On the uniqueness of steady flow past a rotating cylinder with suction

Abstract

The subject of this study is a steady two-dimensional incompressible flow past a rapidly rotating cylinder with suction. The rotation velocity is assumed to be large enough compared with the cross-flow velocity at infinity to ensure that there is no separation. High-Reynolds-number asymptotic analysis of incompressible NavierStokes equations is performed. Prandtl's classical approach of subdividing the flow field into two regions, the outer inviscid region and the boundary layer, was used earlier by Glauert (1957) for analysis of a similar flow without suction. Glauert found that the periodicity of the boundary layer allows the velocity circulation around the cylinder to be found uniquely. In the present study it is shown that the periodicity condition does not give a unique solution for suction velocity much greater than 1/Re. It is found that these non-unique solutions correspond to different exponentially small upstream vorticity levels, which cannot be distinguished from zero when considering terms of only a few powers in a large Reynolds number asymptotic expansion. Unique solutions are constructed for suction of order unity, 1/Re, and 1/ √ Re. In the last case an explicit analysis of the distribution of exponentially small vorticity outside the boundary layer was carried out.

Numerical Study of the Flow Behind a Rotary Oscillating Circular Cylinder

“…Lu (1996) also studied the development of the wake behind a circular cylinder impulsively started into rotatory and rectilinear motion. Baek and Sung (1998) have performed a numerical simulation of the flow behind a rotary oscillating circular cylinder at Re ¼ 110: Recently, Buldakov et al (2000) studied a steady two-dimensional incompressible flow past a rapidly rotating cylinder with suction, based on highReynolds-number asymptotic analysis of incompressible Navier -Stokes equations. Dennis et al (2000) used a series expansion for small time to investigate the temporal development of two-dimensional viscous incompressible flow induced by an impulsively started circular cylinder which performs time-dependent rotational oscillations about its axis and translates at right angles to the axis.…”