Numerical study of equilibrium radial positions of neutrally buoyant balls in circular Poiseuille flows
Tsorng‐Whay Pan, An‐Ping Li, Roland Glowinski
Abstract
In this article, we have studied, via direct numerical simulations, the equilibrium radial positions of neutrally buoyant balls moving in circular Poiseuille flows. For the one ball case, the Segre–Silberberg effect takes place at low Reynolds numbers (Re) as expected. However, at higher Re, the ball moves to one of two equilibrium positions. At even higher Re, the ball is pinched to a radial position closer to the central axis. For the case of two neutrally buoyant balls placed on a line parallel with the central axis initially, this two-ball train is stable at low Re and its mass center moves to the outer Segre–Silberberg equilibrium position like the migration of a single neutrally buoyant ball. Moreover, for Re values greater than the critical value, Rec = 435, the two-ball train is unstable. The two balls interact periodically, suggesting a (kind of) Hopf bifurcation phenomenon. Nevertheless, the averaged mass center of the two balls is located at the inner equilibrium radial position.