scholarly journals Numerical Computations of Vortex Formation Length in Flow Past an Elliptical Cylinder

Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 157
Author(s):  
Matthew Karlson ◽  
Bogdan G. Nita ◽  
Ashwin Vaidya
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Vortex Shedding ◽  
Critical Reynolds Number ◽  
Vortex Formation ◽  
Project Based Learning ◽  
Unsteady Regime ◽  
Karman Vortex ◽  
Elliptical Cylinders ◽  
Asymmetric Configuration

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the bifurcation of the Karman vortex from steady symmetric to the unsteady, asymmetric configuration. Additionally, relationships between the vortex length and aspect ratio are also explored. The work presented here is an example of a module that can be used in a project based learning course on computational fluid dynamics.

Moderate-aspect-ratio elliptical cylinders in simple shear with inertia

2001 ◽  
Vol 442 ◽  
pp. 241-266 ◽  
Author(s):  
C. M. ZETTNER ◽  
M. YODA
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Simple Shear ◽  
Critical Reynolds Number ◽  
Rotation Period ◽  
Elliptical Cylinder ◽  
Aspect Ratios ◽  
Periodic Behaviour ◽  
Elliptical Cylinders ◽  
Stationary Behaviour

The effects of fluid inertia, geometry and flow confinement upon the dynamics of neutrally buoyant elliptical and non-elliptical cylinders over a wide range of aspect ratios in simple shear are studied experimentally for moderate shear-based Reynolds numbers Re. Unlike circular cylinders, elliptical cylinders of moderate aspect ratio cease to rotate, coming to rest at a nearly horizontal equilibrium orientation above a critical Reynolds number Recr (‘stationary behaviour’). Simple dynamics arguments are proposed to explain the effects of aspect ratio and flow confinement upon critical Reynolds number and particle dynamics. Experiments confirm results from previous numerical simulations that the normalized rotation period for Re < Recr (‘periodic behaviour’) is proportional to (Recr − Re)−0.5 for small Recr − Re. For periodic behaviour, maximum and minimum angular cylinder speeds both decrease, and period increases, as Recr − Re decreases. For stationary behaviour, the cylinder rotates until it achieves a nearly horizontal equilibrium orientation, which increases as the Reynolds number approaches the critical value. The experimental results are in good agreement with previous lattice-Boltzmann simulations for a 0.5 aspect ratio cylinder.Variation in angular speed over a rotation period decreases as aspect ratio increases, while Recr increases as flow confinement and aspect ratio increase. A non-elliptical cylinder of 0.33 aspect ratio also ceases to rotate above a certain Reynolds number. Although Recr is different from the corresponding elliptical case, the scaling of the normalized rotation period for this body as Recr → Re is identical to that for the elliptical cylinder, suggesting that this scaling is independent of particle shape (i.e. ‘universal’, as conjectured in previous numerical studies). The results also demonstrate that a variety of centrosymmetric bodies with aspect ratios below unity transition from periodic to stationary behaviour.

Flow past finite cylinders of constant curvature

2018 ◽  
Vol 837 ◽  
pp. 896-915 ◽  
Author(s):  
Jessica K. Shang ◽  
H. A. Stone ◽  
A. J. Smits
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Vortex Shedding ◽  
Angle Of Incidence ◽  
Number Range ◽  
Independence Principle ◽  
Laminar Wake ◽  
The Difference ◽  
Visualization Experiments ◽  
Local Angle

