Pulsatile Blood Flow and Oxygen Transport Past a Circular Cylinder

2007 ◽  
Vol 129 (2) ◽  
pp. 202-215 ◽  
Author(s):  
Jennifer R. Zierenberg ◽  
Hideki Fujioka ◽  
Ronald B. Hirschl ◽  
Robert H. Bartlett ◽  
James B. Grotberg
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Circular Cylinder ◽  
Oxygen Transport ◽  
Schmidt Number ◽  
Gas Mixtures ◽  
Cylinder Surface ◽  
Shear Stresses ◽  
Saturation Curve ◽  
Pulsatile Blood Flow

The fundamental study of blood flow past a circular cylinder filled with an oxygen source is investigated as a building block for an artificial lung. The Casson constitutive equation is used to describe the shear-thinning and yield stress properties of blood. The presence of hemoglobin is also considered. Far from the cylinder, a pulsatile blood flow in the x direction is prescribed, represented by a time periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest for the characterization of the flow and transport are the steady Reynolds number (Re), Womersley parameter (α), pulsation amplitude (A), and the Schmidt number (Sc). The Hill equation is used to describe the saturation curve of hemoglobin with oxygen. Two different feed-gas mixtures were considered: pure O2 and air. The flow and concentration fields were computed for Re=5, 10, and 40, 0≤A≤0.75, α=0.25, 0.4, and Schmidt number, Sc=1000. The Casson fluid properties result in reduced recirculations (when present) downstream of the cylinder as compared to a Newtonian fluid. These vortices oscillate in size and strength as A and α are varied. Hemoglobin enhances mass transport and is especially important for an air feed which is dominated by oxyhemoglobin dispersion near the cylinder. For a pure O2 feed, oxygen transport in the plasma dominates near the cylinder. Maximum oxygen transport is achieved by operating near steady flow (small A) for both feed-gas mixtures. The time averaged Sherwood number, Sh̿, is found to be largely influenced by the steady Reynolds number, increasing as Re increases and decreasing with A. Little change is observed with varying α for the ranges investigated. The effect of pulsatility on Sh̿ is greater at larger Re. Increasing Re aids transport, but yields a higher cylinder drag force and shear stresses on the cylinder surface which are potentially undesirable.

Mitigating Blockage Effects on Flow Over a Circular Cylinder in an Adaptive-Wall Wind Tunnel

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Michael Bishop ◽  
Serhiy Yarusevych
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Circular Cylinder ◽  
Shear Layer ◽  
Cylinder Surface ◽  
Blockage Ratio ◽  
Shear Layer Instability ◽  
Frequency Increase ◽  
Pressure Distributions ◽  
Instability Frequency

The effect of wall streamlining on flow development over a circular cylinder was investigated experimentally in an adaptive-wall wind tunnel. Experiments were carried out for a Reynolds number of 57,000 and three blockage ratios of 5%, 8%, and 17%. Three test section wall configurations were investigated, namely, geometrically straight walls (GSW), aerodynamically straight walls (ASW), and streamlined walls (SLW). The results show that solid blockage effects are evident in cylinder surface pressure distributions for the GSW and ASW configurations, manifested by an increased peak suction and base suction. Upon streamlining the walls, pressure distributions for each blockage ratio investigated closely match distributions expected for low blockage ratios. Wake blockage limits wake growth in the GSW configuration at 7.75 and 15 diameters downstream of the cylinder for blockages of 17% and 8%, respectively. This adverse effect can be rectified by streamlining the walls, with the resulting wake width development matching that expected for low blockage ratios. Wake vortex shedding frequency and shear layer instability frequency increase in the GSW and ASW configurations with increasing blockage ratio. The observed invariance of the near wake width with wall configuration suggests that the frequency increase is caused by the increased velocity due to solid blockage effects. For all the blockage ratios investigated, this increase is rectified in the SLW configuration, with the resulting Strouhal numbers of about 0.19 matching that expected for low blockage ratios at the corresponding Reynolds number. Blockage effects on the shear layer instability frequency are also successfully mitigated by streamlining the walls.

