Distribution of gyrotactic micro-organisms in complex three-dimensional flows. Part 1. Horizontal shear flow past a vertical circular cylinder

2018 ◽  
Vol 852 ◽  
pp. 358-397 ◽  
Author(s):  
L. Zeng ◽  
T. J. Pedley
Keyword(s):  
Circular Cylinder ◽  
Shear Flow ◽  
Vortex Shedding ◽  
Water Surface ◽  
Concentration Distribution ◽  
Three Dimensional ◽  
Swimming Velocity ◽  
Horizontal Shear ◽  
Active Particles ◽  
Micro Organisms

As a first step towards understanding the distribution of swimming micro-organisms in flowing shallow water containing vegetation, we formulate a continuum model for dilute suspensions in horizontal shear flow, with a maximum Reynolds number of 100, past a single, rigid, vertical, circular cylinder that extends from a flat horizontal bed and penetrates the free water surface. A numerical platform was developed to solve this problem, in four stages: first, a scheme for computation of the flow field; second, a solver for the Fokker–Planck equation governing the probability distribution of the swimming direction of gyrotactic cells under the combined action of gravity, ambient vorticity and rotational diffusion; third, the construction of a database for the mean swimming velocity and the translational diffusivity tensor as functions of the three vorticity components, using parameters appropriate for the swimming alga, Chlamydomonas nivalis; fourth, a solver for the three-dimensional concentration distribution of the gyrotactic micro-organisms. Upstream of the cylinder, the cells are confined to a vertical strip of width equal to the cylinder diameter, which enables us to visualise mixing in the wake. The flow downstream of the cylinder is divided into three zones: parallel vortex shedding in the top zone near the water surface, oblique vortex shedding in the middle zone and quasi-steady flow in the bottom zone. Secondary (vertical) flow occurs just upstream and downstream of the cylinder. Frequency spectra of the velocity components in the wake of the cylinder show two dominant frequencies of vortex shedding, in the parallel- and oblique-shedding zones respectively, together with a low frequency, equal to the difference between those two frequencies, that corresponds to a beating modulation. The concentration distribution is calculated for both active particles and passive, non-swimming, particles for comparison. The concentration distribution is very similar for both active and passive particles, except near the top surface, where upswimming causes the concentration of active particles to reach values greater than in the upstream strip, and in a thin boundary layer on the downstream surface of the cylinder, where a high concentration of active particles occurs as a result of radial swimming.

Vortex shedding from a circular cylinder in moderate-Reynolds-number shear flow

1980 ◽  
Vol 101 (4) ◽  
pp. 721-735 ◽  
Author(s):  
Masaru Kiya ◽  
Hisataka Tamura ◽  
Mikio Arie
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Shear Flow ◽  
Vortex Shedding ◽  
Transverse Velocity ◽  
Number Range ◽  
Uniform Shear ◽  
Reynolds Number Range ◽  
Moderate Reynolds Number ◽  
Shear Parameter

The frequency of vortex shedding from a circular cylinder in a uniform shear flow and the flow patterns around it were experimentally investigated. The Reynolds number Re, which was defined in terms of the cylinder diameter and the approaching velocity at its centre, ranged from 35 to 1500. The shear parameter, which is the transverse velocity gradient of the shear flow non-dimensionalized by the above two quantities, was varied from 0 to 0·25. The critical Reynolds number beyond which vortex shedding from the cylinder occurred was found to be higher than that for a uniform stream and increased approximately linearly with increasing shear parameter when it was larger than about 0·06. In the Reynolds-number range 43 < Re < 220, the vortex shedding disappeared for sufficiently large shear parameters. Moreover, in the Reynolds-number range 100 < Re < 1000, the Strouhal number increased as the shear parameter increased beyond about 0·1.

Experimental Investigation of Uniform-Shear Flow Past a Circular Cylinder

1992 ◽  
Vol 114 (3) ◽  
pp. 457-460 ◽  
Author(s):  
Tae Soon Kwon ◽  
Hyung Jin Sung ◽  
Jae Min Hyun
Keyword(s):  
Circular Cylinder ◽  
Shear Flow ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Laboratory Experiments ◽  
Processing Technique ◽  
Image Processing Technique ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Shear Parameter

Extensive laboratory experiments were carried out to investigate the uniform-shear flow approaching a circular cylinder. The aim was to present the Strouhal number (St)- Reynolds number (Re) diagrams over a broad range of the shear parameter K (0 ≤ K ≤ 0.25) and at higher values of Re (600 ≤ Re ≤ 1600). An image processing technique, in conjunction with flow visualization studies, was used to secure more quantitative depictions of vortex shedding from the cylinder. The Strouhal number increases with increasing shear parameter. The drag coefficient decreases with increasing Re; also, Cd decreases as the shear parameter K increases.

