scholarly journals Rheological Behavior of Physiological Pulsatile Flow through a Model Arterial Stenosis with Moving Wall

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Sumaia Parveen Shupti ◽  
Mir Golam Rabby ◽  
Md. Mamun Molla
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Pulsatile Flow ◽  
Stokes Equations ◽  
Nonlinear Function ◽  
Arterial Stenosis ◽  
Curvilinear Coordinates ◽  
Cross Model ◽  
Moving Wall ◽  
Wall Shear

The paper presents a numerical investigation of non-Newtonian modeling effects on unsteady periodic flows in a two-dimensional (2D) constricted channel with moving wall using finite volume method. The governing Navier-Stokes equations have been modified using the Cartesian curvilinear coordinates to handle complex geometries, such as, arterial stenosis. The physiological pulsatile flow has been used at the inlet position as an inlet velocity. The flow is characterized by the Reynolds numbers 300, 500, and 750 that are appropriate for large arteries. The investigations have been carried out to characterize four different non-Newtonian constitutive equations of blood, namely, the (i) Carreau, (ii) Cross, (iii) Modified-Casson, and (iv) Quemada. In these four models, blood viscosity is a nonlinear function of shear rates. The Newtonian model has been investigated to study the physics of fluid and the results are compared with the non-Newtonian viscosity models. The numerical results are presented in terms of streamwise velocity, wall shear stress, pressure distribution as well as the vorticity, streamlines, and vector plots indicating recirculation zones at the poststenotic region. Comparison has also been illustrated in terms of wall pressure and wall shear stress for the Cross model considering different amplitudes of wall oscillation.

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.

scholarly journals Developing Pulsatile Flow in a Deployed Coronary Stent

2005 ◽  
Vol 128 (3) ◽  
pp. 347-359 ◽  
Author(s):  
Divakar Rajamohan ◽  
Rupak K. Banerjee ◽  
Lloyd H. Back ◽  
Ashraf A. Ibrahim ◽  
Milind A. Jog
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Pulsatile Flow ◽  
Thrombus Formation ◽  
Three Dimensional ◽  
Tissue Growth ◽  
Coronary Stent ◽  
Stress Distributions ◽  
Hemodynamic Parameters ◽  
Wall Shear

A major consequence of stent implantation is restenosis that occurs due to neointimal formation. This patho-physiologic process of tissue growth may not be completely eliminated. Recent evidence suggests that there are several factors such as geometry and size of vessel, and stent design that alter hemodynamic parameters, including local wall shear stress distributions, all of which influence the restenosis process. The present three-dimensional analysis of developing pulsatile flow in a deployed coronary stent quantifies hemodynamic parameters and illustrates the changes in local wall shear stress distributions and their impact on restenosis. The present model evaluates the effect of entrance flow, where the stent is placed at the entrance region of a branched coronary artery. Stent geometry showed a complex three-dimensional variation of wall shear stress distributions within the stented region. Higher order of magnitude of wall shear stress of 530dyn∕cm2 is observed on the surface of cross-link intersections at the entrance of the stent. A low positive wall shear stress of 10dyn∕cm2 and a negative wall shear stress of −10dyn∕cm2 are seen at the immediate upstream and downstream regions of strut intersections, respectively. Modified oscillatory shear index is calculated which showed persistent recirculation at the downstream region of each strut intersection. The portions of the vessel where there is low and negative wall shear stress may represent locations of thrombus formation and platelet accumulation. The present results indicate that the immediate downstream regions of strut intersections are areas highly susceptible to restenosis, whereas a high shear stress at the strut intersection may cause platelet activation and free emboli formation.

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.

The Effect of Asymmetry in Abdominal Aortic Aneurysms Under Physiologically Realistic Pulsatile Flow Conditions

2003 ◽  
Vol 125 (2) ◽  
pp. 207-217 ◽  
Author(s):  
E. A. Finol ◽  
K. Keyhani ◽  
C. H. Amon
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pulsatile Flow ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Aortic Aneurysms ◽  
Pulsatile Blood Flow ◽  
Abdominal Aortic ◽  
Wall Shear

In the abdominal segment of the human aorta under a patient’s average resting conditions, pulsatile blood flow exhibits complex laminar patterns with secondary flows induced by adjacent branches and irregular vessel geometries. The flow dynamics becomes more complex when there is a pathological condition that causes changes in the normal structural composition of the vessel wall, for example, in the presence of an aneurysm. This work examines the hemodynamics of pulsatile blood flow in hypothetical three-dimensional models of abdominal aortic aneurysms (AAAs). Numerical predictions of blood flow patterns and hemodynamic stresses in AAAs are performed in single-aneurysm, asymmetric, rigid wall models using the finite element method. We characterize pulsatile flow dynamics in AAAs for average resting conditions by means of identifying regions of disturbed flow and quantifying the disturbance by evaluating flow-induced stresses at the aneurysm wall, specifically wall pressure and wall shear stress. Physiologically realistic abdominal aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50⩽Rem⩽300, corresponding to a range of peak Reynolds numbers 262.5⩽Repeak⩽1575. The vortex dynamics induced by pulsatile flow in AAAs is depicted by a sequence of four different flow phases in one period of the cardiac pulse. Peak wall shear stress and peak wall pressure are reported as a function of the time-average Reynolds number and aneurysm asymmetry. The effect of asymmetry in hypothetically shaped AAAs is to increase the maximum wall shear stress at peak flow and to induce the appearance of secondary flows in late diastole.

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.

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