Asymptotic solutions for two-dimensional low Reynolds number flow around an impulsively started circular cylinder

1997 ◽  
Vol 334 ◽  
pp. 31-59 ◽  
Author(s):  
MASATO NAKANISHI ◽  
TERUHIKO KIDA ◽  
TOMOYA NAKAJIMA
Keyword(s):  
Circular Cylinder ◽  
Drag Coefficient ◽  
Stokes Flow ◽  
Transient Flow ◽  
Three Dimensional ◽  
Slow Motion ◽  
Two Dimensional ◽  
Initial Flow ◽  
Oseen Flow ◽  
Unsteady Stokes Flow

The unsteady flow field of an incompressible viscous fluid around an impulsively started cylinder with slow motion is studied in detail. Integral expressions are derived from the nonlinear vorticity equation, and are solved by the method of matched asymptotic expansions. To complete the matching process five regions are necessary and their regions are essentially governed by the following relations: (i) the initial flow is unsteady Stokes flow (I), (ii) the early transient flow near the cylinder is steady Stokes flow (II), but the far-field flow is unsteady Stokes flow (III), so that Stokes&–Oseen-like matching is necessary, and (iii) as time increases the inertia terms become significant far downstream; thus the far flow is unsteady Oseen flow (IV), but the flow near the cylinder is steady Stokes flow (V), so that the matching of the Stokes–Oseen equations is necessary. The asymptotic analytical solutions are given for five flow fields around a circular cylinder. Also presented are the drag coefficient, the vorticity, and the streamline. The drag coefficient is verified quantitatively by comparing with earlier theories of the initial flow and the steady flow. The streamline patterns calculated show the generation of a circulating zone close to the circular cylinder just as for the transient flow around a sphere, and the difference between two-dimensional and three-dimensional flows is discussed.

Optimum profiles in two-dimensional Stokes flow

1995 ◽  
Vol 450 (1940) ◽  
pp. 603-622 ◽  
Keyword(s):  
Circular Cylinder ◽  
Cross Section ◽  
Stokes Flow ◽  
Unit Length ◽  
Three Dimensional ◽  
Variational Formula ◽  
Effective Radius ◽  
Two Dimensional ◽  
Equivalent Radius ◽  
Optimum Profile

We consider the problem of designing the section of a cylinder to minimize the drag per unit length it experiences when placed perpendicular to a uniform stream at low Reynolds number; we suppose the area of the cross-section to be given, and the flow to be two-dimensional. The relevant properties of a cylinder of general cross-section in a particular orientation can conveniently be expressed in terms of its equivalent radius; when the drag and flow at infinity are parallel, this equivalent radius is the radius of the circular cylinder giving rise to the same drag per unit length. We obtain a variational formula for this equivalent radius when the surface of the cylinder is perturbed; this shows that the optimum profile we seek must be such that the flow past it has a vorticity of constant magnitude at its surface, and this fact enables the optimum to be determined analytically. The efficacy of a particular section may be measured by its effective radius, this being the equivalent radius when the length scale is chosen to give the section an area π ; thus a circular cylinder has an effective radius of 1. The minimum possible effective radius, achieved by the optimum profile, is 0.88876. To illustrate some of the arguments we exploit in a more familiar setting, we also obtain a variational formula for the drag on a three-dimensional body in Stokes flow when its surface is perturbed.

On angles of separation in Stokes flows

1983 ◽  
Vol 133 ◽  
pp. 427-442 ◽  
Author(s):  
M. E. O'Neill
Keyword(s):  
Circular Cylinder ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Stokes Flows ◽  
Eddy Structure ◽  
Toroidal Vortices ◽  
Mathematical Equivalence ◽  
Infinite Sets

A two-dimensional Stokes flow close to the line of contact of two touching cylinders or three-dimensional axisymmetric Stokes flow close to the point of contact of two touching bodies is shown in general to separate into infinite sets of eddies with angles of separation from the bodies which tend to 58.61° as the line or point of contact is approached. The flow near the vertex of a conical cusp is shown to be a system of nested toroidal vortices and the separation angles tend to 45.25° as the vertex is approached. Stokes flow between parallel planes or within a circular cylinder is shown in general to separate far from the generating disturbances with cellular eddy structure and separation angles which tend to 58.61° and 45.25° respectively. The mathematical equivalence of the various problems is established.

scholarly journals Direct Numerical Simulation of Flow around a Circular Cylinder Controlled Using Plasma Actuators

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Taichi Igarashi ◽  
Hiroshi Naito ◽  
Koji Fukagata
Keyword(s):  
Numerical Simulation ◽  
Circular Cylinder ◽  
Direct Numerical Simulation ◽  
Drag Reduction ◽  
Three Dimensional ◽  
Reduction Rate ◽  
Plasma Actuators ◽  
Two Dimensional ◽  
Freestream Velocity ◽  
The Mean

Flow around a circular cylinder controlled using plasma actuators is investigated by means of direct numerical simulation (DNS). The Reynolds number based on the freestream velocity and the cylinder diameter is set atReD=1000. The plasma actuators are placed at±90° from the front stagnation point. Two types of forcing, that is, two-dimensional forcing and three-dimensional forcing, are examined and the effects of the forcing amplitude and the arrangement of plasma actuators are studied. The simulation results suggest that the two-dimensional forcing is primarily effective in drag reduction. When the forcing amplitude is higher, the mean drag and the lift fluctuations are suppressed more significantly. In contrast, the three-dimensional forcing is found to be quite effective in reduction of the lift fluctuations too. This is mainly due to a desynchronization of vortex shedding. Although the drag reduction rate of the three-dimensional forcing is slightly lower than that of the two-dimensional forcing, considering the power required for the forcing, the three-dimensional forcing is about twice more efficient.

