Onset of Vortex Shedding in a Periodic Array of Circular Cylinders

2006 ◽  
Vol 128 (5) ◽  
pp. 1101-1105 ◽  
Author(s):  
L. Zhang ◽  
S. Balachandar
Keyword(s):  
Reynolds Number ◽  
Hopf Bifurcation ◽  
Vortex Shedding ◽  
Critical Reynolds Number ◽  
Base Flow ◽  
Periodic Array ◽  
Circular Cylinders ◽  
Rectangular Cylinders

Hopf bifurcation of steady base flow and onset of vortex shedding over a transverse periodic array of circular cylinders is considered. The influence of transverse spacing on critical Reynolds number is investigated by systematically varying the gap between the cylinders from a small value to large separations. The critical Reynolds number behavior for the periodic array of circular cylinders is compared with the corresponding result for a periodic array of long rectangular cylinders considered in [Balanchandar, S., and Parker, S. J., 2002, “Onset of Vortex Shedding in an Inline and Staggered Array of Rectangular Cylinders,” Phys. Fluids, 14, pp. 3714–3732]. The differences between the two cases are interpreted in terms of differences between their wake profiles.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Strouhal numbers of rectangular cylinders

1982 ◽  
Vol 123 ◽  
pp. 379-398 ◽  
Author(s):  
Atsushi Okajima
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Velocity Distribution ◽  
Flow Pattern ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Water Tank ◽  
Height Ratio ◽  
Rectangular Cylinders ◽  
Good Agreement

Experiments on the vortex-shedding frequencies of various rectangular cylinders were conducted in a wind tunnel and in a water tank. The results show how Strouhal number varies with a width-to-height ratio of the cylinders in the range of Reynolds number between 70 and 2 × l04. There is found to exist a certain range of Reynolds number for the cylinders with the width-to-height ratios of 2 and 3 where flow pattern abruptly changes with a sudden discontinuity in Strouhal number. The changes in flow pattern corresponding to the discontinuity of Strouhal number have been confirmed by means of measurements of velocity distribution and flow visualization. These data are compared with those of other investigators. The experimental results have been found to show a good agreement with those of numerical calculations.

Experiment on smooth, circular cylinders in cross-flow in the critical Reynolds number regime

2011 ◽  
Vol 51 (4) ◽  
pp. 949-967 ◽  
Author(s):  
J. J. Miau ◽  
H. W. Tsai ◽  
Y. J. Lin ◽  
J. K. Tu ◽  
C. H. Fang ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Cross Flow ◽  
Circular Cylinders

The Forces acting on a Pair of Circular Cylinders Arranged Side by Side near the Critical Reynolds Number

2002 ◽  
Vol 2002.51 (0) ◽  
pp. 37-38
Author(s):  
Ryo IMAI ◽  
Kazuhiko KATO ◽  
Nobuyuki OHKURA ◽  
Hidetoshi HAYAFUJI ◽  
Muneshige OKUDE
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Circular Cylinders

On vortex shedding from a circular cylinder in the critical Reynolds number régime

1969 ◽  
Vol 37 (3) ◽  
pp. 577-585 ◽  
Author(s):  
P. W. Bearman
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Strouhal Number ◽  
Vortex Shedding ◽  
Critical Reynolds Number ◽  
Narrow Band ◽  
Critical Regime ◽  
Number Range ◽  
Velocity Fluctuations ◽  
Reynolds Number Range

The flow around a circular cylinder has been examined over the Reynolds number range 105 to 7·5 × 105, Reynolds number being based on cylinder diameter. Narrow-band vortex shedding has been observed up to a Reynolds number of 5·5 × 105, i.e. well into the critical régime. At this Reynolds number the Strouhal number reached the unusually high value of 0·46. Spectra of the velocity fluctuations measured in the wake are presented for several values of Reynolds number.

