Calculation of Unsteady Flows in Curved Pipes

2001 ◽  
Vol 123 (4) ◽  
pp. 869-877 ◽  
Author(s):  
H. A. Dwyer ◽  
A. Y. Cheer ◽  
T. Rutaganira ◽  
N. Shacheraghi
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Mass Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Velocity Profiles ◽  
Frequency Parameter ◽  
Detailed Knowledge ◽  
Curved Pipes ◽  
Wall Shear

Highly unsteady three-dimensional flows in curved pipes with significant variation of flow geometry and flow parameters are studied. Using improvements in computational efficiency, detailed knowledge concerning flow structures is obtained. The numerical solutions of the Navier-Stokes equations have been obtained with a variation of the projection method, and the numerical method was enhanced by new algorithms derived from the physics of the flow. These enhancements include a prediction of the flow unsteady pressure gradient based on fluid acceleration and global pressure field corrections based on mass flow. This new method yields an order of magnitude improvement in the calculation’s efficiency, allowing the study of complex flow problems. Numerical flow simulations for oscillating flow cycles show that the curved pipe flows have a significant inviscid-like nature at high values of the frequency parameter. The shape of the velocity profiles is strongly influenced by the frequency parameter, whereas the influence of variations on the pipe cross-sectional area is shown to be rather weak. For large values of the frequency parameter the flow history strongly influences the low mass flow part of the cycle leading to highly unusual velocity profiles. The wall shear stress is studied for all the flows calculated. Our results show that wall shear stress is sensitive to area constrictions, the frequency parameter, as well as the shape of the entrance profile.

Patient-Specific Modeling of Atherosclerotic Carotid Arteries From Multi-Modality Image Data

2003 ◽  
Author(s):  
Juan R. Cebral ◽  
Christopher Putman ◽  
Richard Pergolizzi ◽  
James E. Burgess
Keyword(s):  
Shear Stress ◽  
Magnetic Resonance ◽  
Wall Shear Stress ◽  
Carotid Arteries ◽  
Stokes Equations ◽  
Duplex Ultrasound ◽  
Flow Patterns ◽  
Patient Specific ◽  
Detailed Knowledge ◽  
Wall Shear

Estimation of the wall shear stress distribution in stenotic carotid arteries is important for assessing risk of stroke. Since there are no reliable experimental methods to determine wall shear stress distributions, realistic patient-specific computational fluid dynamics models are constructed from medical images. Anatomical and physiologic data are obtained from multiple image modalities including 3D rotational angiography, contrast-enhanced magnetic resonance angiography, carotid duplex ultrasound and phase-contrast magnetic resonance. These images are used to construct patient-specific finite element grids and to solve the incompressible Navier-Stokes equations under physiological pulsatile flow conditions. The detailed knowledge of the carotid hemodynamics derived from these models can be used to enhance our understanding of the relationship between flow patterns and symptoms, and ultimately risk of stroke. This methodology can also be used to correllate flow patterns with the outcome of endovascular procedures such as angioplasty and stenting.

scholarly journals Analytical Study of Non-Newtonian Reiner–Rivlin Model for Blood flow through Tapered Stenotic Artery

2020 ◽  
Vol 15 (2) ◽  
pp. 295-312
Author(s):  
Nibedita Dash ◽  
Sarita Singh
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Constitutive Relation ◽  
Flow Rate ◽  
Axial Velocity ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Closed Form Solution ◽  
Wall Shear

Stenosis, the abnormal narrowing of artery, significantly affects dynamics of blood flow due to increasing resistance to flow of blood. Velocity of blood flow, arterial pressure distribution, wall shear stress and resistance impedance factors are altered at different degree of stenosis. Prior knowledge of flow parameters such as velocity, flow rate, pressure drop in diseased artery is acknowledged to be crucial for preventive and curative medical intervention. The present paper develops the solution of Navier–Stokes equations for conservation of mass and momentum for axis-symmetric steady state case considering constitutive relation for Reiner–Rivlin fluid. Reiner–Rivlin constitutive relation renders the conservation equations non-linear partial differential equations. Few semi-analytical and numerical solutions are found to be reported in literature but no analytical solution. This has motivated the present research to obtain a closed-form solution considering Reiner–Rivlin constitutive relation. Solution yields an expression for axial velocity, which is utilized to obtain pressure gradient, resistance impedance and wall shear stress by considering volumetric flow rate as initial condition. The effect of viscosity, cross viscosity, flow rate, taper angle of artery and degree of stenosis on axial velocity, resistance impedance and wall shear stress are studied.

