation due to flux-wave shape.

scholarly journals Depth-averaged velocity and bed shear stress in unsteady open channel flow over rough bed

2018 ◽  
Vol 40 ◽  
pp. 05071 ◽  
Author(s):  
Jnana Ranjan Khuntia ◽  
Kamalini Devi ◽  
Sebastien Proust ◽  
Kishanjit Kumar Khatua
Keyword(s):  
Shear Stress ◽  
Unsteady Flow ◽  
Steady Flow ◽  
Cross Sections ◽  
Open Channel ◽  
Bed Shear Stress ◽  
Flow Conditions ◽  
Lateral Velocity ◽  
Rough Beds ◽  
Flow Case

Very few studies have been carried out in the past in estimating depth-averaged velocity and bed shear stress in unsteady flow over rough beds. An experiment is thus conducted to investigate the vertical and lateral velocity profiles under unsteady flow conditions in a rough open channel for various flow depths. One hydrogram is repeatedly passed through the rectangular flume with a fixed rigid grass bed. Using micro Pitot tube and Acoustic Doppler Velocimeter (ADV), the flow patterns are investigated at both lateral and longitudinal positions over different cross-sections. For two typical flow depths, the velocities in both the rising limb and falling limb are observed. Hysteresis effect between stage-discharge (h ~ Q) rating curve between rising and falling limbs is illustrated. Lateral distribution of depth-averaged velocity and bed shear stress are plotted at three different cross sections and compared with the steady flow conditions. In falling limb of an unsteady flow case, both depth-averaged velocity and bed shear stress distribution in the central region is higher than that of steady flow case. However, in the rising limb, the bed shear stress of unsteady flow is less than that of steady flow case. Further, in an unsteady flow, the magnitude of depth-averaged velocity is found to increase towards the downstream sections. Along the downstream positions, bed shear stress values increase for lower flow depths and decrease for higher flow depth cases.

Direct numerical simulation of stenotic flows. Part 1. Steady flow

2007 ◽  
Vol 582 ◽  
pp. 253-280 ◽  
Author(s):  
SONU S. VARGHESE ◽  
STEVEN H. FRANKEL ◽  
PAUL F. FISCHER
Keyword(s):  
Shear Stress ◽  
Flow Field ◽  
Steady Flow ◽  
Turbulent Flows ◽  
Pulsatile Flow ◽  
Current Model ◽  
Energy Levels ◽  
Flow Analysis ◽  
Transition To Turbulence ◽  
Hairpin Vortices

Direct numerical simulations (DNS) of steady and pulsatile flow through 75% (by area reduction) stenosed tubes have been performed, with the motivation of understanding the biofluid dynamics of actual stenosed arteries. The spectral-element method, providing geometric flexibility and high-order spectral accuracy, was employed for the simulations. The steady flow results are examined here while the pulsatile flow analysis is dealt with in Part 2 of this study. At inlet Reynolds numbers of 500 and 1000, DNS predict a laminar flow field downstream of an axisymmetric stenosis and comparison to previous experiments show good agreement in the immediate post-stenotic region. The introduction of a geometric perturbation within the current model, in the form of a stenosis eccentricity that was 5% of the main vessel diameter at the throat, resulted in breaking of the symmetry of the post-stenotic flow field by causing the jet to deflect towards the side of the eccentricity and, at a high enough Reynolds number of 1000, jet breakdown occurred in the downstream region. The flow transitioned to turbulence about five diameters away from the stenosis, with velocity spectra taking on a broadband nature, acquiring a -5/3 slope that is typical of turbulent flows. Transition was accomplished by the breaking up of streamwise, hairpin vortices into a localized turbulent spot, reminiscent of the turbulent puff observed in pipe flow transition, within which r.m.s. velocity and turbulent energy levels were highest. Turbulent fluctuations and energy levels rapidly decayed beyond this region and flow relaminarized. The acceleration of the fluid through the stenosis resulted in wall shear stress (WSS) magnitudes that exceeded upstream levels by more than a factor of 30 but low WSS levels accompanied the flow separation zones that formed immediately downstream of the stenosis. Transition to turbulence in the case of the eccentric stenosis was found to be manifested as large temporal and spatial gradients of shear stress, with significant axial and circumferential variations in instantaneous WSS.

Flow Structures at the Proximal Side-to-End Anastomosis. Influence of Geometry and Flow Division

1995 ◽  
Vol 117 (2) ◽  
pp. 224-236 ◽  
Author(s):  
P. E. Hughes ◽  
T. V. How
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Pulsatile Flow ◽  
Critical Reynolds Number ◽  
Flow Patterns ◽  
Time Dependent ◽  
Flow Structures ◽  
Proximal Side ◽  
Flow Division ◽  
Distal Artery

Flow structures were visualized in transparent polyurethane models of proximal side-to-end vascular anastomoses, using planar illumination of suspended tracer particles. Both the effects of geometry and flow division were determined under steady and pulsatile flow conditions, for anastomosis angles of 15, 30, and 45 degrees. The flow patterns were highly three-dimensional and were characterized by a series of vortices in the fully occluded distal artery and two helical vortices aligned with the axis of the graft. In steady flow, above a critical Reynolds number, the flow changed from a laminar regime to one displaying time-dependent behavior. In particular, significant fluctuating velocity components were observed in the distal artery and particles were shed periodically from the occluded artery into the graft. Pairs of asymmetric flow patterns were also observed in the graft, before the onset of the time-dependent flow regime. The critical Reynolds number ranged from 427 to 473 and appeared to be independent of anastomosis angle. The presence of a patent distal artery had a significant effect on the overall flow pattern and led to the formation of a large recirculation region at the toe of the anastomosis. The main structures observed in steady flow, such as vortices in the distal artery and helical flow in the graft, were also seen during the pulsatile cycle. However, the secondary flow components in the graft were more pronounced in pulsatile flow particularly during deceleration of the flow waveform. At higher mean Reynolds numbers, there was also a greater mixing between fluid in the occluded arterial section and that in the graft.

Unidirectional to bidirectional subtidal sandwaves influenced by gradually decreasing steady flow velocity

1997 ◽  
Vol 134 (4) ◽  
pp. 557-561
Author(s):  
KATSUHIRO NAKAYAMA
Keyword(s):  
Grain Size ◽  
Flow Velocity ◽  
Steady Flow ◽  
Periodic Flow ◽  
Southwest Japan ◽  
Unit Thickness ◽  
Flow Components ◽  
Flow Velocities

Miocene subtidal sandwave deposits in southwest Japan were influenced by periodic flow and steady flow. The sandwave deposits can be divided into five units, based on lithofacies and thickness. In order of accretion, unit 1 consists of unidirectional sand bedforms without mud drapes, unit 2 of unidirectional sand bedforms with thin, discontinuous mud drapes, unit 3 of bidirectional sand bedforms with thin continuous mud drapes, and units 4 and 5 of relatively thinner and smaller bidirectional sand bedforms with continuous mud drapes. The thickness of units 1 to 3 increase progressively to 2.6 m, and units 4 to 5 subsequently decrease from 2.0 to 1.0 m. Variations between the units are due to differing combinations of periodic and steady flow velocities. Palaeoflow velocity is estimated from grain size and unit thickness. Depth-mean velocities of steady flow components gradually decrease from 0.72 ms−1 to 0.16 ms−1 with unit accumulation.

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