A NONLINEAR UNSTEADY RESPONSE OF NON-NEWTONIAN BLOOD FLOW PAST AN OVERLAPPING ARTERIAL CONSTRICTION

2007 ◽  
Vol 07 (04) ◽  
pp. 463-489
Author(s):  
S. SEN ◽  
S. CHAKRAVARTY
Keyword(s):  
Blood Flow ◽  
Flow Field ◽  
Arterial Wall ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Physiological Flow ◽  
Arterial Lumen ◽  
Shear Dependent Viscosity

The present study deals with an appropriate mathematical model describing blood flow through a constricted artery that is used to analyze the physiological flow field. The time-variant geometry of the arterial segment having an overlapping type of constriction in the arterial lumen — which frequently occurs in diseased arteries, causing flow disorder and leading to malfunction of the cardiovascular system — is framed mathematically. Blood flow contained in the stenosed artery is treated as non-Newtonian (having shear-dependent viscosity) and is considered to be two-dimensional. The motion of the arterial wall and its effect on local fluid mechanics are not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier–Stokes equations for non-Newtonian fluids. The flow field can be obtained by first transforming radial coordinates with the use of appropriate boundary conditions, and then adopting a suitable finite difference scheme numerically. The unsteady response of the system and the influence of the arterial wall distensibility, the non-Newtonian rheology of blood, and the presence of stenosis on the important aspects of the physiological flow phenomena are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby validate the applicability of the present theoretical model.

Non-Newtonian effects of blood on LDL transport inside the arterial lumen and across multi-layered arterial wall with and without stenosis

2016 ◽  
Vol 27 (01) ◽  
pp. 1650003
Author(s):  
Amin Deyranlou ◽  
Hamid Niazmand ◽  
Mahmood-Reza Sadeghi ◽  
Yaser Mesri
Keyword(s):  
Arterial Wall ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Accurate Estimation ◽  
Ldl Transport ◽  
Arterial Lumen ◽  
Newtonian Model ◽  
Stenosis Severity ◽  
Luminal Flow ◽  
Concentration Patterns

Blood non-Newtonian behavior on low-density lipoproteins (LDL) accumulation is analyzed numerically, while fluid-multilayered arteries are adopted for nonstenotic and 30%–60% symmetrical stenosed models. Present model considers non-Newtonian effects inside the lumen and within arterial layers simultaneously, which has not been examined in previous studies. Navier–Stokes equations are solved along with the mass transport convection–diffusion equations and Darcy’s model for species transport inside the luminal flow and across wall layers, respectively. Carreau model for the luminal flow and the modified Darcy equation for the power-law fluid within arterial layers are employed to model blood rheological characteristics, appropriately. Results indicate that in large arteries with relatively high Reynolds number Newtonian model estimates LDL concentration patterns well enough, however, this model seriously incompetent for regions with low WSS. Moreover, Newtonian model for plasma underestimates LDL concentration especially on luminal surface and across arterial wall. Therefore, applying non-Newtonian model seems essential for reaching to a more accurate estimation of LDL distribution in the artery. Finally, blood flow inside constricted arteries demonstrates that LDL concentration patterns along the stenoses inside the luminal flow and across arterial layers are strongly influenced as compared to the nonstenotic arteries. Additionally, among four stenosis severity grades, 40% stenosis is prone to more LDL accumulation along the post-stenotic regions.

scholarly journals Unsteady Reversed Stagnation-Point Flow over a Flat Plate

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Vai Kuong Sin ◽  
Chon Kit Chio
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Asymptotic Solution ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Total Flow ◽  
Navier Stokes Equations

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. Robins and Howarth (1972) stated that this is not true in neglecting the viscous terms within the total flow field. Viscous terms in this analysis are now included, and a similarity solution of two-dimensional reversed stagnation-point flow is investigated by solving the full Navier-Stokes equations.

scholarly journals Unsteady hybrid nanoparticle-mediated magneto-hemodynamics and heat transfer through an overlapped stenotic artery: Biomedical drug delivery simulation

2021 ◽  
pp. 095441192110260
Author(s):  
Jayati Tripathi ◽  
Buddakkagari Vasu ◽  
Osman Anwar Bég ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Drug Delivery ◽  
Blood Flow ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Hybrid Nanoparticles ◽  
Navier Stokes ◽  
Hybrid Nanofluid ◽  
Two Dimensional ◽  
Governing Equations ◽  
Navier Stokes Equations

