On the flow past a sphere at low Reynolds number

1969 ◽  
Vol 37 (4) ◽  
pp. 751-760 ◽  
Author(s):  
W. Chester ◽  
D. R. Breach ◽  
Ian Proudman
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Low Reynolds Number ◽  
Incompressible Viscous Fluid ◽  
Euler’S Constant ◽  
Stokes Drag ◽  
Flow Past ◽  
Low Reynolds ◽  
Euler's Constant ◽  
Flow Past A Sphere

The flow of an incompressible, viscous fluid past a sphere is considered for small values of the Reynolds number. In particular the drag is found to be given by \[ D = D_s\{1+{\textstyle\frac{3}{8}}R+{\textstyle\frac{9}{40}}R^2(\log R+\gamma + {\textstyle\frac{5}{3}}\log 2 - {\textstyle\frac{323}{360}})+{\textstyle\frac{27}{80}}R^3\log R+O(R^3)\}, \] where Ds is the Stokes drag, R is the Reynolds number and γ is Euler's constant.

Low Reynolds number flow past a transverse cylinder at Mach two.

AIAA Journal ◽  
1972 ◽  
Vol 10 (10) ◽  
pp. 1381-1382
Author(s):  
CLARENCE W. KITCHENS ◽  
CLARENCE C. BUSH
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Flow Past ◽  
Number Flow ◽  
Low Reynolds

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.

Stability of the Low Reynolds Number Compressible Flow Past a NACA0012 Airfoil

AIAA Journal ◽  
2021 ◽  
pp. 1-15
Author(s):  
Laura Victoria Rolandi ◽  
Thierry Jardin ◽  
Jérôme Fontane ◽  
Jérémie Gressier ◽  
Laurent Joly
Keyword(s):  
Reynolds Number ◽  
Compressible Flow ◽  
Low Reynolds Number ◽  
Naca0012 Airfoil ◽  
Flow Past ◽  
Low Reynolds

Laminar Flow Past a Circular Cylinder: Reduction of Drag and Fluctuating Lift Using Upstream and Downstream Rods

2014 ◽  
Vol 493 ◽  
pp. 9-14
Author(s):  
Dedy Zulhidayat Noor ◽  
Eddy Widiyono ◽  
Suhariyanto ◽  
Lisa Rusdiyana ◽  
Joko Sarsetiyanto
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Circular Cylinder ◽  
Drag Reduction ◽  
Passive Control ◽  
Low Reynolds Number ◽  
Tandem Arrangement ◽  
Single Cylinder ◽  
Flow Past ◽  
Low Reynolds

Laminar flow past a circular cylinder has been studied numerically at low Reynolds number. The upstream and downstream rods have been used as passive control in order to reduce hydrodynamics forces acting on the cylinder. Both the upstream and downstream rods significantly contribute in reduction of drag and fluctuating lift compared to single cylinder without the rods. More detail, the upstream installation rod is more dominant in drag reduction than the downstream one. On the contrary, the downstream rod has suppressed the magnitude of the fluctuating lift almost twice that of the upstream configuration. Placing the two rods together as the upstream and downstream passive control in tandem arrangement has given more hydrodynamics forces reduction than the single rod configurations.Keywords:circular cylinder, passive control, tandem, drag, lift.

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