Flow Structures at the Proximal Side-to-End Anastomosis. Influence of Geometry and Flow Division

1995 ◽  
Vol 117 (2) ◽  
pp. 224-236 ◽  
Author(s):  
P. E. Hughes ◽  
T. V. How
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Pulsatile Flow ◽  
Critical Reynolds Number ◽  
Flow Patterns ◽  
Time Dependent ◽  
Flow Structures ◽  
Proximal Side ◽  
Flow Division ◽  
Distal Artery

Flow structures were visualized in transparent polyurethane models of proximal side-to-end vascular anastomoses, using planar illumination of suspended tracer particles. Both the effects of geometry and flow division were determined under steady and pulsatile flow conditions, for anastomosis angles of 15, 30, and 45 degrees. The flow patterns were highly three-dimensional and were characterized by a series of vortices in the fully occluded distal artery and two helical vortices aligned with the axis of the graft. In steady flow, above a critical Reynolds number, the flow changed from a laminar regime to one displaying time-dependent behavior. In particular, significant fluctuating velocity components were observed in the distal artery and particles were shed periodically from the occluded artery into the graft. Pairs of asymmetric flow patterns were also observed in the graft, before the onset of the time-dependent flow regime. The critical Reynolds number ranged from 427 to 473 and appeared to be independent of anastomosis angle. The presence of a patent distal artery had a significant effect on the overall flow pattern and led to the formation of a large recirculation region at the toe of the anastomosis. The main structures observed in steady flow, such as vortices in the distal artery and helical flow in the graft, were also seen during the pulsatile cycle. However, the secondary flow components in the graft were more pronounced in pulsatile flow particularly during deceleration of the flow waveform. At higher mean Reynolds numbers, there was also a greater mixing between fluid in the occluded arterial section and that in the graft.

Bifurcation for flow past a cylinder between parallel planes

1995 ◽  
Vol 284 ◽  
pp. 23-41 ◽  
Author(s):  
J.-H. Chen ◽  
W. G. Pritchard ◽  
S. J. Tavener
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Numerical Experiments ◽  
Critical Reynolds Number ◽  
Vortex Pair ◽  
Dynamical Problem ◽  
Time Dependent ◽  
Blockage Ratio ◽  
Flow Past ◽  
Good Agreement

Numerical experiments are described to ascertain how the steady flow past a circular cylinder loses stability as the Reynolds number is increased. A novel feature of the present study is that the cylinder is confined between parallel planes, allowing a more definitive specification of the flow, both experimentally and computationally, than is possible for the unbounded case. Since the structure of the bifurcation is unclear from the extant literature, with the experimental and computational evidence not in good agreement, a critical appraisal of both sets of evidence is presented.A study has been made of the formation of the steady vortex pair behind the cylinder, and it has been determined that the first appearance of the vortices is not associated with a bifurcation of the full dynamical problem but instead it is probably associated with a bifurcation of a restricted kinematical problem.A set of numerical experiments has been made in which the steady flow past the cylinder was perturbed slightly and the ensuing time-dependent motions were computed. These experiments revealed that, for a given blockage ratio, the perturbation would die away at small Reynolds numbers but that, above a critical Reynolds number, the disturbance would be amplified and the flow would eventually settle down to a new state comprising a time-periodic motion.Experiments were also carried out to determine the bifurcation point numerically by considering an eigenvalue problem based on a linearization about the computed steady flow past the cylinder. The calculations showed that stability is lost through a symmetry-breaking Hopf bifurcation and that, for a given blockage ratio, the critical Reynolds number was in very good agreement with that estimated from the time-dependent computations.

scholarly journals Numerical study of the flow around a circular cylinder with the slip length boundary effect at a critical Reynolds number

2021 ◽  
Vol 2119 (1) ◽  
pp. 012002
Author(s):  
A. Sentyabov ◽  
A. Gavrilov ◽  
A. Dekterev
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Critical Reynolds Number ◽  
Numerical Study ◽  
Slip Length ◽  
Boundary Effect ◽  
Flow Patterns ◽  
Length Effect ◽  
Model Calculations ◽  
Sst Model

Abstract The paper presents an investigation of the slip length effect on the flow around a circular cylinder at Reynolds number Re = 2.5·105. The study was performed by means of numerical simulation of the flow with the URANS approach based on the k-ω SST model. Calculations show a significant effect of the slip length on the flow patterns. With an increase in the slip length, the drag coefficient noticeably decreases and the pulsations of the lift force reduce. With an increase in the slip length, the separation of the flow from the cylinder is delayed, which significantly affects the flow patterns in the wake behind the cylinder.