An Experimental Investigation of Flow Past a Smooth Circular Cylinder at the Sub-Critical Region

2002 ◽  
Author(s):  
Chuan He ◽  
Tianyu Long ◽  
Mingdao Xin ◽  
Benjamin T. F. Chung
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Circular Cylinder ◽  
Critical Region ◽  
Algebraic Expression ◽  
Cylinder Surface ◽  
Local Pressure ◽  
Flow Past ◽  
Nadir Point ◽  
Experimental Findings

An experimental investigation for the incompressible flow past a smooth circular cylinder at the sub-critical region is presented in detail. A smooth circular cylinder is placed in a wind tunnel and the local pressure distribution on the cylinder surface is measured subtly. The Reynolds Number ranges from 104 to 8 × 104. The experimental data show that there exists a nadir point of the surface pressure in the front the across section of the cylinder and the pressure nadir position varies with the Reynolds number. It is found that this point tends to move forward of the cylinder as Reynolds number increases. Based on the present experimental findings, a simple algebraic expression describing the relationship between the location of the pressure’s nadir and Reynolds number is proposed.

Mitigating Blockage Effects on Flow Over a Circular Cylinder in an Adaptive-Wall Wind Tunnel

2010 ◽  
Author(s):  
Michael Bishop ◽  
Serhiy Yarusevych
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Circular Cylinder ◽  
Shear Layer ◽  
Cylinder Surface ◽  
Blockage Ratio ◽  
Shear Layer Instability ◽  
Frequency Increase ◽  
Pressure Distributions ◽  
Instability Frequency

The effect of wall streamlining on flow development over a circular cylinder was investigated experimentally in an adaptive-wall wind tunnel. Experiments were carried out for a Reynolds number of 57,000 and three blockage ratios of 5%, 8%, and 17%. Three test section wall configurations were investigated, namely, geometrically straight walls (GSW), aerodynamically straight walls (ASW), and streamlined walls (SLW). The results show that solid blockage effects are clearly evident in cylinder surface pressure distributions for the GSW and ASW configurations, manifested by an increased peak suction and base suction. Upon streamlining the walls, pressure distributions for each blockage ratio investigated closely match distributions expected for low blockage ratios. Wake blockage limits wake growth in the GSW configuration at 7.75 and 15 diameters downstream of the cylinder for blockages of 17% and 8%, respectively. This adverse effect can be rectified by streamlining the walls, with the resulting wake width development matching that expected for low blockage ratios. Wake vortex shedding frequency and shear layer instability frequency increase in the GSW and ASW configurations with increasing blockage ratio. The observed invariance of the near wake width with wall configuration suggests that the frequency increase is caused by the increased velocity due to solid blockage effects. For all the blockage ratios investigated, this increase is rectified in the SLW configuration, with the resulting Strouhal numbers of about 0.19 matching that expected for low blockage ratios at the corresponding Reynolds number. Blockage effects on the shear layer instability frequency are also successfully mitigated by streamlining the walls.

An experimental investigation of the oscillating lift and drag of a circular cylinder shedding turbulent vortices

1961 ◽  
Vol 11 (2) ◽  
pp. 244-256 ◽  
Author(s):  
J. H. Gerrard
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Cylinder Surface ◽  
Fluctuating Pressure ◽  
Order Of Magnitude ◽  
Lift And Drag

The oscillating lift and drag on circular cylinders are determined from measurements of the fluctuating pressure on the cylinder surface in the range of Reynolds number from 4 × 103 to just above 105.The magnitude of the r.m.s. lift coefficient has a maximum of about 0.8 at a Reynolds number of 7 × 104 and falls to about 0.01 at a Reynolds number of 4 × 103. The fluctuating component of the drag was determined for Reynolds numbers greater than 2 × 104 and was found to be an order of magnitude smaller than the lift.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

2009 ◽  
Vol 621 ◽  
pp. 69-102 ◽  
Author(s):  
MURALI R. CHOLEMARI ◽  
JAYWANT H. ARAKERI
Keyword(s):  
Reynolds Number ◽  
Rayleigh Number ◽  
Turbulent Flow ◽  
Density Gradient ◽  
Schmidt Number ◽  
Shear Stresses ◽  
Mean Flow ◽  
Vertical Pipe ◽  
Velocity Correlation ◽  
Number Range

