On the low-Reynolds-number flow about two rotating circular cylinders

Abstract

International audienceThe viscous and steady flow about two distinct parallel infinite rotating circular cylinders is theoretically investigated. Because any inner steady Stokes flow is not quiescent far from the cylinders, a strictly steady analysis requires matching an inner steady Stokes approximation with an outer solution of the steady Navier-Stokes equations. However, except for the case of identical cylinders of equal angular velocities, it is impossible to determine this outer solution. In the same spirit as Nakanishi et al. (1997) and Ueda et al. (2001), the present work therefore first addresses the unsteady viscous flow induced by cylinders impulsively set into both steady rotation and translation W. Using integral representations of the stream function and the vorticity, the resulting long-time flow is approximated in the limit of large viscosity. Letting time tend to infinity for W non-zero extends Lee & Leal (1986) and agrees with Watson (1996), whereas the required steady flow is obtained by making W vanish before letting time go to infinity. At the obtained leading-order approximation, the 'lift' and 'drag' forces on each cylinder (parallel and normal to the line of centres) are respectively zero and independent of the Reynolds number. The drag experienced by each body is plotted versus the gap between the cylinders for several values of the rotation, both for identical and non-identical cylinders

Self-propulsion of a counter-rotating cylinder pair in a viscous fluid

“…9 Since then, several authors have presented extensive analytical studies for the behaviour of the flow at low Reynolds numbers. 10,11 Numerical results for the flow past a fixed counter-rotating cylinder pair at non-zero Reynolds numbers were presented by Chan et al 12 They found that for certain combinations of inflow and rotational velocities, the vortical wake was suppressed resulting in zero or negative drag values. In the context of self-propulsion, steady-state solutions were found numerically for two counter-rotating cylinders 13,14 and an axisymmetric torus.…”

High-Order Spectral Difference Simulation of Laminar Compressible Flow Over Two Counter-Rotating Cylinders

“…The nature of the investigation, however, has remained mainly theoretical and mathematical. 3,4 With current Computational Fluid Dynamic capability, the characteristics of this special flow can certainly be more fully quantified numerically by solving the full governing equations with a high-order accurate scheme, hence the motivation of the present study.…”

Dynamic self-assembly and directed flow of rotating colloids in microchannels

“…Micropumps based on this principle have been studied experimentally [48] and numerically [20,21]. Moreover, pairs of corotating cylinders in an unbounded viscous fluid mutually exert forces on each other that are perpendicular to their connecting line at leading-order of approximation [49], causing the pairs to circulate about each other.…”