scholarly journals Pulsatile Flow of a Two-Fluid Model for Blood Flow through Arterial Stenosis

2010 ◽  
Vol 2010 ◽  
pp. 1-26 ◽  
Author(s):  
D. S. Sankar
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pulsatile Flow ◽  
Fluid Model ◽  
Core Radius ◽  
Flow Through ◽  
Wall Shear ◽  
Two Fluid Model ◽  
Two Fluid

Pulsatile flow of a two-fluid model for blood flow through stenosed narrow arteries is studied through a mathematical analysis. Blood is treated as two-phase fluid model with the suspension of all the erythrocytes in the as Herschel-Bulkley fluid and the plasma in the peripheral layer as a Newtonian fluid. Perturbation method is used to solve the system of nonlinear partial differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The variations of these flow quantities with stenosis size, yield stress, axial distance, pulsatility and amplitude are analyzed. It is found that pressure drop, plug core radius, wall shear stress and resistance to flow increase as the yield stress or stenosis size increases while all other parameters held constant. It is observed that the percentage of increase in the magnitudes of the wall shear stress and resistance to flow over the uniform diameter tube is considerably very low for the present two-fluid model compared with that of the single-fluid model of the Herschel-Bulkley fluid. Thus, the presence of the peripheral layer helps in the functioning of the diseased arterial system.

Development of a Transient Mechanistic Two-Phase Flow Model for Wellbores

SPE Journal ◽  
2012 ◽  
Vol 17 (03) ◽  
pp. 942-955 ◽  
Author(s):  
Mahdy Shirdel ◽  
Kamy Sepehrnoori
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Flow Regimes ◽  
Phase Flow ◽  
Two Phase ◽  
Wall Shear ◽  
Two Fluid Model ◽  
Two Fluid

Summary A great deal of research has been focused on transient two-phase flow in wellbores. However, there is lack of a comprehensive two-fluid model in the literature. In this paper, we present an implementation of a pseudo-compositional, thermal, fully implicit, transient two-fluid model for two-phase flow in wellbores. In this model, we solve gas/liquid mass balance, gas/liquid momentum balance, and two-phase energy balance equations to obtain five primary variables: liquid velocity, gas velocity, pressure, holdup, and temperature. This simulator can be used as a stand-alone code or can be used in conjunction with a reservoir simulator to mimic wellbore/reservoir dynamic interactions. In our model, we consider stratified, bubbly, intermittent, and annular flow regimes using appropriate closure relations for interphase and wall-shear stress terms in the momentum equations. In our simulation, we found that the interphase and wall-shear stress terms for different flow regimes can significantly affect the model's results. In addition, the interphase momentum transfer terms mainly influence the holdup value. The outcome of this research leads to a more accurate simulation of multiphase flow in the wellbore and pipes, which can be applied to the surface facility design, well-performance optimization, and wellbore damage estimation.

scholarly journals A Physiologic Model for the Problem of Blood Flow through Diseased Blood Vessels

2016 ◽  
Vol 5 (2) ◽  
pp. 58
Author(s):  
Sapna Ratan Shah ◽  
S. U. Siddiqui
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Shape Parameter ◽  
Fluid Model ◽  
Porous Wall ◽  
Volumetric Flow Rate ◽  
Wall Model ◽  
Flow Through ◽  
Wall Shear

This study focuses on the behavior of blood flow through diseased artery in the presence of porous effects. The laminar, incompressible, fully developed, non-Newtonian in an artery having axially non-symmetric but radially symmetric stenosis is numerically studied. Here blood is represented as Herschel-Bulkley fluid model and flow model is shown by the Navier-Stokes and the continuity equations. Using appropriate boundary conditions, numerical expression for volumetric flow rate, pressure drop and wall shear stress have been derived. The expressions are computed numerically and results are presented graphically. The effects of porous parameter on wall shear stress, stenosis length, stenosis size and stenosis shape parameter are discussed. The wall shear stress increases as the porous parameter, stenosis size and stenosis length increases, but as the stenosis shape parameter increases, the wall shear stress decreases. The work shows that the results obtained from the porous wall model are significantly different from those obtained by the rigid wall model.

scholarly journals The Polar Fluid Model for Blood Flow through a Tapered Artery with Overlapping Stenosis: Effects of Catheter and Velocity Slip

