Steady Motion of a Second-Order Fluid past a Circular Cylinder and between Two Coaxial Circular Cylinders with Suction and Injection

1966 ◽  
Vol 21 (1) ◽  
pp. 173-176 ◽  
Author(s):  
H. G. Sharma
Keyword(s):  
Circular Cylinder ◽  
Steady Motion ◽  
Second Order ◽  
Circular Cylinders

Steady approach of unsteady low-Reynolds-number flow past two rotating circular cylinders

2013 ◽  
Vol 736 ◽  
pp. 414-443 ◽  
Author(s):  
Y. Ueda ◽  
T. Kida ◽  
M. Iguchi
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Vortex Method ◽  
The Self ◽  
Circular Cylinders ◽  
Far Field ◽  
Flow Past ◽  
Low Reynolds

AbstractThe long-time viscous flow about two identical rotating circular cylinders in a side-by-side arrangement is investigated using an adaptive numerical scheme based on the vortex method. The Stokes solution of the steady flow about the two-cylinder cluster produces a uniform stream in the far field, which is the so-called Jeffery’s paradox. The present work first addresses the validation of the vortex method for a low-Reynolds-number computation. The unsteady flow past an abruptly started purely rotating circular cylinder is therefore computed and compared with an exact solution to the Navier–Stokes equations. The steady state is then found to be obtained for $t\gg 1$ with ${\mathit{Re}}_{\omega } {r}^{2} \ll t$, where the characteristic length and velocity are respectively normalized with the radius ${a}_{1} $ of the circular cylinder and the circumferential velocity ${\Omega }_{1} {a}_{1} $. Then, the influence of the Reynolds number ${\mathit{Re}}_{\omega } = { a}_{1}^{2} {\Omega }_{1} / \nu $ about the two-cylinder cluster is investigated in the range $0. 125\leqslant {\mathit{Re}}_{\omega } \leqslant 40$. The convection influence forms a pair of circulations (called self-induced closed streamlines) ahead of the cylinders to alter the symmetry of the streamline whereas the low-Reynolds-number computation (${\mathit{Re}}_{\omega } = 0. 125$) reaches the steady regime in a proper inner domain. The self-induced closed streamline is formed at far field due to the boundary condition being zero at infinity. When the two-cylinder cluster is immersed in a uniform flow, which is equivalent to Jeffery’s solution, the streamline behaves like excellent Jeffery’s flow at ${\mathit{Re}}_{\omega } = 1. 25$ (although the drag force is almost zero). On the other hand, the influence of the gap spacing between the cylinders is also investigated and it is shown that there are two kinds of flow regimes including Jeffery’s flow. At a proper distance from the cylinders, the self-induced far-field velocity, which is almost equivalent to Jeffery’s solution, is successfully observed in a two-cylinder arrangement.

Elasticity Solution for a Radially Nonhomogeneous Hollow Circular Cylinder

1999 ◽  
Vol 66 (3) ◽  
pp. 598-606 ◽  
Author(s):  
Xiangzhou Zhang ◽  
Norio Hasebe
Keyword(s):  
Circular Cylinder ◽  
Continuous Functions ◽  
Variable Coefficients ◽  
Circular Cylinders ◽  
Explicit Solutions ◽  
Elasticity Solution ◽  
First Order ◽  
Hollow Circular Cylinder ◽  
Homogeneous Elasticity ◽  
Ordinary Differential Equation Systems

An exact elasticity solution is developed for a radially nonhomogeneous hollow circular cylinder of exponential Young’s modulus and constant Poisson’s ratio. In the solution, the cylinder is first approximated by a piecewise homogeneous one, of the same overall dimension and composed of perfectly bonded constituent homogeneous hollow circular cylinders. For each of the constituent cylinders, the solution can be obtained from the theory of homogeneous elasticity in terms of several constants. In the limit case when the number of the constituent cylinders becomes unboundedly large and their thickness tends to infinitesimally small, the piecewise homogeneous hollow circular cylinder reverts to the original nonhomogeneous one, and the constants contained in the solutions for the constituent cylinders turn into continuous functions. These functions, governed by some systems of first-order ordinary differential equations with variable coefficients, stand for the exact elasticity solution of the nonhomogeneous cylinder. Rigorous and explicit solutions are worked out for the ordinary differential equation systems, and used to generate a number of numerical results. It is indicated in the discussion that the developed method can also be applied to hollow circular cylinders with arbitrary, continuous radial nonhomogeneity.

A Model for High-Reynolds-Number Flow Past Rough-Walled Circular Cylinders

1977 ◽  
Vol 99 (3) ◽  
pp. 486-493 ◽  
Author(s):  
O. Gu¨ven ◽  
V. C. Patel ◽  
C. Farell
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Pressure Coefficient ◽  
Empirical Relation ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Circular Cylinders ◽  
Mean Flow

A simple analytical model for two-dimensional mean flow at very large Reynolds numbers around a circular cylinder with distributed roughness is presented and the results of the theory are compared with experiment. The theory uses the wake-source potential-flow model of Parkinson and Jandali together with an extension to the case of rough-walled circular cylinders of the Stratford-Townsend theory for turbulent boundary-layer separation. In addition, a semi-empirical relation between the base-pressure coefficient and the location of separation is used. Calculation of the boundary-layer development, needed as part of the theory, is accomplished using an integral method, taking into account the influence of surface roughness on the laminar boundary layer and transition as well as on the turbulent boundary layer. Good agreement with experiment is shown by the results of the theory. The significant effects of surface roughness on the mean-pressure distribution on a circular cylinder at large Reynolds numbers and the physical mechanisms giving rise to these effects are demonstrated by the model.