Analysis of Fully Developed Unsteady Viscous Flow in a Curved Elastic Tube Model to Provide Fluid Mechanical Data for Some Circulatory Path-Physiological Situations and Assist Devices

1979 ◽  
Vol 101 (2) ◽  
pp. 114-123 ◽  
Author(s):  
K. B. Chandran ◽  
R. R. Hosey ◽  
D. N. Ghista ◽  
V. W. Vayo
Keyword(s):  
Shear Stress ◽  
Unsteady Flow ◽  
Steady Flow ◽  
Pulsatile Flow ◽  
Flow Patterns ◽  
Elastic Tube ◽  
Flow Component ◽  
Flow Response ◽  
Elastic Tubes ◽  
Flow Components

The unsteady and steady flow components of pulsatile flow response, to an experimentally monitored representative pressure pulse, are computed to provide fluid mechanical data for the etiology of arteriosclerosis at arterial curvature sites and for the design analysis of some extracorporeal dialysis and oxygenatory systems. The unsteady flow component of pulsatile flow in curved elastic tubes is simulated by the superposition of the first six Fourier components of a derived oscillatory flow solution of a viscous, incompressible fluid through an elastic tube of small curvature. The computer flow patterns, wall shear stress and hoop and axial stresses in the wall, due to unsteady and steady flow components of pulsatile flow response, are compared and their implications are discussed. The results show that the unsteady component yields shear stress of an order of magnitude greater than the steady flow, but the steady flow component has a greater variation in the shear stress distribution over a cross section. The steady and unsteady flow patterns are presented for several values of the tube diameters and curvature parameters typical of major arteries in the human circulatory system. The flow pattern and the stress variations could also prove useful in the design of extracorporeal systems such as dialysis machines and oxygenators.

Transition to Turbulence Downstream of a Stenosis for Whole Blood and a Newtonian Analog Under Steady Flow Conditions

2021 ◽  
Author(s):  
Rayanne Pinto Costa ◽  
Blaise Simplice Talla Nwotchouang ◽  
Junyao Yao ◽  
Dipankar Biswas ◽  
David Casey ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Whole Blood ◽  
Critical Reynolds Number ◽  
Blood Rheology ◽  
Transition To Turbulence ◽  
Flow Conditions ◽  
Shear Rates ◽  
The Impact

Abstract Blood, a multiphase fluid comprised of plasma, blood cells, and platelets, is known to exhibit a shear-thinning behavior at low shear rates and near-Newtonian behavior at higher shear rates. However, less is known about the impact of its multiphase nature on the transition to turbulence. In this study, we experimentally determined the critical Reynolds number at which the flow began to transition to turbulence downstream of an eccentric stenosis for whole porcine blood and a Newtonian blood analog (water-glycerin mixture). Velocity profiles for both fluids were measured under steady-state flow conditions using an ultrasound Doppler probe placed 12 diameters downstream of an eccentric stenosis. Velocity was recorded at 21 locations along the diameter at 11 different flow rates. Normalized turbulent kinetic energy was used to determine the critical Reynolds number for each fluid. Blood rheology was measured before and after each experiment. Tests were conducted on five samples of each fluid inside a temperature-controlled in-vitro flow system. The viscosity at shear rate 1000 s 1 was used to define the Reynolds number for each fluid. The mean critical Reynolds numbers for blood and water-glycerin were 470 ± 27.5 and 395 ± 10, respectively, indicating a ~19% delay in transition to turbulence for whole blood compared to the Newtonian fluid. This finding is consistent with a previous report for steady flow in a straight pipe, suggesting some aspect of blood rheology may serve to suppress, or at least delay, the onset of turbulence in vivo.

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.

