Flow around a confined rotating cylinder at small Reynolds number

Abstract

A numerical finite-volume technique to solve the two-dimensional Navier-Stokes equations is applied to the rotation of a rigid circular cylinder between parallel plane walls. In this confined situation, the torque exerted on the cylinder is a function of both the distance between the two walls and the position between them. In the absence of experimental results for this problem, we propose here new data of the torque in a wide range of confinements and we study the influence of the eccentricity of the cylinder. When the cylinder rotates close to a wall, there is also a fall of pressure that is likely to create cavitation in the fluid, in accordance with experimental results. Finally, a force parallel to the plane parallel boundaries is numerically obtained, whereas it is theoretically found to be equal to zero in the presence of a single wall. This phenomenon is studied in detail and an explanation is proposed here. The same results could be obtained for the torque experienced by a cylinder translating parallel to the parallel walls.

Forces and Torques on Rotating Spirochete Flagella

“…For this case, a rotating (translating) cylinder experiences no force (torque). However, recent computational analysis has shown that the presence of a second wall leads to a net force on a purely rotating cylinder [13]. We have analyzed this problem using lubrication theory and numerical analysis [14,15] and have found that the force on the rotating cylinder arises from the constraint that the volume flux of fluid in the gap above the cylinder must equal the flux of fluid through the lower gap.…”

Oscillations and translation of a free cylinder in a viscous confined flow

“…This results from the backflow near the second wall and has a sizable influence on the force distribution on the cylinder. 10 The displacement of a free cylinder released from an eccentric position inside a vertical gap has been computed by Hu 6 for three values of the Reynolds number Re based on the terminal velocity and the diameter of the particle. For Re ≤ 5, the cylinder reaches a final stable transverse position in the middle of the gap.…”

Force and torque on a cylinder rotating in a narrow gap at low Reynolds number: Scaling and lubrication analyses

“…Typically, 1.5-3 channel widths on each side of the particle are sufficient for the calculated characteristics to be independent of channel length." A few cases were implemented to validate the numerical results presented in Champmartin et al, 13 and consistent results were obtained. The numerical solutions obtained with COMSOL were therefore employed as a reference solution for comparison with the corresponding lubrication and scaling solutions.…”

“…It is perhaps then even more surprising that the force deviates from zero as a second wall (see Figure 3(b)), parallel to the first, is brought in from infinity. 13 As we shall see in the three geometries of Figure 2, the presence of a new boundary affects the previous interactions in a nontrivial, non-additive way.…”

“…Recently, Day and Stone 2 studied a rotating cylinder in a narrow-channel Poiseuille flow using lubrication analysis, as well as numerics. Champmartin et al 13 also looked at the same channel geometry and via numerical calculations they were able to investigate the entire parameter space. And more recently, Götze and Gompper 4 studied various configurations of multiple colloidal magnetic microspheres spinning in microchannels in geometries corresponding to our Types I and III.…”