Flow around a rotating cylinder near a plane boundary

Abstract

Penalty finite-element solutions have been obtained for steady uniform flow from the left to the right over a clockwise rotating circular cylinder near a plane wall. Results are presented for Reynolds numbers 20 and 40, the non-dimensional speed of rotation of the cylinder 0.0 ~ 0.5 and the gap between the plane wall and the cylinder surface 0.2 ~ 4.5 times the diameter of the cylinder. The motion is assumed to be two-dimensional and to be governed by the Navier-Stokes equations for incompressible fluids. The finite element approach is utilized and the frontal method is used to solve the stiffness matrix. In the cases of the cylinder without rotation, the results show that when the gap is large (H>2D), the effect of the wall makes the pressure on the cylinder surface decrease, and Cl, Cd and Ct increase. When the gap becomes small (H < 2D), it makes the pressure and Cl increase, and Ct and Cd decrease. For the gap H < 0.7D, a recirculation zone is formed on the plane wall behind the cylinder. The smaller the gap, the recirculation zone is closer to the cylinder. The average rate of variation of Cl and Cd for H < 1D is about ten times those for H > 1D.In the cases of the cylinder with rotation, effect of the rotation makes the upper separation point shift upstream and the lower one downstream, the pressure on the lower surface of the cylinder increase and on the upper surface decrease, and Cl increase linearly and Cd decrease non-linearly. But when H > 2D, Cd is independent of the rotation speed of the cylinder. When the rotation speed of the cylinder becomes large enough, the fully reversed flow in the gap occurs; the lower separation point and the wake pair behind the cylinder disappear. The effects of the wall and cylindrical rotation on Cl and Ct may be superposed linearly for H > 1D.In addition, the cylindrical rotation affects mainly the location of the separation point but not the value of the vorticity. It does not alter the central position of the recirculation zone but diminishes its size. When Re = 20, Cl, Cd and Ct vary greatly with H < 1D, but when Re = 40, they

Analysis of Viscous Micropumps and Microturbines

“…The bulk velocities obtained were as high as 10 % of the surface speed of the rotating cylinder. A finite-element solution for low-Reynolds-number, uniform, 2-D flow past a rotating cylinder near an impermeable plane boundary has already been obtained by Liang and Liou (1995). However detailed two-dimensional Navier-Stokes simulations of the pump described above have been carried out by Sharatchandra et al (1997a), who extended the operating range of Re beyond 100.· The effects of varying the channel height H and the rotor eccentricity e have been studied.…”

Micropumps, microturbines, and flow physics in microdevices

“…A finite-element solution for low-Reynolds-number, uniform flow past a rotating cylinder near an impermeable plane boundary has already been obtained by Liang and Liou (1995). However a detailed two-dimensional Navier-Stokes simulations of the pump described above have been carried out by Sharatchandra et al (1997), who extended the operating range of Re beyond 100.…”