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.

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.

Three-Dimensional Thermocapillary Convection in Open Cylindrical Annuli

2000 ◽  
Author(s):  
Bok-Cheol Sim ◽  
Abdelfattah Zebib
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Critical Frequency ◽  
Thermocapillary Convection ◽  
Three Dimensional ◽  
Time Dependent ◽  
Infinite Layer ◽  
Aspect Ratios ◽  
Temperature Oscillations ◽  
Good Agreement

Abstract Three-dimensional, time-dependent thermocapillary convection in open cylindrical containers is investigated numerically. Results for aspect ratios (Ar) of 1, 2.5, 8, and 16 and a Prandtl number of 6.84 are obtained to compare the results of numerical simulations with ongoing experiments. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number (Re). Transition to oscillatory states occurs at critical values of Re which depend on Ar. With Ar = 1.0 and 2.5, we observe, respectively, 5 and 9 azimuthal wavetrains travelling clockwise at the free surface near the critical Re. With Ar = 8.0 and 16.0, there are substantially more, but pulsating waves near the critical Re. In the case of Ar = 16.0, which approaches the conditions in an infinite layer, our results are in good agreement with linear theory. While the critical Reynolds number decreases with increasing aspect ratio in the case of azimuthal rotating waves, it increases with increasing aspect ratio in the case of azimuthal pulsating waves. The critical frequency of temperature oscillations is found to decrease linearly with increasing Ar. We have also computed supercritical time-dependent states and find that while the frequency increases with increasing Re near the critical region, the frequency of supercritical convection decreases with Re.

scholarly journals The steady oblique path of buoyancy-driven disks and spheres

2012 ◽  
Vol 707 ◽  
pp. 24-36 ◽  
Author(s):  
David Fabre ◽  
Joël Tchoufag ◽  
Jacques Magnaudet
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Density Ratio ◽  
Steady Motion ◽  
The Body ◽  
Body Motion ◽  
Angle Of Incidence ◽  
Weakly Nonlinear ◽  
Numerical Studies ◽  
Flow Past

AbstractWe consider the steady motion of disks of various thicknesses in a weakly viscous flow, in the case where the angle of incidence $\ensuremath{\alpha} $ (defined as that between the disk axis and its velocity) is small. We derive the structure of the steady flow past the body and the associated hydrodynamic force and torque through a weakly nonlinear expansion of the flow with respect to $\ensuremath{\alpha} $. When buoyancy drives the body motion, we obtain a solution corresponding to an oblique path with a non-zero incidence by requiring the torque to vanish and the hydrodynamic and net buoyancy forces to balance each other. This oblique solution is shown to arise through a bifurcation at a critical Reynolds number ${\mathit{Re}}^{\mathit{SO}} $ which does not depend upon the body-to-fluid density ratio and is distinct from the critical Reynolds number ${\mathit{Re}}^{\mathit{SS}} $ corresponding to the steady bifurcation of the flow past the body held fixed with $\ensuremath{\alpha} = 0$. We then apply the same approach to the related problem of a sphere that weakly rotates about an axis perpendicular to its path and show that an oblique path sets in at a critical Reynolds number ${\mathit{Re}}^{\mathit{SO}} $ slightly lower than ${\mathit{Re}}^{\mathit{SS}} $, in agreement with available numerical studies.

scholarly journals Very Large-Eddy Simulations of the Flow Past an Oscillating Cylinder at a Subcritical Reynolds Number

2020 ◽  
Vol 10 (5) ◽  
pp. 1870
Author(s):  
Zhongying Xiong ◽  
Xiaomin Liu
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Lift Coefficient ◽  
Vortex Pair ◽  
Excitation Amplitude ◽  
Oscillating Cylinder ◽  
Flow Past ◽  
Large Eddy ◽  
Lift And Drag ◽  
Strong Vortex

This work focuses on flow past a circular cylinder at a subcritical Reynolds number. Although this classical study has been a concern for many years, it is still a challenging task due to the complexity of flow characteristics. In this paper, a high-efficiency very large-eddy simulation method is adopted and verified in order to handle the oscillating boundary. A series of numerical simulations are conducted to investigate the transient flow around the oscillating cylinder. The results show that the vortex shedding mode varies with an increase in the excitation amplitude and the excitation frequency. Vortex shedding is a lasting process under the condition of a low excitation amplitude that leads to irregular fluctuations of the lift and drag coefficients. For a vortex shedding mode that exhibits a strong vortex pair and a weak vortex pair or a weak single vortex, the temporal evolution of the lift coefficient of the oscillating cylinder shows irregular ”jumping” at a specific time per cycle corresponding to the shedding of the strong vortex pair. The vortex shedding mode and the frequency and time of the vortex shedding co-determine the temporal evolutions of the lift and drag coefficient.

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.

A planar pulsating jet

2009 ◽  
Vol 638 ◽  
pp. 161-172 ◽  
Author(s):  
N. RILEY ◽  
M. SÁNCHEZ-SANZ ◽  
E. J. WATSON
Keyword(s):  
Reynolds Number ◽  
Numerical Solution ◽  
Steady Flow ◽  
Exponential Decay ◽  
Asymptotic Theory ◽  
Two Dimensional ◽  
Time Harmonic ◽  
Pulsating Jet ◽  
Streamwise Distance ◽  
Good Agreement

We are concerned with the behaviour of a two-dimensional jet that issues from a planar orifice, with a ‘top-hat’ profile. At the orifice the steady flow is modulated by a time-harmonic fluctuation. A suitably defined Reynolds number is assumed to be large throughout. At large streamwise distances from the orifice, the time-averaged flow yields the classical, Bickley, jet with a suitable virtual origin. This decays algebraically whilst, by contrast, the unsteady component decays exponentially with streamwise distance. An asymptotic theory confirms the exponential decay and provides a good agreement with the numerical solution.

The effects of surface roughness and tunnel blockage on the flow past spheres

1974 ◽  
Vol 65 (1) ◽  
pp. 113-125 ◽  
Author(s):  
Elmar Achenbach
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Critical Reynolds Number ◽  
Measurement Techniques ◽  
Flow Conditions ◽  
Number Range ◽  
Flow Past ◽  
Reynolds Number Range ◽  
Shedding Frequency

The effect of surface roughness on the flow past spheres has been investigated over the Reynolds number range 5 × 104 < Re < 6 × 106. The drag coefficient has been determined as a function of the Reynolds number for five surface roughnesses. With increasing roughness parameter the critical Reynolds number decreases. At the same time the transcritical drag coefficient rises, having a maximum value of 0·4.The vortex shedding frequency has been measured under subcritical flow conditions. It was found that the Strouhal number for each of the various roughness conditions was equal to its value for a smooth sphere. Beyond the critical Reynolds number no prevailing shedding frequency could be detected by the measurement techniques employed.The drag coefficient of a sphere under the blockage conditions 0·5 < ds/dt < 0·92 has been determined over the Reynolds number range 3 × 104 < Re < 2 × 106. Increasing blockage causes an increase in both the drag coefficient and the critical Reynolds number. The characteristic quantities were referred to the flow conditions in the smallest cross-section between sphere and tube. In addition the effect of the turbulence level on the flow past a sphere under various blockage conditions was studied.

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