Analysis of Blood flow Through Artery with Mild Stenosis

2020 ◽  
Vol 25 (2) ◽  
pp. 33-38
Author(s):  
Puskar R. Pokhrel ◽  
Jeevan Kafle ◽  
Parameshwari Kattel ◽  
Hari Prasad Gaire
Keyword(s):  
Blood Flow ◽  
Pressure Drop ◽  
Stokes Equations ◽  
Arterial Stenosis ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Navier Stokes Equations ◽  
Other Substances ◽  
Blood Flow Dynamics ◽  
Flow Through

Arterial stenosis is an abnormal condition in arteries due to the deposition of fats and other substances, called atherosclerosis.  As it restricts the blood flow, it may induce a heart attack. Employing the Navier-Stokes equations, we consider the blood flow in an artery with the presence of a stenosis in an axisymmetric shape. We analyze the blood flow dynamics in cylindrical form by evaluating pressure, pressure drop against the wall, shear stress on the wall. We also analyze the dynamics by evaluating the ratio of pressure drop with stenosis to the pressure drop without stenosis against the wall, and the ratio of maximum to minimum shear stresses with the ratios of various thicknesses of stenosis to radius of the artery.

scholarly journals Numerical simulation of pulsatile blood flow: a study with normal artery, and arteries with single and multiple stenosis

2021 ◽  
Vol 68 (1) ◽  
Author(s):  
Md. Alamgir Kabir ◽  
Md. Ferdous Alam ◽  
Md. Ashraf Uddin
Keyword(s):  
Blood Flow ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Area Reduction ◽  
Significant Difference ◽  
Stenosed Artery ◽  
Fluid Properties ◽  
Flow Through

AbstractNumerical simulations of pulsatile transitional blood flow through symmetric stenosed arteries with different area reductions were performed to investigate the behavior of the blood. Simulations were carried out through Reynolds averaged Navier-Stokes equations and well-known k-ω model was used to evaluate the numerical simulations to assess the changes in velocity distribution, pressure drop, and wall shear stress in the stenosed artery, artery with single and double stenosis at different area reduction. This study found a significant difference in stated fluid properties among the three types of arteries. The fluid properties showed a peak in an occurrence at the stenosis for both in the artery with single and double stenosis. The magnitudes of stated fluid properties increase with the increase of the area reduction. Findings may enable risk assessment of patients with cardiovascular diseases and can play a significant role to find a solution to such types of diseases.

scholarly journals Numerical Modeling of Blood Flow in Irregular Stenosed Artery with the Effects of Gravity

2013 ◽  
Vol 62 (3) ◽  
Author(s):  
Tan Yan Bin ◽  
Norzieha Mustapha
Keyword(s):  
Blood Flow ◽  
Gravitational Force ◽  
Stokes Equations ◽  
Numerical Study ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Stenosed Artery ◽  
Flow Through

A numerical study on the influences of gravitational force on an unsteady two–dimensional nonlinear model of blood flow through a stenosed artery is presented. Blood flow through the constricted region with an irregular stenosis is considered as incompressible Newtonian fluid. The governing equations are derived from the Navier–Stokes equations, which also comprise a significant term for gravitational force in the axial momentum equation. The numerical method chosen in this study is the finite difference approximations based on Marker and Cell (MAC) method at which governing equations are develop in staggered grids for discretization. The Poisson equation of pressure is solved by successive–over–relaxation (S.O.R.) method. Pressure–velocity corrector is imposed to increase accuracy. Streamlines, wall shear stress and axial velocity profiles are plotted.

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

A 3D Unsteady Flow Analysis in a Doubly Constricted Tube

2000 ◽  
Author(s):  
B. V. Rathish Kumar ◽  
T. Yamaguchi ◽  
H. Liu ◽  
R. Himeno
Keyword(s):  
Pressure Drop ◽  
Unsteady Flow ◽  
Stokes Equations ◽  
Vortex Formation ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
In Series ◽  
3D Unsteady Flow

Abstract Unsteady flow dynamics in a doubly constricted vessel is analyzed by using a time accurate Finite Volume solution of three dimensional incompressible Navier-Stokes equations. Computational experiments are carried out for various values of Reynolds number in order to assess the criticality of multiple mild constrictions in series and also to bring out the subtle 3D features like vortex formation. Studies reveal that pressure drop across a series of mild constrictions can get physiologically critical. Further this pressure drop is found to be sensitive to the spacing between the constrictions and also to the oscillatory nature of the inflow profile.

