Flow regimes for a square cross-section cylinder in oscillatory flow

2017 ◽  
Vol 813 ◽  
pp. 85-109 ◽  
Author(s):  
Feifei Tong ◽  
Liang Cheng ◽  
Chengwang Xiong ◽  
Scott Draper ◽  
Hongwei An ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Cross Section ◽  
Oscillatory Flow ◽  
Vortex Formation ◽  
Flow Regimes ◽  
Oscillation Period ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Square Cylinder ◽  
Vortex Formation Time

Two-dimensional direct numerical simulation and Floquet stability analysis have been performed at moderate Keulegan–Carpenter number ($KC$) and low Reynolds number ($Re$) for a square cross-section cylinder with its face normal to the oscillatory flow. Based on the numerical simulations a map of flow regimes is formed and compared to the map of flow around an oscillating circular cylinder by Tatsuno & Bearman (J. Fluid Mech., vol. 211, 1990, pp. 157–182). Two new flow regimes have been observed, namely A$^{\prime }$ and F$^{\prime }$. The regime A$^{\prime }$ found at low $KC$ is characterised by the transverse convection of fluid particles perpendicular to the motion; and the regime F$^{\prime }$ found at high $KC$ shows a quasi-periodic feature with a well-defined secondary period, which is larger than the oscillation period. The Floquet analysis demonstrates that when the two-dimensional flow breaks the reflection symmetry about the axis of oscillation, the quasi-periodic instability and the synchronous instability with the imposed oscillation occur alternately for the square cylinder along the curve of marginal stability. This alternate pattern in instabilities leads to four distinct flow regimes. When compared to the vortex shedding in otherwise unidirectional flow, the two quasi-periodic flow regimes are observed when the oscillation frequency is close to the Strouhal frequency (or to half of it). Both the flow regimes and marginal stability curve shift in the $(Re,KC)$-space compared to the oscillatory flow around a circular cylinder and this shift appears to be consistent with the change in vortex formation time associated with the lower Strouhal frequency of the square cylinder.

Oscillatory flow regimes for a circular cylinder near a plane boundary

2018 ◽  
Vol 844 ◽  
pp. 127-161 ◽  
Author(s):  
Chengwang Xiong ◽  
Liang Cheng ◽  
Feifei Tong ◽  
Hongwei An
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Oscillatory Flow ◽  
Flow Regimes ◽  
Plane Boundary ◽  
Marginal Stability ◽  
Hysteresis Phenomenon ◽  
Physical Mechanisms ◽  
Large Hysteresis

Oscillatory flow around a circular cylinder close to a plane boundary is numerically investigated at low-to-intermediate Keulegan–Carpenter ($KC$) and Stokes numbers ($\unicode[STIX]{x1D6FD}$) for different gap-to-diameter ratios ($e/D$). A set of unique flow regimes is observed and classified based on the established nomenclature in the ($KC,\unicode[STIX]{x1D6FD}$)-space. It is found that the flow is not only influenced by $e/D$ but also by the ratio of the thickness of the Stokes boundary layer ($\unicode[STIX]{x1D6FF}$) to the gap size (e). At relatively large $\unicode[STIX]{x1D6FF}/e$ values, vortex shedding through the gap is suppressed and vortices are only shed from the top of the cylinder. At intermediate values of $\unicode[STIX]{x1D6FF}/e$, flow through the gap is enhanced, resulting in horizontal gap vortex shedding. As $\unicode[STIX]{x1D6FF}/e$ is further reduced below a critical value, the influence of $\unicode[STIX]{x1D6FF}/e$ becomes negligible and the flow is largely dependent on $e/D$. A hysteresis phenomenon is observed for the transitions in the flow regime. The physical mechanisms responsible for the hysteresis and the variation of marginal stability curves with $e/D$ are explored at $KC=6$ through specifically designed numerical simulations. The Stokes boundary layer over the plane boundary is found to be responsible for the relatively large hysteresis range over $0.25<e/D<1.0$. Three mechanisms have been identified to the change of the marginal stability curve over $e/D$, which are the blockage effect due to the geometry setting, the favourable pressure gradient over the gap and the location of the leading eigenmode relative to the cylinder.