Two-dimensional laminar hemodynamics through a diseased artery featuring an overlapped stenosis was simulated theoretically and computationally. This study presented a mathematical model for the unsteady blood flow with hybrid biocompatible nanoparticles (Silver and Gold) inspired by drug delivery applications. A modified Tiwari-Das volume fraction model was adopted for nanoscale effects. Motivated by the magneto-hemodynamics effects, a uniform magnetic field was applied in the radial direction to the blood flow. For realistic blood behavior, Reynolds’ viscosity model was applied in the formulation to represent the temperature dependency of blood. Fourier’s heat conduction law was assumed and heat generation effects were included. Therefore, the governing equations were an extension of the Navier–Stokes equations with magneto-hydrodynamic body force included. The two-dimensional governing equations were transformed and normalized with appropriate variables, and the mild stenotic approximation was implemented. The strongly nonlinear nature of the resulting dimensionless boundary value problem required a robust numerical method, and therefore the FTCS algorithm was deployed. Validation of solutions for the particular case of constant viscosity and non-magnetic blood flow was included. Using clinically realistic hemodynamic data, comprehensive solutions were presented for silver, and silver-gold hybrid mediated blood flow. A comparison between silver and hybrid nanofluid was also included, emphasizing the use of hybrid nanoparticles for minimizing the hemodynamics. Enhancement in magnetic parameter decelerated the axial blood flow in stenotic region. Colored streamline plots for blood, silver nano-doped blood, and hybrid nano-doped blood were also presented. The simulations were relevant to the diffusion of nano-drugs in magnetic targeted treatment of stenosed arterial diseases.

Feasibility Verification of Blood Viscosity Estimation by Two-Dimensional Ultrasonic-Measurement-Integrated Blood Flow Analysis

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Hiroko Kadowaki ◽  
Takuya Kishimoto ◽  
Takeshi Tokunaga ◽  
Koji Mori ◽  
Takashi Saito
Keyword(s):  
Blood Flow ◽  
Flow Field ◽  
Blood Viscosity ◽  
Flow Analysis ◽  
Ultrasonic Measurement ◽  
Doppler Velocity ◽  
Two Dimensional ◽  
Blood Flow Analysis ◽  
Analysis System

Abstract Although blood viscosity has attracted much attention for its effect on hemodynamic parameters related to atherosclerosis, quantitative method for evaluating blood viscosity in vivo is not currently established. The purpose of this study was to verify the feasibility of blood viscosity estimation by a two-dimensional ultrasonic-measurement-integrated (2D-UMI) analysis system that computes an intravascular blood flow field by feeding back an ultrasonic measurement data to a numerical simulation. A method to estimate blood viscosity was proposed by reproducing the flow field of an analysis object in the feedback domain of ultrasonic Doppler velocity in a 2D-UMI blood flow analysis system, and evaluating the variation of the Doppler velocity caused by the analysis viscosity in the nonfeedback domain at the downstream side. In a numerical experiment, a viscosity estimation was performed for numerical solutions of sinusoidal oscillating flows analyzed as a blood flow model in a human common carotid artery at four different types of blood viscosities. The estimation viscosities were made to correspond to those of all analysis objects by giving proper conditions on the feedback gain and feedback domain to optimize the accuracy of the 2D-UMI blood flow analysis. In conclusion, the feasibility of blood viscosity estimation by 2D-UMI analysis was established. Simultaneous measurement of the in vivo blood viscosity and flow field can be easily performed in many clinical cases by its widespread use at clinical sites, thereby clarifying the relationship between hemodynamics and vascular pathology for various blood flow fields.

Navier-Stokes Computation of Radial Inflow Turbine Distributor

1988 ◽  
Vol 110 (1) ◽  
pp. 29-32 ◽  
Author(s):  
T. C. Vu ◽  
W. Shyy
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Energy Loss ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Two Dimensional Flow ◽  
Radial Inflow Turbine

A two-dimensional flow analysis of a radial inflow turbine distributor using full steady-state Reynolds-averaged Navier-Stokes equations is made. The numerical prediction of the total energy loss and the wicket gate torque is compared with experimental data. Also, a parametric study is carried out in order to evaluate the behavior of the numerical algorithm.

scholarly journals BLOOD FLOW ANALYSIS OF POLYURETHANE HEART VALVES AT PEAK SYSTOLE

2006 ◽  
Vol 18 (01) ◽  
pp. 13-18
Author(s):  
CHEUNG-HWA HSU
Keyword(s):  
Blood Flow ◽  
Heart Valves ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Anticoagulation Therapy ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Maximum Flow ◽  
Navier Stokes ◽  
Hemodynamic Characteristics

Polyurethane (PU) heart valves provide central flow at peak systole and the associated hemodynamic characteristics are superior to that of mechanical valves with almost no anticoagulation therapy for patients. Durability performances, on the other hand, are also superior to those of biological valves. This paper analyzes blood flow characteristics of the PU heart valves at fully open position with computational fluid dynamics. These data provide information for the improvement of leaflets and leaflet support geometry to minimize the scale of recirculation zone of the flow field. To simulate the hemodynamic characteristics of the blood flow, CFX-4.3 software with the finite volume method is utilized to analyze the three-dimensional Reynolds-averaged Navier-Stokes equations. By modifying the geometry of leaflets along with the supports, the scale of vortex flow and blood velocity are reduced obviously. Maximum flow velocity reduces 33% compared to that of original model at peak systole.