scholarly journals The Investigation of Mutual Interference Vortex Flow around Two Circular Cylinders by Flow Visualization and Pressure Measurement

2019 ◽  
Vol 291 ◽  
pp. 02001
Author(s):  
Yoshifumi Yokoi ◽  
Rut Vitkovičová
Keyword(s):  
Circular Cylinder ◽  
Pressure Measurement ◽  
Pressure Coefficient ◽  
Visual Observation ◽  
Mutual Interference ◽  
Circular Cylinders ◽  
Cylinder Surface ◽  
Visualization Experiment ◽  
Flow Apparatus ◽  
Measurement Experiment

In order to understand the aspect of the mutual interference flow from two circular cylinders, the visual observation experiment and the pressure measurement experiment were performed by use a water flow apparatus. Two circular cylinders with a diameter of D=10mm were used, and they have been arranged at staggered or tandem. The flow velocity was U=0.25m/s (Re=UD/í, í is kinematic viscosity of fluid). The dye oozing streak method was used in the visualization experiment. In the pressure measurement experiment, the pressure on the surface of a circular cylinder was detected by the single tube manometer, and measurement was performed by image processing using a computer. As a result, distribution of the circular cylinder surface pressure coefficient CP corresponding to the flow pattern and it in each circular cylinder arrangement was obtained. The drag coefficient CD was calculated from the pressure coefficient CP, and change of the resistance in each arrangement was found.

Three-dimensional wakes behind cylinders of square and circular cross-section: early and long-time dynamics

2019 ◽  
Vol 870 ◽  
pp. 419-432 ◽  
Author(s):  
G. Agbaglah ◽  
C. Mavriplis
Keyword(s):  
Circular Cylinder ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Early Time ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Square Cylinder ◽  
Saturation Regime ◽  
Time Dynamics ◽  
Significant Difference

The flow in the near wake of a square cylinder at Reynolds numbers of 205 and 225, corresponding to three-dimensional wake instability modes $A$ and $B$, respectively, and that of the square’s circumscribed circular cylinder are examined by using three-dimensional Navier–Stokes numerical simulations. At small times, prior to the streamwise vortex shedding, a self-similar velocity is observed in the wake and no significant difference is observed in the dynamics of the flows past the square and the circular cylinders. The exponential growth of the three-dimensional instability reaches a saturation regime during this early time for the considered Reynolds numbers. Vortical structures in the wake at long times and shedding frequencies are very close for the square and the circular cylinders. The flow separation on the forward top and bottom corners of the square cylinder have the effect of increasing its effective width, making it comparable with the diameter of the circumscribed circular cylinder. Thus, Floquet multipliers and modes of the associated three-dimensional instabilities are shown to be very close for the two cylinders when using the circumscribed circular cylinder as the basis for a characteristic length scale. Most importantly, the wavenumber with the maximum growth rate, for modes $A$ and $B$, is approximately identical for the two cylinders.

Three-dimensional instabilities in oscillatory flow past elliptic cylinders

2016 ◽  
Vol 798 ◽  
pp. 371-397 ◽  
Author(s):  
José P. Gallardo ◽  
Helge I. Andersson ◽  
Bjørnar Pettersen
Keyword(s):  
Circular Cylinder ◽  
Flow Direction ◽  
Three Dimensional ◽  
Circular Cylinders ◽  
Flow Structures ◽  
Three Dimensional Flow ◽  
Elliptical Cross ◽  
Dimensional Flow ◽  
Aspect Ratios ◽  
Flow Past

We investigate the early development of instabilities in the oscillatory viscous flow past cylinders with elliptic cross-sections using three-dimensional direct numerical simulations. This is a classical hydrodynamic problem for circular cylinders, but other configurations have received only marginal attention. Computed results for some different aspect ratios ${\it\Lambda}$ from 1 : 1 to 1 : 3, all with the major axis of the ellipse aligned in the main flow direction, show good qualitative agreement with Hall’s stability theory (J. Fluid Mech., vol. 146, 1984, pp. 347–367), which predicts a cusp-shaped curve for the onset of the primary instability. The three-dimensional flow structures for aspect ratios larger than 2 : 3 resemble those of a circular cylinder, whereas the elliptical cross-section with the lowest aspect ratio of 1 : 3 exhibits oblate rather than tubular three-dimensional flow structures as well as a pair of counter-rotating spanwise vortices which emerges near the tips of the ellipse. Contrary to a circular cylinder, instabilities for an elliptic cylinder with sufficiently high eccentricity emerge from four rather than two different locations in accordance with the Hall theory.

An Energy Method for Certain Second-Order Effects With Application to Torsion of Elastic Bars Under Tension

1980 ◽  
Vol 47 (1) ◽  
pp. 75-81 ◽  
Author(s):  
R. T. Shield
Keyword(s):  
Axial Force ◽  
Strain Energy Function ◽  
Incompressible Material ◽  
Elastic Cylinder ◽  
Second Order ◽  
The Other ◽  
Circular Cylinders ◽  
Order Effects ◽  
First Order ◽  
Wide Range

When a mechanical system has a potential energy, it is a simple matter to show that if the generalized force corresponding to a coordinate p is known to first order in p for a range of the other coordinates of the system, then the other generalized forces can be found immediately to second order in p, without requiring a second-order analysis of the system. By this method the second-order change in the axial force when a finitely extended elastic cylinder is twisted is found from the first-order value of the twisting moment. Numerical results for a realistic form of the strain-energy function for an incompressible material suggest that the second-order expression for the axial force is very accurate for a wide range of twist for circular cylinders of rubber-like materials extended 100 percent or more.

Sign in / Sign up

Export Citation Format

Share Document