Two-dimensional motion of a rolling non-circular cylinder on a flat horizontal surface

2018 ◽  
Vol 96 (6) ◽  
pp. 627-632
Author(s):  
Amir Aghamohammadi ◽  
Mohammad Khorrami
Keyword(s):  
Circular Cylinder ◽  
Energy Conservation ◽  
Cross Section ◽  
Equilibrium Configuration ◽  
Focal Point ◽  
Center Of Mass ◽  
Horizontal Surface ◽  
Two Dimensional ◽  
Small Oscillations ◽  
Equilibrium Configurations

The two dimensional motion of a generally non-circular non-uniform cylinder on a flat horizontal surface is investigated. Assuming that the cylinder does not slip, energy conservation is used to study the motion in general. Points of returns, and small oscillations around equilibrium configuration are studied. As examples, cylinders are studied for which the cross section is an ellipse, with the center of mass at the center of the ellipse or at a focal point, and the frequencies of small oscillations around their equilibrium configurations are found. The conditions for losing contact or sliding are also investigated. Finally, the motion is studied in more detail for the case of a nearly circular cylinder.

Optimum profiles in two-dimensional Stokes flow

1995 ◽  
Vol 450 (1940) ◽  
pp. 603-622 ◽  
Keyword(s):  
Circular Cylinder ◽  
Cross Section ◽  
Stokes Flow ◽  
Unit Length ◽  
Three Dimensional ◽  
Variational Formula ◽  
Effective Radius ◽  
Two Dimensional ◽  
Equivalent Radius ◽  
Optimum Profile

We consider the problem of designing the section of a cylinder to minimize the drag per unit length it experiences when placed perpendicular to a uniform stream at low Reynolds number; we suppose the area of the cross-section to be given, and the flow to be two-dimensional. The relevant properties of a cylinder of general cross-section in a particular orientation can conveniently be expressed in terms of its equivalent radius; when the drag and flow at infinity are parallel, this equivalent radius is the radius of the circular cylinder giving rise to the same drag per unit length. We obtain a variational formula for this equivalent radius when the surface of the cylinder is perturbed; this shows that the optimum profile we seek must be such that the flow past it has a vorticity of constant magnitude at its surface, and this fact enables the optimum to be determined analytically. The efficacy of a particular section may be measured by its effective radius, this being the equivalent radius when the length scale is chosen to give the section an area π ; thus a circular cylinder has an effective radius of 1. The minimum possible effective radius, achieved by the optimum profile, is 0.88876. To illustrate some of the arguments we exploit in a more familiar setting, we also obtain a variational formula for the drag on a three-dimensional body in Stokes flow when its surface is perturbed.

Two-dimensional numerical study of vortex shedding regimes of oscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers

2014 ◽  
Vol 751 ◽  
pp. 1-37 ◽  
Author(s):  
Ming Zhao ◽  
Liang Cheng
Keyword(s):  
Vortex Shedding ◽  
Oscillatory Flow ◽  
Flow Regimes ◽  
Reynolds Numbers ◽  
The Other ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Low Reynolds Numbers ◽  
Single Cylinder ◽  
Gap Ratio

AbstractOscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers is simulated numerically by solving the two-dimensional Navier–Stokes (NS) equations using a finite-element method (FEM). The aim of this study is to identify the flow regimes of the two-cylinder system at different gap arrangements and Keulegan–Carpenter numbers (KC). Simulations are conducted at seven gap ratios $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G$ ($G=L/D$ where $L$ is the cylinder-to-cylinder gap and $D$ the diameter of a cylinder) of 0.5, 1, 1.5, 2, 3, 4 and 5 and KC ranging from 1 to 12 with an interval of 0.25. The flow regimes that have been identified for oscillatory flow around a single cylinder are also observed in the two-cylinder system but with different flow patterns due to the interactions between the two cylinders. In the side-by-side arrangement, the vortex shedding from the gap between the two cylinders dominates when the gap ratio is small, resulting in the gap vortex shedding (GVS) regime, which is different from any of the flow regimes identified for a single cylinder. For intermediate gap ratios of 1.5 and 2 in the side-by-side arrangement, the vortex shedding mode from one side of each cylinder is not necessarily the same as that from the other side, forming a so-called combined flow regime. When the gap ratio between the two cylinders is sufficiently large, the vortex shedding from each cylinder is similar to that of a single cylinder. In the tandem arrangement, when the gap between the two cylinders is very small, the flow regimes are similar to that of a single cylinder. For large gap ratios in the tandem arrangement, the vortex shedding flows from the gap side of the two cylinders interact and those from the outer sides of the cylinders are less affected by the existence of the other cylinder and similar to that of a single cylinder. Strong interaction between the vortex shedding flows from the two cylinders makes the flow very irregular at large KC values for both side-by-side and tandem arrangements.