Wake visualization experiments were conducted on a finite curved cylinder whose plane of curvature is aligned with the free stream. The stagnation face of the cylinder is oriented concave or convex to the flow at $230\leqslant Re_{D}\leqslant 916$, where $Re_{D}$ is the cylinder Reynolds number and the curvature is constant and ranges from a straight cylinder to a quarter-ring. While the magnitude of the local angle of incidence to the flow is the same for both orientations, the contrast in their wakes demonstrates a violation of a common approximation known as the ‘independence principle’ for curved cylinders. Vortex shedding always occurred for the convex-oriented cylinder for the Reynolds-number range investigated, along most of the cylinder span, at a constant vortex shedding angle. In contrast, a concave-oriented cylinder could exhibit multiple concurrent wake regimes along its span: two shedding regimes (oblique, normal) and two non-shedding regimes. The occurrence of these wake regimes depended on the curvature, aspect ratio and Reynolds number. In some cases, vortex shedding was entirely suppressed, particularly at higher curvatures. In the laminar wake regime, increasing the curvature or decreasing the aspect ratio restricts vortex shedding to smaller regions along the span of the cylinder. Furthermore, the local angle of incidence where vortex shedding occurs is self-similar across cylinders of the same aspect ratio and varying curvature. After the wake transitions to turbulence, the vortex shedding extends along most of the cylinder span. The difference in the wakes between the concave and convex orientations is attributed to the spanwise flow induced by the finite end conditions, which reduces the generation of spanwise vorticity and increases the incidence of non-shedding and obliquely shedding wakes for the concave cylinder.

PIV and POD Investigations of Coherent Vortices Downstream Circular or Rectangular Obstacles Located Between Two Parallel Plates

2019 ◽  
Author(s):  
Fethi Aloui ◽  
Amal Elawady ◽  
Khaled J. Hammad
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Chaotic Behavior ◽  
Rectangular Channel ◽  
Experimental Investigations ◽  
Parallel Plates ◽  
Piv Measurements ◽  
Coherent Vortices ◽  
Karman Vortex ◽  
Proper Orthogonal

Abstract The study is an experimental investigations using PIV. The measurements were obtained by PIV for an unsteady laminar flow across a rectangular channel with a cross-section 300 × 30mm2, in the middle of which is located a cylindrical or a square obstacle. In the case of the cylindrical configuration and due to the confinement, PIV measurements in the range of 40 &lt; Re &lt; 200 clearly show that the von Karman vortex shedding appears at a critical Reynolds number which is about 66. A post-processing of these PIV measurements using the Proper Orthogonal Decomposition (POD) technique is by keeping only the first most energetic six modes, can be used as a filtering process to remove noise from instantaneous velocity signals. In the case of the square obstacle, PIV measurements obtained in the range of 30 &lt; Re &lt; 350 show the absence of vortex detachments and the chaotic behavior of the wake behind the obstacle beyond a certain Reynolds number. By examining the POD post-possessing results, the existence of a dynamic detachments’ regime (instantaneous breaking and coalescence of vortices), can be clearly observed. Given the chaotic behavior of the wake behind the obstacle, the application of the POD filtering process to only the first most energetic modes, cannot lead to good results.

Experimental Study of Vortex Shedding From a Solid Sphere in Turbulent Freestream

2005 ◽  
Author(s):  
Himanshu Tyagi ◽  
Rui Liu ◽  
David S.-K. Ting ◽  
Clifton R. Johnston
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Flow Velocity ◽  
Vortex Shedding ◽  
Isotropic Turbulence ◽  
Vortex Formation ◽  
Perforated Plate ◽  
Solid Sphere ◽  
Mean Flow ◽  
Static Pressure Distribution

The study of vortex shedding from a sphere assumes an important role because of its relevance to numerous aerodynamic and hydrodynamic applications. Parameters such as coefficient of drag and static pressure distribution are largely influenced by vortex shedding, and it is found by past studies that the freestream turbulence can interact and alter the vortex formation and shedding drastically. Most of these studies, however, were conducted in the low Reynolds number regime and the vortex shedding results had been described only qualitatively. To better understand the aerodynamics of a sphere in turbulent flow, an experimental study was initiated in a low speed wind tunnel to quantify the vortex shedding characteristics. The Reynolds number of the flow, based on the diameter of the sphere (d), was set at 3.3 × 104, 5 × 104 and 6.6 × 104 by varying the mean flow velocity. The sphere was placed at 20D (= 7.5d) downstream from a perforated plate, where D = 37.5 mm is the size of the holes in the perforated plate, uniquely designed for generating near-isotropic turbulence. Hot-wire measurements were taken at 10D (= 3.75d), 20D (= 7.5d) and 30D (= 11.25d) downstream of the sphere in absence and presence of the perforated plate. The vortex shedding frequency was deduced from the instantaneous flow velocity data.