scholarly journals Numerical Simulation of Dispersed Particle-Blood Flow in the Stenosed Coronary Arteries

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Mongkol Kaewbumrung ◽  
Somsak Orankitjaroen ◽  
Pichit Boonkrong ◽  
Buraskorn Nuntadilok ◽  
Benchawan Wiwatanapataphee
Keyword(s):  
Numerical Simulation ◽  
Blood Flow ◽  
Shear Stress ◽  
Coronary Artery ◽  
Pressure Drop ◽  
Wall Shear Stress ◽  
Stokes Equations ◽  
Spherical Shape ◽  
Shear Stresses ◽  
Wall Shear

A mathematical model of dispersed bioparticle-blood flow through the stenosed coronary artery under the pulsatile boundary conditions is proposed. Blood is assumed to be an incompressible non-Newtonian fluid and its flow is considered as turbulence described by the Reynolds-averaged Navier-Stokes equations. Bioparticles are assumed to be spherical shape with the same density as blood, and their translation and rotational motions are governed by Newtonian equations. Impact of particle movement on the blood velocity, the pressure distribution, and the wall shear stress distribution in three different severity degrees of stenosis including 25%, 50%, and 75% are investigated through the numerical simulation using ANSYS 18.2. Increasing degree of stenosis severity results in higher values of the pressure drop and wall shear stresses. The higher level of bioparticle motion directly varies with the pressure drop and wall shear stress. The area of coronary artery with higher density of bioparticles also presents the higher wall shear stress.

scholarly journals Biorheological Model on Flow of Herschel-Bulkley Fluid through a Tapered Arterial Stenosis with Dilatation

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
S. Priyadharshini ◽  
R. Ponalagusamy
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Power Law ◽  
Flow Resistance ◽  
Velocity Profiles ◽  
Arterial Stenosis ◽  
Axial Distance ◽  
Tapered Artery ◽  
Wall Shear

An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move fromr/R=0tor/R=1and it follows a concave pattern when we move fromr/R=0tor/R=-1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature.

scholarly journals Effect of reverse flow on the pattern of wall shear stress near arterial branches

2011 ◽  
Vol 8 (64) ◽  
pp. 1594-1603 ◽  
Author(s):  
A. Kazakidi ◽  
A. M. Plata ◽  
S. J. Sherwin ◽  
P. D. Weinberg
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Steady Flow ◽  
Stokes Equations ◽  
Reverse Flow ◽  
Side Branch ◽  
Navier Stokes ◽  
Wall Region ◽  
Wall Shear ◽  
Near Wall

Atherosclerotic lesions have a patchy distribution within arteries that suggests a controlling influence of haemodynamic stresses on their development. The distribution near aortic branches varies with age and species, perhaps reflecting differences in these stresses. Our previous work, which assumed steady flow, revealed a dependence of wall shear stress (WSS) patterns on Reynolds number and side-branch flow rate. Here, we examine effects of pulsatile flow. Flow and WSS patterns were computed by applying high-order unstructured spectral/hp element methods to the Newtonian incompressible Navier–Stokes equations in a geometrically simplified model of an aorto-intercostal junction. The effect of pulsatile but non-reversing side-branch flow was small; the aortic WSS pattern resembled that obtained under steady flow conditions, with high WSS upstream and downstream of the branch. When flow in the side branch or in the aortic near-wall region reversed during part of the cycle, significantly different instantaneous patterns were generated, with low WSS appearing upstream and downstream. Time-averaged WSS was similar to the steady flow case, reflecting the short duration of these events, but patterns of the oscillatory shear index for reversing aortic near-wall flow were profoundly altered. Effects of reverse flow may help explain the different distributions of lesions.