Critical Reynolds number and galloping instabilities: experiments on circular cylinders

2011 ◽  
Vol 52 (5) ◽  
pp. 1295-1306 ◽  
Author(s):  
N. Nikitas ◽  
J. H. G. Macdonald ◽  
J. B. Jakobsen ◽  
T. L. Andersen
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Circular Cylinders

Ultrasonic Doppler Velocimetry Measurement of Flow and Instabilities in a Rotating Lid-Driven Cylinder

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Zhao C. Kong ◽  
Duncan O. Eddy ◽  
Nathan K. Martin ◽  
Brent C. Houchens
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Spectral Element ◽  
Velocity Profiles ◽  
Base Flow ◽  
Doppler Velocimetry ◽  
Two Parameters ◽  
Ultrasonic Doppler Velocimetry

The steady, axisymmetric base flow and instabilities in a rotating lid-driven cylinder are investigated experimentally via ultrasonic Doppler velocimetry and verified with computations. The flow is governed by two parameters: the Reynolds number (based on the angular velocity of the top lid, the cylinder radius, and kinematic viscosity) and the aspect ratio (cylinder height/radius). Base states and instabilities are explored using ultrasonic Doppler velocimetry in two mixtures of glycerol and water. Velocity profiles in the cylinder are constructed for aspect ratio 2.5 and Reynolds numbers between 1000 and 3000. The results are compared to computational spectral element simulations, as well as previously published findings. The base flow velocity profiles measured by ultrasonic Doppler velocimetry are in good agreement with the numerical results below the critical Reynolds number. The same is true for time-averaged results above the critical Reynolds number. Prediction of the first axisymmetric instability is demonstrated, although not always at the expected critical Reynolds number. Advantages and limitations of ultrasonic Doppler velocimetry are discussed.

scholarly journals Linear stability of Hunt's flow

2010 ◽  
Vol 649 ◽  
pp. 115-134 ◽  
Author(s):  
JĀNIS PRIEDE ◽  
SVETLANA ALEKSANDROVA ◽  
SERGEI MOLOKOV
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Linear Stability ◽  
Critical Reynolds Number ◽  
Transverse Magnetic ◽  
Base Flow ◽  
Maximal Velocity ◽  
Square Duct ◽  
Stream Function Formulation ◽  
The Magnetic Field

We analyse numerically the linear stability of the fully developed flow of a liquid metal in a square duct subject to a transverse magnetic field. The walls of the duct perpendicular to the magnetic field are perfectly conducting whereas the parallel ones are insulating. In a sufficiently strong magnetic field, the flow consists of two jets at the insulating walls and a near-stagnant core. We use a vector stream function formulation and Chebyshev collocation method to solve the eigenvalue problem for small-amplitude perturbations. Due to the two-fold reflection symmetry of the base flow the disturbances with four different parity combinations over the duct cross-section decouple from each other. Magnetic field renders the flow in a square duct linearly unstable at the Hartmann number Ha ≈ 5.7 with respect to a disturbance whose vorticity component along the magnetic field is even across the field and odd along it. For this mode, the minimum of the critical Reynolds number Rec ≈ 2018, based on the maximal velocity, is attained at Ha ≈ 10. Further increase of the magnetic field stabilizes this mode with Rec growing approximately as Ha. For Ha > 40, the spanwise parity of the most dangerous disturbance reverses across the magnetic field. At Ha ≈ 46 a new pair of most dangerous disturbances appears with the parity along the magnetic field being opposite to that of the previous two modes. The critical Reynolds number, which is very close for both of these modes, attains a minimum, Rec ≈ 1130, at Ha ≈ 70 and increases as Rec ≈ 91Ha1/2 for Ha ≫ 1. The asymptotics of the critical wavenumber is kc ≈ 0.525Ha1/2 while the critical phase velocity approaches 0.475 of the maximum jet velocity.

Cell structure on circular cylinders near the critical Reynolds number

1998 ◽  
Author(s):  
Takashi Yoshinaga ◽  
Mamoru Sato ◽  
Atsushi Tate ◽  
Norikazu Sudani ◽  
Kunio Soga
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Cell Structure ◽  
Circular Cylinders
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