Pulsatile Flow in Tapered Tubes: A Model of Blood Flow With Large Disturbances

1983 ◽  
Vol 105 (2) ◽  
pp. 112-119 ◽  
Author(s):  
E. Kimmel ◽  
U. Dinnar
Keyword(s):  
Blood Flow ◽  
Pulsatile Flow ◽  
Mean Value ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Pressure Gradients ◽  
Navier Stokes Equation ◽  
Rigid Tube ◽  
Flow Through ◽  
Uniform Tube

Blood flow-through segments of large arteries of man, between adjacent bifurcations, can be modeled as pulsatile flow in tapered converging tubes, of small angle of convergence, up to 2 deg. Assuming linearity, rigid tube and homogeneous Newtonian fluid, the physiological flow field is governed by the Navier-Stokes equation with dominant nonlinear and unsteady terms. Analytical solution of this problem is presented based on an integral method technique. The solution shows that even for small tapering the flow pattern is markedly different from the flow obtained for a uniform tube. The periodic shear stresses at the wall and pressure gradients increase both in their mean value and amplitude with increased distance downstream. These results are highly significant in the process of atherogenesis.

scholarly journals Effects of Stenting on Blood Flow in a Coronary Artery Network Model

2006 ◽  
Vol 3 (2) ◽  
pp. 77-86
Author(s):  
R. Raghu ◽  
A. Pullan ◽  
N. Smith
Keyword(s):  
Blood Flow ◽  
Coronary Artery ◽  
Finite Difference Method ◽  
Vessel Wall ◽  
Flow Patterns ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Computationally Efficient ◽  
Navier Stokes Equation ◽  
Local Flow

The effect of stenting on blood flow is investigated using a model of the coronary artery network. The parameters in a generic non-linear pressure–radius relationship are varied in the stented region to model the increase in stiffness of the vessel due to the presence of the stent. A computationally efficient form of the Navier–Stokes equation is solved using a Lax–Wendroff finite difference method. Pressure, vessel radius and flow velocity are computed along the vessel segments. Results show negative pressure gradients at the ends of the stent and increased velocity through the middle of the stented region. Changes in local flow patterns and vessel wall stresses due to the presence of the stent have been shown to be important in restenosis of vessels. Local and global pressure gradients affect local flow patterns and vessel wall stresses, and therefore may be an important factor associated with restenosis. The model presented in this study can be easily extended to solve flows for stented vessels in a full, anatomically realistic coronary network. The framework to allow for the effects of the deformation of the myocardium on the coronary network is also in place.

scholarly journals Numerical Simulation of Nonlinear Pulsatile Newtonian Blood Flow through a Multiple Stenosed Artery

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Satyasaran Changdar ◽  
Soumen De
Keyword(s):  
Blood Flow ◽  
Flow Model ◽  
Cylindrical Tube ◽  
Navier Stokes ◽  
Normal Functioning ◽  
Arterial Segment ◽  
Navier Stokes Equation ◽  
Stenosed Artery ◽  
Incompressible Newtonian Fluid ◽  
Flow Through

An appropriate nonlinear blood flow model under the influence of periodic body acceleration through a multiple stenosed artery is investigated with the help of finite difference method. The arterial segment is simulated by a cylindrical tube filled with a viscous incompressible Newtonian fluid described by the Navier-Stokes equation. The nonlinear equation is solved numerically with the proper boundary conditions and pressure gradient that arise from the normal functioning of the heart. Results are discussed in comparison with the existing models.

An Experiment on the Pulsatile Flow at Transitional Reynolds Numbers—The Fluid Dynamical Meaning of the Blood Flow Parameters in the Aorta

1993 ◽  
Vol 115 (4A) ◽  
pp. 412-417 ◽  
Author(s):  
Masahide Nakamura ◽  
Wataru Sugiyama ◽  
Manabu Haruna
Keyword(s):  
Blood Flow ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Pulsatile Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Human Aorta ◽  
Navier Stokes Equation ◽  
Wall Shear

An experiment on the fully developed sinusoidal pulsatile flow at transitional Reynolds numbers was performed to evaluate the basic characteristics of the wall shear stress. In this experiment, the wall shear stress was calculated from the measured section averaged axial velocity and the pressure gradient by using the section averaged Navier-Stokes equation. The experimental results showed that the ratio of the amplitude of the wall shear stress to the amplitude of the pressure gradient had the maximum value when the time averaged Reynolds number was about 4000 and the Womersley number was about 10. As this condition is close to the blood flow condition in the human aorta, it is suggested that the parameter of the aorta has an effect to increase the amplitude of the wall shear stress acting on the arterial wall.