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

Pulsatile Blood Flow in a Channel of Small Exponential Divergence—III. Unsteady Flow Separation

1977 ◽  
Vol 99 (2) ◽  
pp. 333-338 ◽  
Author(s):  
Daniel J. Schneck
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Steady State ◽  
Flow Separation ◽  
Reynolds Numbers ◽  
Critical Value ◽  
Flow Oscillation ◽  
Pulsatile Blood Flow ◽  
Steady Streaming ◽  
Flow Through

Analysis of pulsatile flow through exponentially diverging channels reveals the existence of critical mean Reynolds numbers for which the flow separates at a downstream axial station. These Reynolds numbers vary directly with the frequency of flow oscillation and inversely with the rate of channel divergence. Increasing the Reynolds number above its critical value results in a rapid upstream displacement of the point of separation. For a tube of fixed geometry, periodic unsteadiness causes flow separation to occur at lower Reynolds numbers and upstream of a corresponding steady-state situation. The point of separation moves progressively downstream, however, towards its steady-state location, as the frequency of oscillation increases. These results are discussed as consequences of the nonlinear steady streaming phenomenon described in an earlier paper.

scholarly journals Computational Investigation of the Stability of Stenotic Carotid Artery under Pulsatile Blood Flow Using a Fluid-Structure Interaction Approach

2020 ◽  
pp. 2050110
Author(s):  
Amirhosein Manzoori ◽  
Famida Fallah ◽  
Mohammadali Sharzehee ◽  
Sina Ebrahimi
Keyword(s):  
Blood Flow ◽  
Carotid Artery ◽  
Fluid Structure Interaction ◽  
Circumferential Stress ◽  
Artery Stenosis ◽  
Shear Stresses ◽  
Pulsatile Blood Flow ◽  
Fluid Structure ◽  
Structure Interaction ◽  
The Stability

Stenosis can disrupt the normal pattern of blood flow and make the artery more susceptible to buckling which may cause arterial tortuosity. Although the stability simulations of the atherosclerotic arteries were conducted based on solid modeling and static internal pressure, the mechanical stability of stenotic artery under pulsatile blood flow remains unclear while pulsatile nature of blood flow makes the artery more critical for stresses and stability. In this study, the effect of stenosis on arterial stability under pulsatile blood flow was investigated. Fluid–structure interaction (FSI) simulations of artery stenosis under pulsatile flow were conducted. 3D idealized geometries of carotid artery stenosis with symmetric and asymmetric plaques along with different percentages of stenosis were created. It was observed that the stenosis percentage, symmetry/asymmetry of the plaque, and the stretch ratio can dramatically affect the buckling pressure. Buckling makes the plaques (especially in asymmetric ones) more likely to rupture due to increasing the stresses on it. The dominant stresses on plaques are the circumferential, axial and radial ones, respectively. Also, the highest shear stresses on the plaques were detected in [Formula: see text] and [Formula: see text] planes for the symmetric and asymmetric stenotic arteries, respectively. In addition, the maximum circumferential stress on the plaques was observed in the outer point of the buckled configuration for symmetric and asymmetric stenosis as well as at the ends of the asymmetric plaque. Furthermore, the artery buckling causes a large vortex flow at the downstream of the plaque. As a result, the conditions for the penetration of lipid particles and the formation of new plaques are provided.

Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100

1970 ◽  
Vol 42 (3) ◽  
pp. 471-489 ◽  
Author(s):  
S. C. R. Dennis ◽  
Gau-Zu Chang
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Steady Flow ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Reliable Data ◽  
Time Dependent ◽  
Cylinder Surface ◽  
Number Range

Finite-difference solutions of the equations of motion for steady incompressible flow around a circular cylinder have been obtained for a range of Reynolds numbers from R = 5 to R = 100. The object is to extend the Reynolds number range for reliable data on the steady flow, particularly with regard to the growth of the wake. The wake length is found to increase approximately linearly with R over the whole range from the value, just below R = 7, at which it first appears. Calculated values of the drag coefficient, the angle of separation, and the pressure and vorticity distributions over the cylinder surface are presented. The development of these properties with Reynolds number is consistent, but it does not seem possible to predict with any certainty their tendency as R → ∞. The first attempt to obtain the present results was made by integrating the time-dependent equations, but the approach to steady flow was so slow at higher Reynolds numbers that the method was abandoned.