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
J. V. Ramana Reddy ◽  
D. Srikanth
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Fluid Flow ◽  
Wall Shear Stress ◽  
Fluid Model ◽  
Velocity Slip ◽  
Maximum Height ◽  
Tapered Artery ◽  
Flow Through ◽  
Wall Shear

The blood flow through an overlapping clogged tapered artery in the presence of catheter is discussed. Since cholesterol deposition is resulting in the stenosis formation, velocity slip at the arterial wall is considered. The equations governing the fluid flow have been solved analytically under the assumption of the mild stenosis. The analysis with respect to various parameters arising out of fluid and geometry considered, on physiological parameters such as impedance and wall shear stress at the maximum height of the stenosis as well as across the entire length of the stenosis has been reported. A table summarizing the locations of extreme heights and the corresponding annular radii is provided. It is observed that the wall shear stress is the same at both the locations corresponding to the maximum height of the stenosis in case of nontapered artery while it varies in case of tapered artery. It is also observed that slip velocity and diverging tapered artery facilitate the fluid flow. Shear stress at the wall is increasing as micropolar parameter is decreasing and the trend is reversed in case of coupling number. The results obtained are validated by comparing them with the experimental and theoretical results.

Mathematical analysis of Phan-Thien–Tanner fluid model for blood in arteries

2015 ◽  
Vol 08 (05) ◽  
pp. 1550064
Author(s):  
Noreen Sher Akbar ◽  
S. Nadeem
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Fluid Model ◽  
Shearing Stress ◽  
Small Arteries ◽  
Tapered Artery ◽  
Impedance Wall ◽  
Flow Through ◽  
Parameters Of Interest

In the present paper, we have studied the blood flow through tapered artery with a stenosis. The non-Newtonian nature of blood in small arteries is analyzed mathematically by considering the blood as Phan-Thien–Tanner fluid. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Exact solutions have been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different type of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.

Achievement of Pentoxifylline for Blood Flow through Stenosed Artery

2012 ◽  
Vol 13 ◽  
pp. 81-89
Author(s):  
Sapna Ratan Shah ◽  
S.U. Siddiqui
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Apparent Viscosity ◽  
Fluid Model ◽  
Plasma Viscosity ◽  
Diabetic Patients ◽  
Newtonian Viscosity ◽  
Stenosed Artery ◽  
Wall Shear

Blood-viscosity reducing drugs like “Pentoxifylline” improve blood flow by making the blood less viscous. The resistance to flow of blood in diabetic patients is higher than in non-diabetic patients. Thus diabetic patients with higher resistance to flow are more prone to high blood pressure. Therefore the resistance to blood flow in case of diabetic patients may be reduced by reducing viscosity of the plasma. Viscosity of plasma can be reducing by giving Pentoxifylline. In this paper an attempt has been made to investigate the blood flow behaviour and significance of non-Newtonian viscosity through a stenosed artery using Bingham Plastic fluid model. Numerical illustrations presented at the end of the paper provide the results for the resistance to flow, apparent viscosity and the wall shear stress through their graphical representations. It has been shown that the resistance to flow, apparent viscosity and wall shear stress increases with the size of the stenosis but these increases are comparatively small due to non-Newtonian behaviour of the blood indicating the usefulness of its rheological character in the functioning of the diseased arterial circulation.

Numerical Simulation of Blood Flow Through Stenosed Vessel

2004 ◽  
Author(s):  
Kimie Onogi ◽  
Kazuhiro Kohge ◽  
Kiyoshi Minemura
Keyword(s):  
Heart Rate ◽  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Flow Behavior ◽  
Pressure Change ◽  
Sinusoidal Waveform ◽  
Stenosed Vessel ◽  
Flow Through ◽  
Wall Shear

This article illustrates numerical results on pulsating blood flow through moderately stenosed blood vessel. Two kinds of waveform, that is, a purely sinusoidal waveform and a non-sinusoidal one just like human blood flow are calculated for two cases of heart rate as 60 and 160 (1/s), and resultant flow behavior such as flow velocities, secondary flow, wall shear stress and pressure change are discussed. The abrupt changes in the pressure and wall shear stress occur on the throat of the stenosis, suggesting that this part is easily damaged by the effects when the heart rate is increased.

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