Transient Stokes Flow in a Wedge

1987 ◽  
Vol 54 (1) ◽  
pp. 203-208 ◽  
Author(s):  
Bohou Xu ◽  
E. B. Hansen
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Boundary Element Method ◽  
Circular Cylinder ◽  
Stokes Flow ◽  
Constant Velocity ◽  
Transient Flow ◽  
The Finite Element Method ◽  
Element Method

The transient flow in the sector region bounded by two intersecting planes and a circular cylinder is determined in the Stokes approximation. The plane boundaries are assumed to be at rest while the cylinder is rotating with a constant velocity starting at t = 0. The problem is solved by means of three different methods, a finite element, a finite difference, and a boundary element method. The corresponding problem in which the constant velocity boundary condition on the cylinder is replaced by a condition of constant stress is also solved by means of the finite element method.

Study of three-dimensional unsteady Oseen flow

1978 ◽  
Vol 86 (4) ◽  
pp. 609-622 ◽  
Author(s):  
S. Murata ◽  
Y. Miyake ◽  
Y. Tsujimoto ◽  
F. Yamamoto
Keyword(s):  
Flow Field ◽  
External Force ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Applied Force ◽  
Two Dimensional ◽  
Uniform Velocity ◽  
Pressure Fields ◽  
Oseen Flow ◽  
Impulsive Pressure

In the present paper, it is intended to give the elementary solutions of three-dimensional unsteady Oseen flow when unsteady concentrated lift and/or drag is applied in the flow field. It is shown that the pressure fields due to concentrated impulsive lift and/or drag can be represented by an impulsive pressure doublet in the direction of the applied force and the corresponding velocity fields by diffusing free doublets in the direction of the external force that are shed from the location of the force application and convected downstream with otherwise uniform velocity. It is also confirmed that combination of the elementary solutions given in the present paper yields the two-dimensional ones.

Transient Growth of Three-Dimensional Vortex Perturbations During Near-Parallel Collision With a Circular Cylinder

2006 ◽  
Author(s):  
X. Liu ◽  
J. S. Marshall
Keyword(s):  
Circular Cylinder ◽  
Vortex Core ◽  
Computational Study ◽  
Three Dimensional ◽  
The Body ◽  
Transient Growth ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Flow Features

A computational study is reported that examines the transient growth of three-dimensional flow features for nominally parallel vortex-cylinder interaction problems. We consider a helical vortex with small-amplitude perturbations that is advected onto a circular cylinder whose axis is parallel to the nominal vortex axis. The study assesses the applicability of the two-dimensional flow assumption for parallel vortex-body interaction problems in which the body impinges on the vortex core. The computations are performed using an unstructured finite-volume method for an incompressible flow, with periodic boundary conditions along the cylinder axis. Growth of three-dimensional flow features is quantified by use of a proper-orthogonal decomposition of the Fourier-transformed velocity and vorticity fields in the cylinder azimuthal and axial directions. The interaction is examined for different axial wavelengths and amplitudes of the initial helical waves on the vortex core, and the results for cylinder force are compared to the two-dimensional results. The degree of perturbation amplification as the vortex approaches the cylinder is quantified and shown to be mostly dependent on the dominant axial wavenumber of the perturbation. The perturbation amplification is observed to be greatest for perturbations with axial wavelength of about 1.5 times the cylinder diameter.

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.

On steady Stokes flow in a trihedral rectangular corner

2003 ◽  
Vol 476 ◽  
pp. 159-177 ◽  
Author(s):  
A. M. GOMILKO ◽  
V. S. MALYUGA ◽  
V. V. MELESHKO
Keyword(s):  
Velocity Field ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Stagnation Line ◽  
Stagnation Points ◽  
Boundary Velocity ◽  
Different Types ◽  
Spiral Shape ◽  
Induced Flow

Motivated by the recent paper of Hills & Moffatt (2000), we investigate the Stokes flow in a trihedral corner formed by three mutually orthogonal planes, induced by a non-zero velocity distribution over one of the walls of the corner. It is shown that the local behaviour of the velocity field near the edges of the corner, where a discontinuity of the boundary velocity is assumed, coincides with the Goodier–Taylor solution for a two-dimensional wedge. Analysis of the streamline patterns confirms the existence of eddies near the stationary edge in the flow, induced either by uniform translation of one of the walls of the corner in the direction perpendicular to its bisectrix or by uniform rotation of a side about the vertex of the corner. These flows are shown to be quasi-two-dimensional. If the wall rotates about a centre displaced from the vertex, the induced flow is essentially three-dimensional. In the antisymmetric velocity field, a stagnation line appears composed of stagnation points of different types. Otherwise the three-dimensionality manifests itself in a non-closed spiral shape of the streamlines.

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