scholarly journals Numerical Study of Flow Characteristics Around Confined Cylinder using OpenFOAM

2018 ◽  
Vol 7 (4.35) ◽  
pp. 617
Author(s):  
P. Mathupriya ◽  
L. Chan ◽  
H. Hasini ◽  
A. Ooi
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Numerical Study ◽  
Vortex Formation ◽  
Plane Channel ◽  
Flow Characteristics ◽  
Strong Interactions ◽  
Two Dimensional ◽  
Computational Fluid Dynamics Cfd ◽  
Shedding Frequency

The numerical study of the flow over a two-dimensional cylinder which is symmetrically confined in a plane channel is presented to study the characteristics of vortex shedding. The numerical model has been established using direct numerical simulation (DNS) based on the open source computational fluid dynamics (CFD) code named OpenFOAM. In the present study, the flow fields have been computed at blockage ratio, β of 0.5 and at Reynolds number, Re of 200 and 300. Two-dimensional simulations investigated on the effects of Reynolds number based on the vortex formation and shedding frequency. It was observed that the presence of two distinct shedding frequencies appear at higher Reynolds number due to the confinement effects where there is strong interactions between boundary layer, shear layer and the wake of the cylinder. The range of simulations conducted here has shown to produce results consistent with that available in the open literature. Therefore, OpenFOAM is found to be able to accurately capture the complex physics of the flow.

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.

On vortex formation from a cylinder. Part 1. The initial instability

1988 ◽  
Vol 190 ◽  
pp. 491-512 ◽  
Author(s):  
M. F. Unal ◽  
D. Rockwell
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Circular Cylinder ◽  
Shear Layer ◽  
Vortex Shedding ◽  
Vortex Formation ◽  
Absolute Instability ◽  
Near Wake ◽  
Lower Range ◽  
Fluctuation Amplitude

Vortex shedding from a circular cylinder is examined over a tenfold range of Reynolds number, 440 ≤ Re ≤ 5040. The shear layer separating from the cylinder shows, to varying degrees, an exponential variation of fluctuating kinetic energy with distance downstream of the cylinder. The characteristics of this unsteady shear layer are interpreted within the context of an absolute instability of the near wake. At the trailing-end of the cylinder, the fluctuation amplitude of the instability correlates well with previously measured values of mean base pressure. Moreover, this amplitude follows the visualized vortex formation length as Reynolds number varies. There is a drastic decrease in this near-wake fluctuation amplitude in the lower range of Reynolds number and a rapid increase at higher Reynolds number. These trends are addressed relative to the present, as well as previous, observations.

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.

Vortex Formation in the Wake of a Vibrating, Flexible Cable

1974 ◽  
Vol 96 (4) ◽  
pp. 317-322 ◽  
Author(s):  
S. E. Ramberg ◽  
O. M. Griffin
Keyword(s):  
Vortex Shedding ◽  
Vortex Formation ◽  
Reynolds Numbers ◽  
Hot Wire ◽  
Near Wake ◽  
Formation Region ◽  
Vortex Streets ◽  
Region Length ◽  
Karman Vortex ◽  
Flexible Cables

The von Karman vortex streets formed in the wakes of vibrating, flexible cables were studied using a hot-wire anemometer. All the experiments took place in the flow regime where the vibration and vortex-shedding frequencies lock together, or synchronize, to control the wake formation. Detailed measurements were made of the vortex formation flow for Reynolds numbers between 230 and 650. As in the case of vibrating cylinders, the formation-region length is dependent on a shedding parameter St* related to the natural Strouhal number and the vibrational conditions. Furthermore, the near wake configuration is found to be dependent on the local amplitude of vibration suggesting that the vibrating cylinder rseults are directly applicable in that region.

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