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.

Numerical and experimental study on the dynamic bearing properties of a four-pad and eight-pad tilting pad journal bearings in a vertical rotor

2021 ◽  
pp. 1-24
Author(s):  
Gudeta Berhanu Benti ◽  
David Jose Rondon ◽  
Rolf Gustavsson ◽  
Jan-Olov Aidanpää
Keyword(s):  
Dynamic Properties ◽  
Mean Value ◽  
Journal Bearings ◽  
Navier Stokes ◽  
Rigid Rotor ◽  
Navier Stokes Equation ◽  
Vertical Rotor ◽  
Tilting Pad ◽  
Fifth Order ◽  
Tilting Pad Journal Bearings

Abstract In this paper, the dynamics of tilting pad journal bearings with four and eight pads are studied and compared experimentally and numerically. The experiments are performed on a rigid vertical rotor supported by two identical bearings. Two sets of experiments are carried out under similar test setup. One set is performed on a rigid rotor with two four-pad bearings, while the other is on a rigid rotor with two eight-pad bearings. The dynamic properties of the two bearing types are compared with each other by studying the unbalance response of the system at different rotor speeds. Numerically, the test rig is modeled as a rigid rotor and the bearing coefficients are calculated based on Navier-Stokes equation. A nonlinear bearing model is developed and used in the steady state response simulation. The measured and simulated displacement and force orbits show similar patterns for both bearing types. Compared to the measurement, the simulated mean value and range (peak-to-peak amplitude) of the bearing force deviate with a maximum of 16 % and 38 %, respectively. It is concluded that, unlike the eight-pad TPJB, the four-pad TPJB excite the system at the third and fifth-order frequencies, which are due to the number of pads, and the amplitudes of these frequencies increase with the rotor speed.

Steady Laminar Flow through Twisted Pipes: Fluid Flow in Square Tubes

1981 ◽  
Vol 103 (4) ◽  
pp. 785-790 ◽  
Author(s):  
J. H. Masliyah ◽  
K. Nandakumar
Keyword(s):  
Laminar Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Dissipation Term ◽  
Axial Velocity Profile ◽  
Secondary Motion ◽  
Qualitative Nature ◽  
Flow Through ◽  
Steady Laminar

The Navier-Stokes equation in a rotating frame of reference is solved numerically to obtain the flow field for a steady, fully developed laminar flow of a Newtonian fluid in a twisted tube having a square cross-section. The macroscopic force and energy balance equations and the viscous dissipation term are presented in terms of variables in a rotating reference frame. The computed values of friction factor are presented for dimensionless twist ratios, (i.e., length of tube over a rotation of π radians normalized with respect to half the width of tube) of 20, 10, 5 and 2.5 and for Reynolds numbers up to 2000. The qualitative nature of the axial velocity profile was observed to be unaffected by the swirling motion. The secondary motion was found to be most important near the wall.

scholarly journals Physiologic blood flow is turbulent

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Khalid M. Saqr ◽  
Simon Tupin ◽  
Sherif Rashad ◽  
Toshiki Endo ◽  
Kuniyasu Niizuma ◽  
...  
Keyword(s):  
Blood Flow ◽  
Stokes Equation ◽  
Initial Conditions ◽  
Hydrodynamic Instability ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Frequency Spectra ◽  
Hydrodynamic Stability Theory

Abstract Contemporary paradigm of peripheral and intracranial vascular hemodynamics considers physiologic blood flow to be laminar. Transition to turbulence is considered as a driving factor for numerous diseases such as atherosclerosis, stenosis and aneurysm. Recently, turbulent flow patterns were detected in intracranial aneurysm at Reynolds number below 400 both in vitro and in silico. Blood flow is multiharmonic with considerable frequency spectra and its transition to turbulence cannot be characterized by the current transition theory of monoharmonic pulsatile flow. Thus, we decided to explore the origins of such long-standing assumption of physiologic blood flow laminarity. Here, we hypothesize that the inherited dynamics of blood flow in main arteries dictate the existence of turbulence in physiologic conditions. To illustrate our hypothesis, we have used methods and tools from chaos theory, hydrodynamic stability theory and fluid dynamics to explore the existence of turbulence in physiologic blood flow. Our investigation shows that blood flow, both as described by the Navier–Stokes equation and in vivo, exhibits three major characteristics of turbulence. Womersley’s exact solution of the Navier–Stokes equation has been used with the flow waveforms from HaeMod database, to offer reproducible evidence for our findings, as well as evidence from Doppler ultrasound measurements from healthy volunteers who are some of the authors. We evidently show that physiologic blood flow is: (1) sensitive to initial conditions, (2) in global hydrodynamic instability and (3) undergoes kinetic energy cascade of non-Kolmogorov type. We propose a novel modification of the theory of vascular hemodynamics that calls for rethinking the hemodynamic–biologic links that govern physiologic and pathologic processes.

