On the steady flow of a viscous fluid past a sphere at small reynolds numbers using Oseen's approximation

1961 ◽  
Vol 12 (6) ◽  
pp. 546-558
Author(s):  
Prabhu L. Bhatnagar ◽  
Purushattam D. Verma
Keyword(s):  
Viscous Fluid ◽  
Steady Flow ◽  
Reynolds Numbers ◽  
Small Reynolds Numbers

scholarly journals The steady flow of viscous fluid past a fixed spherical obstacle at small reynolds numbers

1929 ◽  
Vol 123 (791) ◽  
pp. 225-235 ◽  
Keyword(s):  
Viscous Fluid ◽  
Steady Flow ◽  
Kinematic Viscosity ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Great Distance ◽  
Small Reynolds Numbers

It was proposed by Oseen that, in considering the steady flow of a viscous fluid past a fixed obstacle, the velocity of disturbance should be considered small, and terms depending on its square neglected. This approximation is to be taken to hold not only at a great distance from the obstacle, but also right up to its surface; and involves the assumption that U d/v is small, where d is some representative length of the obstacle, which in the case of a sphere is taken to be its diameter, U is the undisturbed velocity of the stream, and v the kinematic viscosity of the fluid. With this approximation, the equations of motion become linear, and can be solved; the condition of no slip at the boundary is then applied to complete the solution. We take the obstacle to be a sphere of radius and take the origin of coordinates at its centre.

Calculations of unsteady viscous flow past a circular cylinder

1958 ◽  
Vol 4 (1) ◽  
pp. 81-86 ◽  
Author(s):  
R. B. Payne
Keyword(s):  
Circular Cylinder ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Viscous Flow ◽  
Steady Flow ◽  
Reynolds Numbers ◽  
A Value ◽  
Unsteady Viscous Flow ◽  
Starting Flow ◽  
Forward Integration

A numerical solution has been obtained for the starting flow of a viscous fluid past a circular cylinder at Reynolds numbers 40 and 100. The method used is the step-by-step forward integration in time of Helmholtz's vorticity equation. The advantage of working with the vorticity is that calculations can be confined to the region of non-zero vorticity near the cylinder.The general features of the flow, including the formation of the eddies attached to the rear of the cylinder, have been determined, and the drag has been calculated. At R = 40 the drag on the cylinder decreases with time to a value very near that for the steady flow.

Drag of a sphere in an unsteady flow of viscous fluid at small reynolds numbers

1988 ◽  
Vol 23 (1) ◽  
pp. 6-10 ◽  
Author(s):  
M. N. Gaidukov ◽  
V. G. Roman ◽  
Yu. I. Yalamov
Keyword(s):  
Viscous Fluid ◽  
Unsteady Flow ◽  
Reynolds Numbers ◽  
Small Reynolds Numbers
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