Zeitschrift für angewandte Mathematik und Physik ZAMP

, Volume 43, Issue 6, pp 1072–1084

# Separation of streamlines for spatially periodic flow at non-zero Reynolds numbers

• K. Ma
• D. W. Pravica
Original Papers

## Abstract

The flow generated by a small rotating circular cylinder at the center of a corrugated outer cylinder is considered. By using a Stokes expansion, the first order correction in the Reynolds numberR is found for the creeping flow solution. An approximate critical Reynolds numberR c is found at which separation appears, and it is expressed in terms of the boundary parameters. Separation is found to occur in the concave regions of the boundary skewed opposite to the direction of rotation of the inner cylinder. By partially solving for the second order correction in the Stokes expansion, it is found that an increase inR causes an increase in the torque exerted on the outer boundary.

### Keywords

Torque Reynolds Number Mathematical Method Circular Cylinder Outer Boundary

## Preview

### References

1. [1]
K. B. Ranger,Separation of streamlines for spatially periodic flow at zero Reynolds numbers, Quart. Appl. Math.,XLVII, No. 2, 367–373 (1989).Google Scholar
2. [2]
D. W. Pravica and K. B. Ranger,Spatially periodic Stokes flow stirred by a rotlet interior to a closed corrugated boundary, Quart. Appl. Math.,XLIX, No. 3, 453–461 (1991).Google Scholar
3. [3]
K. B. Ranger,The applicability of Stokes expansions to reversed flow, SIAM J. Appl. Math.,23, No. 3, 325–333 (1972).Google Scholar
4. [4]
K. B. Ranger,Diffusion and convection of vorticity at low Reynolds numbers produced by a rotlet interior to a circular cylinder, Quart. Appl. Math.,XLV, No. 4, 669–678 (1987).Google Scholar
5. [5]
I. Proudman, J. R. A. Pearson,Expansion at small Reynolds numbers for the flow past a sphere and a circular cylinder, J. Fluid Mech.,2, 237–262 (1957).Google Scholar
6. [6]
K. Ma and D. W. Pravica,Stakes flow in a two-dimensional spatially periodic boundary driven by a combination of line singularities, Quart. Appl. Math., to appear.Google Scholar
7. [7]
W. R. Dean,On the shearing morion of fluid past a projection, Proc. Cambridge Phil. Soc.,40, 19–36 (1944).Google Scholar