scholarly journals Off-Design Performance Prediction for Radial-Flow Impellers

1988 ◽  
Author(s):  
Shen C. Lee ◽  
Daying Chen
Keyword(s):  
Stokes Equations ◽  
Mechanical Energy ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Pump Impeller ◽  
Navier Stokes Equations ◽  
Measured Velocity ◽  
Production Water ◽  
Performance Predictions ◽  
Stream Functions

A numerical method was developed to consider the two-dimensional flowfield between impeller blades of a given geometry. Solution of the laminar Navier-Stokes equations in geometry-oriented coordinates was obtained for stream functions and vorticities. Velocities and pressures were calculated to determine the output fluid-energy head. The circumferential components of the normal and shear stresses along the blade were evaluated to give the input mechanical-energy head. Performance predictions were obtained for different load conditions. Comparisons were made with the measured velocity vectors of the flowfield of an air-pump impeller and with the measured performance of a production water pump, good agreements were reached.

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 Modelling and Analysis of Complex Viscous Fluid in Thin Elastic Tubes

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yufang Gao ◽  
Zongguo Zhang
Keyword(s):  
Cardiovascular Disease ◽  
Blood Flow ◽  
Viscous Fluid ◽  
Boussinesq Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Term ◽  
Thin Tube ◽  
Elastic Tubes

Cardiovascular disease is a major threat to human health. The study on the pathogenesis and prevention of cardiovascular disease has received special attention. In this paper, we have contributed to the derivation of a mathematical model for the nonlinear waves in an artery. From the Navier–Stokes equations and continuity equation, the vorticity equation satisfied by the blood flow is established. And based on the multiscale analysis and perturbation method, a new model of the Boussinesq equation with viscous term is derived to describe the propagation of a viscous fluid through a thin tube. In order to be more consistent with the flow of the fluid, the time-fractional Boussinesq equation with viscous term is deduced by employing the semi-inverse method and the fractional variational principle. Moreover, the approximate analytical solution of the fractional equation is obtained, and the effect of viscosity on the amplitude and width of the wave is studied. Finally, the effects of the fractional order parameters and vessel radius on blood flow volume are discussed and analyzed.

Effect of a Time-Dependent Stenosis on Flow Through a Tube

1968 ◽  
Vol 90 (2) ◽  
pp. 248-254 ◽  
Author(s):  
D. F. Young
Keyword(s):  
Stokes Equations ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Arterial System ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Dependent Growth ◽  
Abnormal Tissue

A common occurrence in the arterial system is the narrowing of arteries due to the development of atherosclerotic plaques or other types of abnormal tissue development. As these growths project into the lumen of the artery, the flow is disturbed and there develops a potential coupling between the growth and the blood flow through the artery. A discussion of the various possible consequences of this interaction is given. It is noted that very small growths leading to mild stenotic obstructions, although not altering the gross flow characteristics significantly, may be important in triggering biological mechanisms such as intimal cell proliferation or changes in vessel caliber. An analysis of the effect of an axially symmetric, time-dependent growth into the lumen of a tube of constant cross section through which a Newtonian fluid is steadily flowing is presented. This analysis is based on a simplified model in which the convective acceleration terms in the Navier-Stokes equations are neglected. Effect of growth on pressure distribution and wall shearing stress is given and possible biological implications are discussed.

Effect of Blade Numbers on Pressure Drop of Axial Cyclone Separators by CFD

2011 ◽  
Vol 55-57 ◽  
pp. 343-347 ◽  
Author(s):  
Yi Gang Luan ◽  
Hai Ou Sun
Keyword(s):  
Pressure Drop ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Three Dimensional Model ◽  
Navier Stokes Equations ◽  
Pressure Drops ◽  
Computational Fluid Dynamics Cfd ◽  
Cfd Method ◽  
Resistance Performance

In this article, computational fluid dynamics(CFD) method is used to predict the effect of blade numbers on the pressure drop of axial cyclone separators. A three-dimensional model is built to acquire the resistance of axial cyclone separators with different blade numbers. The flow field inside cyclone separators is calculated using 3D Reynolds-averaged Navier-Stokes equations. And turbulence model is used to simulate the Reynold stress. Also pressure drop of cyclone separators with different blade numbers is expressed as a function of different inlet velocities. At the same inlet velocity with increasing the blade numbers, pressure drops of cyclones reduce greatly. And changing the blade number of cyclone separator is an effective method to improve its resistance performance.

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

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