Human Aorta Buckling Related to Dissection

2010 ◽  
Author(s):  
Kostas Karagiozis ◽  
Marco Amabili ◽  
Rosaire Mongrain ◽  
Raymond Cartier ◽  
Michael P. Pai¨doussis
Keyword(s):  
Blood Flow ◽  
Nonlinear Stability ◽  
Shell Theory ◽  
Inviscid Flow ◽  
Mechanical Stresses ◽  
Surrounding Tissue ◽  
Navier Stokes ◽  
Human Aorta ◽  
Navier Stokes Equation ◽  
Viscous Stresses

Human aortas are subjected to large mechanical stresses and loads due to blood flow pressurization and through contact with the surrounding tissue and muscle. It is essential that the aorta does not lose stability for proper functioning. The present work investigates the buckling of human aorta relating it to dissection by means of an analytical model. A full bifurcation analysis is used employing a nonlinear model to investigate the nonlinear stability of the aorta conveying blood flow. The artery is modeled as a shell by means of Donnell’s nonlinear shell theory retaining in-plane inertia, while the fluid is modelled by a Newtonian inviscid flow theory but taking into account viscous stresses via the time-averaged Navier-Stokes equation. The three shell displacements are expanded using trigonometric series that satisfy the boundary conditions exactly. A parametric study is undertaken to determine the effect of aorta length, thickness, Young’s modulus, and transmural pressure on the nonlinear stability of the aorta. As a first attempt to study dissection, a quasi-steady approach is taken, in which the flow is not pulsatile but steady. The effect of increasing flow velocity is studied, particularly where the system loses stability, exhibiting static collapse. Regions of large mechanical stresses on the artery surface are identified for collapsed arteries indicating possible ways for dissection to be initiated.

Viscous drag and energy transfer of pulsatile flow in large arteries

1962 ◽  
Vol 202 (4) ◽  
pp. 661-663 ◽  
Author(s):  
Robert L. Evans ◽  
Eugene F. Bernstein ◽  
Darrel L. Lary
Keyword(s):  
Energy Transfer ◽  
Pressure Gradient ◽  
Pulsatile Flow ◽  
Simultaneous Measurement ◽  
Pulse Wave ◽  
Navier Stokes ◽  
Viscous Drag ◽  
Navier Stokes Equation ◽  
Early Results ◽  
Almost All

Early results of simultaneous measurement of pressure gradient and flow in the thoracic aorta of the dog during systole are used in calculations of viscous drag and energy transfer of actual pulsatile flow. Viscous drag is large when the flow is small, and small when the flow is large, so that almost all the energy of the pulse wave is transmitted along the vessel. The amplitude of the viscous drag is a much greater fraction of the amplitude of the pressure gradient than is predicted by the Navier-Stokes equation, which is only theoretical and may assume an unrealistic form of viscous drag during pulsatile flow.

A Model for an Acoustically Driven Microbubble Inside a Rigid Tube

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Adnan Qamar ◽  
Ravi Samtaney
Keyword(s):  
Bubble Radius ◽  
Coupled Model ◽  
Tube Diameter ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Rigid Tube ◽  
Basic Model ◽  
Proposed Model ◽  
D 12 ◽  
Bubble Fragmentation

A theoretical framework to model the dynamics of acoustically driven microbubble inside a rigid tube is presented. The proposed model is not a variant of the conventional Rayleigh–Plesset category of models. It is derived from the reduced Navier–Stokes equation and is coupled with the evolving flow field solution inside the tube by a similarity transformation approach. The results are computed, and compared with experiments available in literature, for the initial bubble radius of Ro = 1.5 μm and 2 μm for the tube diameter of D = 12 μm and 200 μm with the acoustic parameters as utilized in the experiments. Results compare quite well with the existing experimental data. When compared to our earlier basic model, better agreement on a larger tube diameter is obtained with the proposed coupled model. The model also predicts, accurately, bubble fragmentation in terms of acoustic and geometric parameters.

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