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

Influence of a Magnetic Obstacle on Forced Convection in a Three-Dimensional Duct With a Circular Cylinder

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Xidong Zhang ◽  
Hulin Huang ◽  
Yin Zhang ◽  
Hongyan Wang
Keyword(s):  
Pressure Drop ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Three Dimensional ◽  
Separated Flow ◽  
Optimum Conditions ◽  
Nusselt Numbers ◽  
Maximum Value ◽  
Wide Range ◽  
The Mean

The predictions of flow structure, vortex shedding, and drag force around a circular cylinder are promoted by both academic interest and a wide range of practical situations. To control the flow around a circular cylinder, a magnetic obstacle is set upstream of the circular cylinder in this study for active controlling the separated flow behind bluff obstacle. Moreover, the changing of position, size, and intensity of magnetic obstacle is easy. The governing parameters are the magnetic obstacle width (d/D = 0.0333, 0.1, and 0.333) selected on cylinder diameter, D, and position (L/D) ranging from 2 to 11.667 at fixed Reynolds number Rel (based on the half-height of the duct) of 300 and the relative magnetic effect given by the Hartmann number Ha of 52. Results are presented in terms of instantaneous contours of vorticity, streamlines, drag coefficient, Strouhal number, pressure drop penalty, and local and average Nusselt numbers for various magnetic obstacle widths and positions. The computed results show that there are two flow patterns, one with vortex shedding from the magnetic obstacle and one without vortex shedding. The optimum conditions for drag reduction are L/D = 2 and d/D = 0.0333–0.333, and under these conditions, the pressure drop penalty is acceptable. However, the maximum value of the mean Nusselt number of the downstream cylinder is about 93% of that for a single cylinder.

Oblique vortex shedding from a circular cylinder in linear shear flow

2002 ◽  
Vol 31 (1) ◽  
pp. 1-24 ◽  
Author(s):  
A. Mukhopadhyay ◽  
P. Venugopal ◽  
S.P. Vanka
Keyword(s):  
Circular Cylinder ◽  
Shear Flow ◽  
Vortex Shedding ◽  
Linear Shear

Three-dimensional transition of vortex shedding flow around a circular cylinder at right and oblique attacks

2013 ◽  
Vol 25 (1) ◽  
pp. 014105 ◽  
Author(s):  
Ming Zhao ◽  
Jitendra Thapa ◽  
Liang Cheng ◽  
Tongming Zhou
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Three Dimensional

Numerical investigation of wake flow regimes behind a high-speed rotating circular cylinder in steady flow

2019 ◽  
Vol 878 ◽  
pp. 875-906
Author(s):  
Adnan Munir ◽  
Ming Zhao ◽  
Helen Wu ◽  
Lin Lu
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Rotation Rate ◽  
High Speed ◽  
Three Dimensional ◽  
Flow Regimes ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Rotating Circular Cylinder

Flow around a high-speed rotating circular cylinder for $Re\leqslant 500$ is investigated numerically. The Reynolds number is defined as $UD/\unicode[STIX]{x1D708}$ with $U$, $D$ and $\unicode[STIX]{x1D708}$ being the free-stream flow velocity, the diameter of the cylinder and the kinematic viscosity of the fluid, respectively. The aim of this study is to investigate the effect of a high rotation rate on the wake flow for a range of Reynolds numbers. Simulations are performed for Reynolds numbers of 100, 150, 200, 250 and 500 and a wide range of rotation rates from 1.6 to 6 with an increment of 0.2. Rotation rate is the ratio of the rotational speed of the cylinder surface to the incoming fluid velocity. A systematic study is performed to investigate the effect of rotation rate on the flow transition to different flow regimes. It is found that there is a transition from a two-dimensional vortex shedding mode to no vortex shedding mode when the rotation rate is increased beyond a critical value for Reynolds numbers between 100 and 200. Further increase in rotation rate results in a transition to three-dimensional flow which is characterized by the presence of finger-shaped (FV) vortices that elongate in the wake of the cylinder and very weak ring-shaped vortices (RV) that wrap the surface of the cylinder. The no vortex shedding mode is not observed at Reynolds numbers greater than or equal to 250 since the flow remains three-dimensional. As the rotation rate is increased further, the occurrence frequency and size of the ring-shaped vortices increases and the flow is dominated by RVs. The RVs become bigger in size and the flow becomes chaotic with increasing rotation rate. A detailed analysis of the flow structures shows that the vortices always exist in pairs and the strength of separated shear layers increases with the increase of rotation rate. A map of flow regimes on a plane of Reynolds number and rotation rate is presented.