Hydrodynamic Effects on Particle Deposition in Microchannel Flows at Elevated Temperatures

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Zhibin Yan ◽  
Xiaoyang Huang ◽  
Chun Yang
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Deposition Rate ◽  
Pulsatile Flow ◽  
Heat Exchangers ◽  
Particle Deposition ◽  
Elevated Temperatures ◽  
Solution Temperature ◽  
Particulate Fouling ◽  
Hydrodynamic Effects

Particulate fouling and particle deposition at elevated temperature are crucial issues in microchannel heat exchangers. In this work, a microfluidic system was designed to examine the hydrodynamic effects on the deposition of microparticles in a microchannel flow, which simulate particle deposits in microscale heat exchangers. The deposition rates of microparticles were measured in two typical types of flow, a steady flow and a pulsatile flow. Under a given elevated solution temperature and electrolyte concentration of the particle dispersion in the tested flow rate range, the dimensionless particle deposition rate (Sherwood number) was found to decrease with the Reynolds number of the steady flow and reach a plateau for the Reynolds number beyond 0.091. Based on the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, a mass transport model was developed with considering temperature dependence of the particle deposition at elevated temperatures. The modeling results can reasonably capture our experimental observations. Moreover, the experimental results of the pulsatile flow revealed that the particle deposition rate in the microchannel can be mitigated by increasing the frequency of pulsation within a low-frequency region. Our findings are expected to provide a better understanding of thermally driven particulate fouling as well as to provide useful information for design and operation of microchannel heat exchangers.

The stability of steady and time-dependent plane Poiseuille flow

1968 ◽  
Vol 34 (1) ◽  
pp. 177-205 ◽  
Author(s):  
Chester E. Grosch ◽  
Harold Salwen
Keyword(s):  
Reynolds Number ◽  
Steady Flow ◽  
Poiseuille Flow ◽  
Time Dependent ◽  
Wave Number ◽  
Neutral Stability ◽  
Neutral Stability Curve ◽  
Plane Poiseuille Flow ◽  
Stability Curve ◽  
Wave Numbers

The linear stability of plane Poiseuille flow has been studied both for the steady flow and also for the case of a pressure gradient that is periodic in time. The disturbance streamfunction is expanded in a complete set of functions that satisfy the boundary conditions. The expansion is truncated after N terms, yielding a set of N linear first-order differential equations for the time dependence of the expansion coefficients.For the steady flow, calculations have been carried out for both symmetric and antisymmetric disturbances over a wide range of Reynolds numbers and disturbance wave-numbers. The neutral stability curve, curves of constant amplification and decay rate, and the eigenfunctions for a number of cases have been calculated. The eigenvalue spectrum has also been examined in some detail. The first N eigenvalues are obtained from the numerical calculations, and an asymptotic formula for the higher eigenvalues has been derived. For those values of the wave-number and Reynolds number for which calculations were carried out by L. H. Thomas, there is excellent agreement in both the eigenvalues and the eigenfunctions with the results of Thomas.For the time-dependent flow, it was found, for small amplitudes of oscillation, that the modulation tended to stabilize the flow. If the flow was not completely stabilized then the growth rate of the disturbance was decreased. For a particular wave-number and Reynolds number there is an optimum amplitude and frequency of oscillation for which the degree of stabilization is a maximum. For a fixed amplitude and frequency of oscillation the wave-number of the disturbance and the Reynolds number has been varied and a neutral stability curve has been calculated. The neutral stability curve for the modulated flow shows a higher critical Reynolds number and a narrower band of unstable wave-numbers than that of the steady flow. The physical mechanism responsible for this stabiIization appears to be an interference between the shear wave generated by the modulation and the disturbance.For large amplitudes, the modulation destabilizes the flow. Growth rates of the modulated flow as much as an order of magnitude greater than that of the steady unmodulated flow have been found.

