Relation between strouhal and reynolds numbers for two-dimensional flow about a circular cylinder

1968 ◽  
Vol 1 (2) ◽  
pp. 107-109 ◽  
Author(s):  
S. G. Popov
Keyword(s):  
Circular Cylinder ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow

scholarly journals Two- and three-dimensional wake transitions of an impulsively started uniformly rolling circular cylinder

2017 ◽  
Vol 826 ◽  
pp. 32-59 ◽  
Author(s):  
F. Y. Houdroge ◽  
T. Leweke ◽  
K. Hourigan ◽  
M. C. Thompson
Keyword(s):  
Stability Analysis ◽  
Circular Cylinder ◽  
Rapid Development ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Instability Modes ◽  
Two Dimensional Flow ◽  
Lift And Drag

This paper presents the characteristics of the different stages in the evolution of the wake of a circular cylinder rolling without slipping along a wall at constant speed, acquired through numerical stability analysis and two- and three-dimensional numerical simulations. Reynolds numbers between 30 and 300 are considered. Of importance in this study is the transition to three-dimensionality from the underlying two-dimensional periodic flow and, in particular, the way that the associated transitions influence the fluid forces exerted on the cylinder and the development and the structure of the wake. It is found that the steady two-dimensional flow becomes unstable to three-dimensional perturbations at $Re_{c,3D}=37$, and that the transition to unsteady two-dimensional flow – or periodic vortex shedding – occurs at $Re_{c,2D}=88$, thus validating and refining the results of Stewart et al. (J. Fluid Mech. vol. 648, 2010, pp. 225–256). The main focus here is on Reynolds numbers beyond the transition to unsteady flow at $Re_{c,2D}=88$. From impulsive start up, the wake almost immediately undergoes transition to a periodic two-dimensional wake state, which, in turn, is three-dimensionally unstable. Thus, the previous three-dimensional stability analysis based on the two-dimensional steady flow provides only an element of the full story. Floquet analysis based on the periodic two-dimensional flow was undertaken and new three-dimensional instability modes were revealed. The results suggest that an impulsively started cylinder rolling along a surface at constant velocity for $Re\gtrsim 90$ will result in the rapid development of a periodic two-dimensional wake that will be maintained for a considerable time prior to the wake undergoing three-dimensional transition. Of interest, the mean lift and drag coefficients obtained from full three-dimensional simulations match predictions from two-dimensional simulations to within a few per cent.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

Numerical Solution for Laminar Two Dimensional Flow About a Cylinder Oscillating in a Uniform Stream

1982 ◽  
Vol 104 (2) ◽  
pp. 214-220 ◽  
Author(s):  
S. E. Hurlbut ◽  
M. L. Spaulding ◽  
F. M. White
Keyword(s):  
Reynolds Numbers ◽  
Quantitative Agreement ◽  
Two Dimensional ◽  
Inertia Effects ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Lock In ◽  
Uniform Stream

A finite difference model is presented for viscous two dimensional flow of a uniform stream past an oscillating cylinder. A noninertial coordinate transformation is used so that the grid mesh remains fixed relative to the accelerating cylinder. Three types of cylinder motion are considered: oscillation in a still fluid, oscillation parallel to a moving stream, and oscillation transverse to a moving stream. Computations are made for Reynolds numbers between 1 and 100 and amplitude-to-diameter ratios from 0.1 to 2.0. The computed results correctly predict the lock-in or wake-capture phenomenon which occurs when cylinder oscillation is near the natural vortex shedding frequency. Drag, lift, and inertia effects are extracted from the numerical results. Detailed computations at a Reynolds number of 80 are shown to be in quantitative agreement with available experimental data for oscillating cylinders.

Pressure Distributions and Forces on Rectangular and D-shaped Cylinders

1972 ◽  
Vol 23 (1) ◽  
pp. 1-6 ◽  
Author(s):  
B R Bostock ◽  
W A Mair
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Drag Coefficient ◽  
Pressure Distribution ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Two Dimensional Flow ◽  
Rectangular Cylinders ◽  
Shaped Section

SummaryMeasurements in two-dimensional flow on rectangular cylinders confirm earlier work of Nakaguchi et al in showing a maximum drag coefficient when the height h of the section (normal to the stream) is about 1.5 times the width d. Reattachment on the sides of the cylinder occurs only for h/d < 0.35.For cylinders of D-shaped section (Fig 1) the pressure distribution on the curved surface and the drag are considerably affected by the state of the boundary layer at separation, as for a circular cylinder. The lift is positive when the separation is turbulent and negative when it is laminar. It is found that simple empirical expressions for base pressure or drag, based on known values for the constituent half-bodies, are in general not satisfactory.

Two-dimensional flow under gravity in a jet of viscous liquid

1968 ◽  
Vol 31 (3) ◽  
pp. 481-500 ◽  
Author(s):  
N. S. Clarke
Keyword(s):  
Flow Region ◽  
Reynolds Numbers ◽  
Asymptotic Solutions ◽  
Perturbation Scheme ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Secondary Importance ◽  
Inertia Effects ◽  
Dimensional Flow ◽  
Two Dimensional Flow

This paper is concerned with the steady, symmetric, two-dimensional flow of a viscous, incompressible fluid issuing from an orifice and falling freely under gravity. A Reynolds number is defined and considered to be small. Due to the apparent intractability of the problem in the neighbourhood of the orifice, interest is confined to the flow region below the orifice, where the jet is bounded by two free streamlines. It is assumed that the influence of the orifice conditions will decay exponentially, and so the asymptotic solutions sought have no dependence upon the nature of the flow at the orifice. In the region just downstream of the orifice, it is expected that the inertia effects will be of secondary importance. Accordingly the Stokes solution is sought and a perturbation scheme is developed from it to take account of the inertia effects. It was found possible only to express the Stokes solution and its perturbations in the form of co-ordinate expansions. This perturbation scheme is found to be singular far downstream due to the increasing importance of the inertia effects. Far downstream the jet is expected to be very thin and the velocity and stress variations across it to be small. These assumptions are used as a basis in deriving an asymptotic expansion for small Reynolds numbers, which is valid far downstream. This expansion also has the appearance of being valid very far downstream, even for Reynolds numbers which are not necessarily small. The method of matched asymptotic expansions is used to link the asymptotic solutions in the two regions. An extension of the method deriving the expansion far downstream, to cover the case of an axially-symmetric jet, is given in an appendix.

On the drag of two-dimensional flow about a circular cylinder

2004 ◽  
Vol 16 (10) ◽  
pp. 3828-3831 ◽  
Author(s):  
C.-Y. Wen ◽  
C.-L. Yeh ◽  
M.-J. Wang ◽  
C.-Y. Lin
Keyword(s):  
Circular Cylinder ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow
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