Wake dynamics of external flow past a curved circular cylinder with the free stream aligned with the plane of curvature

2007 ◽  
Vol 592 ◽  
pp. 89-115 ◽  
Author(s):  
A. MILIOU ◽  
A. DE VECCHI ◽  
S. J. SHERWIN ◽  
J. M. R. GRAHAM
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Free Stream ◽  
Three Dimensional ◽  
Axial Flow ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
The Body ◽  
Vertical Extension ◽  
Flow Past

Three-dimensional spectral/hp computations have been performed to study the fundamental mechanisms of vortex shedding in the wake of curved circular cylinders at Reynolds numbers of 100 and 500. The basic shape of the body is a circular cylinder whose centreline sweeps through a quarter section of a ring and the inflow direction lies on the plane of curvature of the quarter ring: the free stream is then parallel to the geometry considered and the part of the ring that is exposed to it will be referred to as the ‘leading edge’. Different configurations were investigated with respect to the leading-edge orientation. In the case of a convex-shaped geometry, the stagnation face is the outer surface of the ring: this case exhibited fully three-dimensional wake dynamics, with the vortex shedding in the upper part of the body driving the lower end at one dominant shedding frequency for the whole cylinder span. The vortex-shedding mechanism was therefore not governed by the variation of local normal Reynolds numbers dictated by the curved shape of the leading edge. A second set of simulations were conducted with the free stream directed towards the inside of the ring, in the so-called concave-shaped geometry. No vortex shedding was detected in this configuration: it is suggested that the strong axial flow due to the body's curvature and the subsequent production of streamwise vorticity plays a key role in suppressing the wake dynamics expected in the case of flow past a straight cylinder. The stabilizing mechanism stemming from the concave curved geometry was still found to govern the wake behaviour even when a vertical extension was added to the top of the concave ring, thereby displacing the numerical symmetry boundary condition at this point away from the top of the deformed cylinder. In this case, however, the axial flow from the deformed cylinder was drawn into the wake of vertical extension, weakening the shedding process expected from a straight cylinder at these Reynolds numbers. These considerations highlight the importance of investigating flow past curved cylinders using a full three-dimensional approach, which can properly take into account the role of axial velocity components without the limiting assumptions of a sectional analysis, as is commonly used in industrial practice. Finally, towing-tank flow visualizations were also conducted and found to be in qualitative agreement with the computational findings.

Beating of a circular cylinder mounted as an inverted pendulum

2008 ◽  
Vol 610 ◽  
pp. 217-247 ◽  
Author(s):  
A. VOORHEES ◽  
P. DONG ◽  
P. ATSAVAPRANEE ◽  
H. BENAROYA ◽  
T. WEI
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Inverted Pendulum ◽  
Three Dimensional ◽  
Detailed Examination ◽  
Circular Cylinders ◽  
Response Analysis ◽  
Amplitude Response ◽  
Number Range ◽  
Spatially Resolved

This paper contains temporally and spatially resolved flow visualization and DPIV measurements characterizing the frequency–amplitude response and three-dimensional vortex structure of a circular cylinder mounted like an inverted pendulum. Two circular cylinders were examined in this investigation. Both were 2.54 cm in diameter and ~140 cm long with low mass ratios, m* = 0.65 and 1.90, and mass–damping ratios, m*ζ = 0.038 and 0.103, respectively. Frequency–amplitude response analysis was done with the lighter cylinder while detailed wake structure visualization and measurements were done using the slightly higher-mass-ratio cylinder. Experiments were conducted over the Reynolds number range 1900≤Re≤6800 corresponding to a reduced velocity range of 3.7 ≤ U* ≤ 9.6. Detailed examination of the upper branch of the synchronization regime permitted, for the first time, the identification of short-time deviations in cylinder oscillation and vortex-shedding frequencies that give rise to beating behaviour. That is, while long-time averages of cylinder oscillation and vortex-shedding frequencies are identical, i.e. synchronized, it is shown that there is a slight mismatch between these frequencies over much shorter periods when the cylinder exhibits quasi-periodic beating. Data are also presented which show that vortex strength is also modulated from one cylinder oscillation to the next. Physical arguments are presented to explain both the origins of beating as well as why the quasi-periodicity of the beating envelopes becomes irregular; it is believed that this result may be generalized to a broader class of fluid–structure interactions. In addition, observations of strong vertical flows associated with the Kármán vortices developing 2–3 diameters downstream of the cylinder are presented. It is hypothesized that these three-dimensionalities result from both the inverted pendulum motion as well as free-surface effects.

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