Multiphysics Simulation of Blood Flow and LDL Transport in a Porohyperelastic Arterial Wall Model

2006 ◽  
Vol 129 (3) ◽  
pp. 374-385 ◽  
Author(s):  
Nobuko Koshiba ◽  
Joji Ando ◽  
Xian Chen ◽  
Toshiaki Hisada
Keyword(s):  
Blood Flow ◽  
Flow Field ◽  
Arterial Wall ◽  
Interaction Analysis ◽  
Concentration Field ◽  
Coupled Analysis ◽  
Filtration Flow ◽  
Ldl Transport ◽  
Arterial Lumen ◽  
Rigid Model

Atherosclerosis localizes at a bend and∕or bifurcation of an artery, and low density lipoproteins (LDL) accumulate in the intima. Hemodynamic factors are known to affect this localization and LDL accumulation, but the details of the process remain unknown. It is thought that the LDL concentration will be affected by the filtration flow, and that the velocity of this flow will be affected by deformation of the arterial wall. Thus, a coupled model of a blood flow and a deformable arterial wall with filtration flow would be invaluable for simulation of the flow field and concentration field in sequence. However, this type of highly coupled interaction analysis has not yet been attempted. Therefore, we performed a coupled analysis of an artery with multiple bends in sequence. First, based on the theory of porous media, we modeled a deformable arterial wall using a porohyperelastic model (PHEM) that was able to express both the filtration flow and the viscoelastic behavior of the living tissue, and simulated a blood flow field in the arterial lumen, a filtration flow field and a displacement field in the arterial wall using a fluid-structure interaction (FSI) program code by the finite element method (FEM). Next, based on the obtained results, we further simulated LDL transport using a mass transfer analysis code by the FEM. We analyzed the PHEM in comparison with a rigid model. For the blood flow, stagnation was observed downward of the bends. The direction of the filtration flow was only from the lumen to the wall for the rigid model, while filtration flows from both the wall to the lumen and the lumen to the wall were observed for the PHEM. The LDL concentration was high at the lumen∕wall interface for both the PHEM and rigid model, and reached its maximum value at the stagnation area. For the PHEM, the maximum LDL concentration in the wall in the radial direction was observed at the position of 3% wall thickness from the lumen∕wall interface, while for the rigid model, it was observed just at the lumen∕wall interface. In addition, the peak LDL accumulation area of the PHEM moved about according to the pulsatile flow. These results demonstrate that the blood flow, arterial wall deformation, and filtration flow all affect the LDL concentration, and that LDL accumulation is due to stagnation and the presence of filtration flow. Thus, FSI analysis is indispensable.

Aerodynamics of a two-dimensional flapping wing hovering in proximity of ground

2019 ◽  
Vol 233 (12) ◽  
pp. 4316-4332 ◽  
Author(s):  
Yunlong Zheng ◽  
Qiulin Qu ◽  
Peiqing Liu ◽  
Yunpeng Qin ◽  
Ramesh K Agarwal
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Aerodynamic Force ◽  
Ground Effect ◽  
Flapping Wing ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Lift Mechanism ◽  
The Difference

The difference in aerodynamic forces of a two-dimensional flapping wing hovering in unbounded flow field and ground effect is studied. The unsteady laminar Navier–Stokes equations are solved by the finite volume method to simulate the flow field around the wing. In the unbounded flow field, the correspondence between the aerodynamic force, pressure distribution on wing, and typical vortex structures is established, and then the high-lift mechanism of the flapping wing is further explained. In the ground effect, based on the lift variation, the dimensionless height H/ C ( H is the height of the wing above ground and C is the chord length of the wing) can be divided into transition and ground effect regimes. In the transition regime ( H/ C > 2.5), the lift decreases with the decreasing height, and the ground indirectly impacts the vortices near wing by changing the shed vortices in space. In the ground effect regime ( H/ C < 2.5), the lift increases with the decreasing height, and the ground directly impacts the vortices near the wing.

A One-Dimensional Unsteady Separable and Reattachable Flow Model for Collapsible Tube-Flow Analysis

1999 ◽  
Vol 121 (2) ◽  
pp. 153-159 ◽  
Author(s):  
T. Ikeda ◽  
Y. Matsuzaki
Keyword(s):  
Unsteady Flow ◽  
Flow Model ◽  
Stokes Equations ◽  
Flow Analysis ◽  
Separated Flow ◽  
Oscillatory Behavior ◽  
Separation Point ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Collapsible Tube

Taking into account both flow separation and reattachment observed in available experimental results on flows in a quasi-two-dimensional channel, we present a onedimensional unsteady flow model, which is applicable to a flow in a collapsible tube. The flow model has been derived from the two-dimensional Navier–Stokes equations by introducing the concept of a dividing streamline, which divides a separated flow into a jet and a dead-water zone. We also present a criterion for the determination of a separation point. Numerical results show that the locations of the predicted separation points agree well with the experimental data. The predicted static pressure of the separated flow is almost constant downstream of the separation point and increases quickly just before the reattachment point, as observed in the experiment. Finally, using the present flow model and the separation criterion, we examine the oscillatory behavior of an unsteady flow in a symmetric channel whose walls move sinusoidally.

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