Axisymmetric Model of an Intracranial Saccular Aneurysm: Theory and Computation

2013 ◽  
Author(s):  
Colin W. Curtis ◽  
Michael L. Calvisi
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Computational Models ◽  
Stokes Equations ◽  
Spherical Geometry ◽  
Element Model ◽  
Saccular Aneurysm ◽  
Vortical Flow ◽  
Axisymmetric Model ◽  
Wall Shear

An axisymmetric model of an intracranial saccular aneurysm is presented and analyzed. The model assumes a simplified spherical geometry for the aneurysm in order to develop insight into the mechanisms that effect wall shear stress and deformation of the membrane. A theoretical model is first developed based on Stokes’ equations for viscous flow in order to derive a stream function that describes vortical flow inside a sphere representative of flow inside a real aneurysm. This flow pattern is implemented in a finite element model of a spherical aneurysm using the software COMSOL Multiphysics. The results indicate close agreement between the theoretical and computational models in terms of the flow streamlines and location of the maximum wall shear stress. Furthermore, the computational model accounts for the deformation and stress of the membrane, showing regions of maximum tension and compression at opposite poles of the saccular membrane. This work elucidates many important results regarding the mechanics of saccular aneurysms and provides a basis for developing more physiologically realistic analyses.

Characterization of a Sudden Expansion Flow Chamber to Study the Response of Endothelium to Flow Recirculation

1995 ◽  
Vol 117 (2) ◽  
pp. 203-210 ◽  
Author(s):  
George A. Truskey ◽  
Kevin M. Barber ◽  
Thomas C. Robey ◽  
Lauri A. Olivier ◽  
Marty P. Combs
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Recirculation Zone ◽  
Numerical Solutions ◽  
Flow Chamber ◽  
Sudden Expansion ◽  
Shear Stresses ◽  
Stress Gradients ◽  
Wall Shear

In order to simulate regions of flow separation observed in vivo, a conventional parallel plate flow chamber was modified to produce an asymmetric sudden expansion. The flow field was visualized using light reflecting particles and the size of the recirculation zone was measured by image analysis of the particles. Finite element numerical solutions of the two and three-dimensional forms of the Navier-Stokes equation were used to determine the wall shear stress distribution and predict the location of reattachment. For two different size expansions, numerical estimates of the reattachment point along the centerline of the flow chamber agreed well with experimental values for Reynolds numbers below 473. Even at a Reynolds number of 473, the flow could be approximated as two-dimensional for 80 percent of the chamber width. Peak shear stresses in the recirculation zone as high as 80 dyne/cm2 and shear stress gradients of 2500 (dyne/cm2)/cm were produced. As an application of this flow chamber, subconfluent bovine aortic endothelial cell shape and orientation were examined in the zone of recirculation during a 24 h exposure to flow at a Reynolds number of 267. After 24 h, gradients in cell orientation and shape were observed within the recirculation zone. At the location of reattachment, where the wall shear stress was zero but the shear stress gradients were large, cells plated at low density were still aligned with the direction of flow. No preferred orientation was observed at the gasket edge where the wall shear stress and shear stress gradients were zero. At higher cell densities, no alignment was observed at the separation point. The results suggest that endothelial cells can respond to spatial gradients of wall shear stress.

Unsteady Wall Shear Stress in Transient Flow Using Electrochemical Method

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
H. Zidouh ◽  
L. Labraga ◽  
M. William-Louis
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Electrochemical Method ◽  
Transient Flow ◽  
Flow Behavior ◽  
Velocity Profiles ◽  
Electrochemical Technique ◽  
Transient Flows ◽  
Acceleration Model ◽  
Wall Shear

Experimental measurements of the wall shear stress combined with those of the velocity profiles via the electrochemical technique and ultrasonic pulsed Doppler velocimetry are used to analyze the flow behavior in transient flows caused by a downstream short pipe valve closure. The Reynolds number of the steady flow based on the pipe diameter is Re=148,600. The results show that the quasisteady approach of representing unsteady friction is valid during the initial phase for relatively large decelerations. For higher decelerations, the unsteady wall shear stress is consistently higher than the quasisteady values obtained from the velocity profiles. Attention has been focused on the friction acceleration model. The results obtained from this study show the ability of the electrochemical method in determining the local unsteady wall shear stress even in severe decelerating transient flows.

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