Comparison of Steady and Pulsatile Flow Near the Ventral and Dorsal Walls of Casts of Human Aortic Bifurcations

1984 ◽  
Vol 106 (1) ◽  
pp. 79-82 ◽  
Author(s):  
O. J. Deters ◽  
F. F. Mark ◽  
C. B. Bargeron ◽  
M. H. Friedman ◽  
G. M. Hutchins
Keyword(s):  
Secondary Flow ◽  
Steady Flow ◽  
Pulsatile Flow ◽  
Flow Direction ◽  
Flow Patterns ◽  
Laser Doppler Anemometer ◽  
Common Features ◽  
Fluid Velocities ◽  
Pulsatile Flows ◽  
The Common

Steady and pulsatile flows were passed through casts of human aortic bifurcations and, by means of a laser Doppler anemometer, fluid velocities were measured at selected sites near the ventral and dorsal walls. At these sites, in the vicinity of the bifurcation, the influence of secondary flow is significant and therefore an appreciation of the phasic variation of secondary flow patterns is important. Results are presented comparing the flow direction in both steady and pulsatile flow at sites in three casts. The common features of the flow at these sites were the persistence of the flow direction during the accelerating and decelerating phases of the pulsatile cycle, and the consistently smaller angle (measured from the inlet centerline) of the pulsatile flow direction as compared to the angle of the flow direction in steady flow.

A Comparison of Steady and Pulsatile Flow in Symmetrically Branched Tubes

1982 ◽  
Vol 104 (1) ◽  
pp. 66-68 ◽  
Author(s):  
F. J. Walburn ◽  
P. D. Stein
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Steady Flow ◽  
Pulsatile Flow ◽  
Area Ratio ◽  
Secondary Velocity

The purpose of this study was to compare the characteristics of flow in the region of symmetrical bifurcations having branch-to-trunk area ratios of 0.4, 0.8 and 1.2 during steady and pulsatile flow. Flow was visualized with neutrally bouyant particles. Secondary flow was not observed in the branches during either steady or pulsatile flow when the branch-to-trunk area ratio was 0.4. Secondary velocity patterns were not observed in the branches with branch-to-trunk area ratios of 0.8 and 1.2 during pulsatile flow, although they were observed during steady flow. It may be inaccurate, therefore, to characterize pulsatile flow at an instantaneous Reynolds number on the basis of steady flow at the same Reynolds number.

Transition Scenario of Periodic and Quasiperiodic Flow Bifurcations in Symmetric Communicating Channels

2007 ◽  
Author(s):  
Amador M. Guzman ◽  
Maximiliano P. Beiza ◽  
Paul F. Fischer
Keyword(s):  
Reynolds Number ◽  
Hopf Bifurcation ◽  
Pressure Gradient ◽  
Friction Factor ◽  
Fundamental Frequency ◽  
Critical Reynolds Number ◽  
Time Dependent ◽  
Periodic Flow ◽  
Wavy Channels ◽  
Transition Scenario

The flow transition scenario in symmetric communicating channels has been investigated using direct numerical simulations of the mass and momentum conservation equations in the Reynolds numbers range of Re = [170–227]. The governing equations are solved for laminar and time-dependent transitional flow regimes by the spectral element method, using a periodic computational domain, for a periodic length of nL and an aspect ratio of r = aˆ / (2Lˆ) = 0.0405, where aˆ = 2a is the height of block within the channel, n an integer and Lˆ = L + 1 is the periodic length. Periodic computational domains with n = 1 and 2 are used in this investigation to determine the periodic length effect on the flow pattern characteristics. Numerical investigations with different domain meshes are carried out for determining the appropriate discretization for capturing transitional time-dependent flows. The numerical results show a transition scenario with two-flow Hopf bifurcations which develop as the pressure gradient is increased from a laminar to a time-dependent flow regime. The first Hopf bifurcation occurs to a critical Reynolds number of Rec1 and leads to a time-dependent periodic flow characterized by a fundamental frequency ω1. Further increases in the pressure gradient lead to successive quasi periodic flows after a second Hopf bifurcation B2 occurring to a critical Reynolds number Rec2 < Rec1, with two fundamental frequencies ω1 and ω2, and linear combinations of both frequencies—where the fundamental frequency ω1 increases continuously—and ω2 > ω1. This transition scenario is somewhat different from the Ruelle-Takens-Newhouse transition scenario obtained for symmetric wavy channels; in symmetric wavy channels, periodic and quasi periodic flow regimes develop as the Reynolds number increases. The friction factor for the symmetric communicating channel in the transitional regime is higher than the friction factor for the Poiseuille plane channel. The qualitative and quantitative behavior is compared to other channel geometries that also develop other transition scenarios.

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