Cylinders with square cross-section: wake instabilities with incidence angle variation

Sheard, Gregory J.; Fitzgerald, Matthew J.; Ryan, Kris

doi:10.1017/s0022112009006879

Cited by 138 publications

(132 citation statements)

References 45 publications

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“…Breaking this symmetry can change the nature of three-dimensional bifurcations that are possible from the two-dimensional basic state. Of particular significance in relation to the present work is the fact that subharmonic modes which can arise in systems with broken Z 2 symmetry (as shown by Sheard et al 2003, Carmo et al 2008, Sheard, Fitzgerald & Ryan 2009, respectively, for wakes of rings, of a staggered pair of circular cylinders, and of a rotated square cylinder) are suppressed as generic bifurcations in symmetric systems. This outcome is a direct consequence of Z 2 spatio-temporal symmetry, as originally explained for simple systems by Swift & Wiesenfeld (1984), and in depth for Z 2 ×O(2) systems by Marques et al (2004).…”

Section: Introductionmentioning

confidence: 75%

“…Blackburn & Lopez 2003b;Sheard, Thompson & Hourigan 2004;Blackburn et al 2005;Sheard et al 2009). Especially in Cartesian geometries, this may seem a reasonable expedient since the spanwise spectrum is continuous in the infinite-geometry case, although examples in which this issue was tackled by expanding the extent of the discrete spectrum are provided by Henderson (1997) and Avila et al (2007).…”

Section: Nonlinear Mixed Modesmentioning

confidence: 99%

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Modulated waves in a periodically driven annular cavity

Blackburn

Lopez

2010

J. Fluid Mech.

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Time-periodic flows with spatio-temporal symmetry Z 2 × O(2) -invariance in the spanwise direction generating the O(2) symmetry group and a half-period-reflection symmetry in the streamwise direction generating a spatio-temporal Z 2 symmetry group -are of interest largely because this is the symmetry group of periodic laminar two-dimensional wakes of symmetric bodies. Such flows are the base states for various three-dimensional instabilities; the periodically shedding two-dimensional circular cylinder wake with three-dimensional modes A and B being the generic example. However, it is not easy to physically realize the ideal flows owing to the presence of end effects and finite spanwise geometries. Flows past rings are sometimes advanced as providing a relevant idealization, but in fact these have symmetry group O(2) and only approach Z 2 × O(2) symmetry in the infinite aspect ratio limit. The present work examines physically realizable periodically driven annular cavity flows that possess Z 2 × O(2) spatio-temporal symmetry. The flows have three distinct codimension-1 instabilities: two synchronous modes (A and B), and two manifestations of a quasi-periodic (QP) mode, either as modulated standing waves or modulated travelling waves. It is found that the curvature of the system can determine which of these modes is the first to become unstable with increasing Reynolds number, and that even in the nonlinear regime near onset of three-dimensional instabilities the dynamics are dominated by mixed modes with complicated spatio-temporal structure. Supplementary movies illustrating the spatio-temporal dynamics are available at journals.cambridge.org/flm.

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Section: Introductionmentioning

confidence: 75%

Section: Nonlinear Mixed Modesmentioning

confidence: 99%

Modulated waves in a periodically driven annular cavity

Blackburn

Lopez

2010

J. Fluid Mech.

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“…Considering the experimental uncertainty, it can be said that the results presented above matches the previous observations. Furthermore, Sheard et al 31 mentioned that a spanwise wavelength of 2.6 diameters for the Mode-C in square cylinders. However, in stability calculations of the flow around bluff rings, Sheard et al 8 found a maximum growth rate for Mode-C instability for spanwise wavelengths between 1.6D and 1.7D.…”

Section: B Streamwise Vorticesmentioning

confidence: 99%

Energy contents and vortex dynamics in Mode-C transition of wired-cylinder wake

2013

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The 3D transition of the flow behind a circular cylinder with a near-wake wire disturbance has been investigated experimentally. The flow is oriented horizontally and the wire is positioned in the upper half of the wake. We performed flow visualization and particle image velocimetry experiments to investigate the influence of the wire on various properties of the flow, such as the dynamics of the spanwise structures. Experiments were performed in the Reynolds number range of Re = 165–300. It is shown that in Mode-C transition of the wired cylinder wake, some part of the streamwise vorticity content of the upper von Kármán vortices located at the perturbed side, is transferred to the secondary vortices. This vorticity transfer results in upper von Kármán vortices which are weaker than the lower ones. The analysis of the discrete energy content of the wake supports this analysis by showing that the energy intensity at von Kármán vortex shedding frequency f0 at the perturbed side of the wake is less than the energy intensity in the lower half. This leads to conclusion that the excess energy is transferred to the subharmonic frequency f1 ≈ f0/2.

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“…An example of such an application is the design of buildings. Most experimental [1,2] and numerical studies [2][3][4][5][6][7][8][9] concerning the external flow past a stationary square cylinder have been carried out at moderate to high Reynolds numbers. In this regime, the flow is unsteady.…”

Section: Introductionmentioning

confidence: 99%

Flow past a square cylinder at low Reynolds numbers

Sen

Mittal

Biswas

2010

Numerical Methods in Fluids

161

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SUMMARYResults are presented for the flow past a stationary square cylinder at zero incidence for Reynolds number, Re 150. A stabilized finite-element formulation is employed to discretize the equations of incompressible fluid flow in two-dimensions. For the first time, values of the laminar separation Reynolds number, Re s , and separation angle, s , at Re s are predicted. Also, the variation of s with Re is presented. It is found that the steady separation initiates at Re = 1.15. Contrary to the popular belief that separation originates at the rear sharp corners, it is found to originate from the base point, i.e. s = 180 • at Re = Re s . For Re>5, s approaches the limit of 135 • . The length of the separation bubble increases approximately linearly with increasing Re. The drag coefficient varies as Re −0.66 . Flow characteristics at Re 40 are also presented for elliptical cylinders of aspect ratios 0.2, 0.5, 0.8 and 1 (circle) having the same characteristic dimension as the square and major axis oriented normal to the free-stream. Compared with a circular cylinder, the flow separates at a much lower Re from a square cylinder leading to the formation of a bigger wake (larger bubble length and width). Consequently, at a given Re, the drag on a square cylinder is more than the drag of a circular cylinder. This suggests that a cylinder with square section is more bluff than the one with circular section. Among all the cylinder shapes studied, the square cylinder with sharp corners generates the largest amount of drag.

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Cylinders with square cross-section: wake instabilities with incidence angle variation

Cited by 138 publications

References 45 publications

Modulated waves in a periodically driven annular cavity

Modulated waves in a periodically driven annular cavity

Energy contents and vortex dynamics in Mode-C transition of wired-cylinder wake

Flow past a square cylinder at low Reynolds numbers

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