Viscous Incompressible Flow past a Circular Cylinder at Moderate Reynolds Numbers

1969 ◽  
Vol 12 (12) ◽  
pp. II-279
Author(s):  
Robert Leigh Underwood
Keyword(s):  
Circular Cylinder ◽  
Incompressible Flow ◽  
Reynolds Numbers ◽  
Viscous Incompressible Flow ◽  
Flow Past

Calculation of incompressible flow past a circular cylinder at moderate Reynolds numbers

1969 ◽  
Vol 37 (1) ◽  
pp. 95-114 ◽  
Author(s):  
Robert Leigh Underwood
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Differential Equations ◽  
Incompressible Flow ◽  
Equations Of Motion ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Number Range ◽  
Flow Parameters ◽  
Flow Past

The steady, two-dimensional, incompressible flow past a circular cylinder is calculated for Reynolds numbers up to ten. An accurate description of the flow field is found by employing the semi-analytical method of series truncation to reduce the governing partial differential equations of motion to a system of ordinary differential equations which can be integrated numerically. Results are given for Reynolds numbers between 0.4 and 10.0 (based on diameter). The Reynolds number at which separation first occurs behind the cylinder is found to be 5.75. Over the entire Reynolds number range investigated, characteristic flow parameters such as the drag coefficient, pressure coefficient, standing eddy length, and streamline pattern compare favourably with available experimental data and numerical solution results.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder

1957 ◽  
Vol 2 (3) ◽  
pp. 237-262 ◽  
Author(s):  
Ian Proudman ◽  
J. R. A. Pearson
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Reynolds Numbers ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Flow Past ◽  
Small Reynolds Numbers ◽  
Cylindrical Polar Coordinates ◽  
Flow Past A Sphere

This paper is concerned with the problem of obtaining higher approximations to the flow past a sphere and a circular cylinder than those represented by the well-known solutions of Stokes and Oseen. Since the perturbation theory arising from the consideration of small non-zero Reynolds numbers is a singular one, the problem is largely that of devising suitable techniques for taking this singularity into account when expanding the solution for small Reynolds numbers.The technique adopted is as follows. Separate, locally valid (in general), expansions of the stream function are developed for the regions close to, and far from, the obstacle. Reasons are presented for believing that these ‘Stokes’ and ‘Oseen’ expansions are, respectively, of the forms $\Sigma \;f_n(R) \psi_n(r, \theta)$ and $\Sigma \; F_n(R) \Psi_n(R_r, \theta)$ where (r, θ) are spherical or cylindrical polar coordinates made dimensionless with the radius of the obstacle, R is the Reynolds number, and $f_{(n+1)}|f_n$ and $F_{n+1}|F_n$ vanish with R. Substitution of these expansions in the Navier-Stokes equation then yields a set of differential equations for the coefficients ψn and Ψn, but only one set of physical boundary conditions is applicable to each expansion (the no-slip conditions for the Stokes expansion, and the uniform-stream condition for the Oseen expansion) so that unique solutions cannot be derived immediately. However, the fact that the two expansions are (in principle) both derived from the same exact solution leads to a ‘matching’ procedure which yields further boundary conditions for each expansion. It is thus possible to determine alternately successive terms in each expansion.The leading terms of the expansions are shown to be closely related to the original solutions of Stokes and Oseen, and detailed results for some further terms are obtained.

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