Numerical investigation of the oscillatory flow around a circular cylinder close to a wall at moderate Keulegan–Carpenter and low Reynolds numbers

2009 ◽  
Vol 627 ◽  
pp. 259-290 ◽  
Author(s):  
PIETRO SCANDURA ◽  
VINCENZO ARMENIO ◽  
ENRICO FOTI
Keyword(s):  
Circular Cylinder ◽  
Oscillatory Flow ◽  
Three Dimensional ◽  
Hydrodynamic Forces ◽  
Transverse Force ◽  
Vortex Structures ◽  
Time Development ◽  
Two Dimensional ◽  
Wide Range ◽  
Three Dimensional Simulations

The oscillatory flow around a circular cylinder close to a plane wall is investigated numerically, by direct numerical simulation of the Navier–Stokes equations. The main aim of the research is to gain insight into the effect of the wall on the vorticity dynamics and the forces induced by the flow over the cylinder. First, two-dimensional simulations are performed for nine values of the gap-to-diameter ratio e. Successively, three-dimensional simulations are carried out for selected cases to analyse the influence of the gap on the three-dimensional organization of the flow. An attempt to explain the pressure distribution around the cylinder in terms of vorticity time development is presented. Generally, the time development of the hydrodynamic forces is aperiodic (i.e. changes from cycle to cycle). In one case (Re = 200), when the distance of the cylinder from the wall is reduced, the behaviour of the flow changes from aperiodic to periodic. When the cylinder approaches the wall the drag coefficient of the in-line force increases in a qualitative agreement with the results reported in literature. The transverse force is not monotonic with the reduction of the gap: it first decreases down to a minimum, and then increases with a further reduction of the gap. For intermediate values of the gap the decrease of the transverse force is due to the reduction of the angle of ejection of the shedding vortices caused by the closeness of the wall; for small gaps the increase of the transverse force is due to the strong interaction between the vortex system ejected from the cylinder and the shear layer generated on the wall.Three-dimensional simulations show that the flow is unstable with respect to spanwise perturbations which cause the development of three-dimensional vortices and the distortion of the two-dimensional ones generated by flow separation.In all the analysed cases, the three-dimensional effects on the hydrodynamic forces are clearly attenuated when the cylinder is placed close to the wall.The spanwise modulation of the vortex structures induces oscillations of the sectional forces along the axis of the cylinder which in general are larger for the transverse sectional force. In the high-Reynolds-number case (Re = 500), the reduction of the gap produces a large number of three-dimensional vortex structures developing over a wide range of spatial scales. This produces homogenization of the flow field along the spanwise direction and a consequent reduction of the amplitudes of oscillation of the sectional forces.

Vortex Formation and Resistance in Unsteady Flow

1963 ◽  
Vol 30 (1) ◽  
pp. 16-24 ◽  
Author(s):  
Turgut Sarpkaya ◽  
C. J. Garrison
Keyword(s):  
Circular Cylinder ◽  
Unsteady Flow ◽  
Potential Theory ◽  
Vortex Formation ◽  
Relative Displacement ◽  
Two Dimensional ◽  
Constant Acceleration ◽  
Drag Forces ◽  
Lift And Drag ◽  
Unique Relationship

The strength, growth, and motion of vortices behind a circular cylinder immersed in a two-dimensional uniform flow with constant acceleration are analyzed. Equations for lift and drag forces are obtained from potential theory in terms of the flow and vortex characteristics. By combining the theoretical equations with the experimental results, drag and inertia coefficients are separated and shown to be a function of the relative displacement of the fluid. The results are striking evidence of the existence of a unique relationship between the drag and inertia coefficients.

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