scholarly journals Finite Element Modelling of Pulsatile Blood Flow in Idealized Model of Human Aortic Arch: Study of Hypotension and Hypertension

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Paritosh Vasava ◽  
Payman Jalali ◽  
Mahsa Dabagh ◽  
Pertti J. Kolari
Keyword(s):  
Finite Element ◽  
Blood Flow ◽  
Shear Stress ◽  
Aortic Arch ◽  
Human Aorta ◽  
Shear Stresses ◽  
Pulsatile Blood Flow ◽  
Increased Risk ◽  
Pulsatile Pressure ◽  
Wall Shear

A three-dimensional computer model of human aortic arch with three branches is reproduced to study the pulsatile blood flow with Finite Element Method. In specific, the focus is on variation of wall shear stress, which plays an important role in the localization and development of atherosclerotic plaques. Pulsatile pressure pulse is used as boundary condition to avoid flow entry development, and the aorta walls are considered rigid. The aorta model along with boundary conditions is altered to study the effect of hypotension and hypertension. The results illustrated low and fluctuating shear stress at outer and inner wall of aortic arch, proximal wall of branches, and entry region. Despite the simplification of aorta model, rigid walls and other assumptions results displayed that hypertension causes lowered local wall shear stresses. It is the sign of an increased risk of atherosclerosis. The assessment of hemodynamics shows that under the flow regimes of hypotension and hypertension, the risk of atherosclerosis localization in human aorta may increase.

scholarly journals Computational Investigation of the Stability of Stenotic Carotid Artery under Pulsatile Blood Flow Using a Fluid-Structure Interaction Approach

2020 ◽  
Author(s):  
Amirhosein Manzoori ◽  
Famida Fallah ◽  
Mohammadali Sharzehee ◽  
Sina Ebrahimi
Keyword(s):  
Blood Flow ◽  
Plaque Rupture ◽  
Fluid Structure Interaction ◽  
Circumferential Stress ◽  
Shear Stresses ◽  
Pulsatile Blood Flow ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Lipid Particles ◽  
The Stability

Abstract Background Stenosis can disrupt the normal pattern of blood flow, and thus make the artery more susceptible to buckling which may cause arterial tortuosity. Although the stability simulations of the atherosclerotic arteries were conducted based on solid modelling and static internal pressure, the mechanical stability of stenotic artery under pulsatile blood flow remains unclear while pulsatile nature of blood flow makes the artery more critical for stresses and stability. The aim of this study was to investigate the effect of stenosis on arterial stability under pulsatile blood flow. Methods To this end, fluid-structure interaction (FSI) simulations of arteries stenosis under pulsatile flow were conducted. 3D idealized geometries of carotid arteries stenosis with symmetric and asymmetric plaques along with different percentages of stenosis were created. Arterial wall was modelled as an anisotropic hyperelasic material. Results It is observed that the stenosis percentage, symmetry/asymmetry of the plaque, and the stretch ratio can dramatically affect the buckling pressure. Buckling makes the plaque rupture (especially in asymmetric ones) more likely due to increasing the stresses on it. The dominant stresses on plaques are the circumferential, axial and radial ones, respectively. Also, the highest shear stresses on the plaques were detected in \theta -z and r-\theta planes for the symmetric and asymmetric stenotic arteries, respectively. In addition, the maximum circumferential stress on the plaques was observed in the outer point of the buckled configuration for symmetric and asymmetric stenosis as well as at the ends of the asymmetric plaque. Furthermore, the artery buckling caused a large vortex flow at the downstream of the plaque. As a result, the conditions for the penetration of lipid particles and the formation of new plaques were provided. Conclusion Buckling makes the plaque rupture more likely due to increasing the stresses on it especially in asymmetric plaques. In addition, the artery buckling provides the condition for the penetration of lipid particles and the formation of new plaques at the downstream of the plaque.

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