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The motion of a neutrally buoyant particle of an elliptic shape in two dimensional shear flow: a numerical study

In this paper, we investigate the motion of a neutrally buoyant cylinder of an elliptic shape freely moving in two dimensional shear flow by direct numerical simulation. An elliptic shape cylinder in shear flow, when initially being placed at the middle between two walls, either keeps rotating or has a stationary inclination angle depending on the particle Reynolds number $Re=G_r r_a^2/ν$, where $G_r$ is the shear rate, $r_a$ is the semi-long axis of the elliptic cylinder and $ν$ is the kinetic viscosity of the fluid. The critical particle Reynolds number $Re_{cr}$ for the transition from a rotating motion to a stationary orientation depends on the aspect ratio $AR=r_b/r_a$ and the confined ratio $K=2r_a/H$ where $r_b$ is the semi-short axis of the elliptic cylinder and $H$ is the distance between two walls. Although the increasing of either parameters makes an increase in $Re_{cr}$, the dynamic mechanism is distinct. The $AR$ variation causes the change of geometry shape; however, the $K$ variation influences the wall effect. The stationary inclination angle of non-rotating slender elliptic cylinder with smaller confined ratio seems to depend only on the value of $Re-Re_{cr}$. An expected equilibrium position of the cylinder mass center in shear flow is the centerline between two walls, but when placing the particle away from the centerline initially, it migrates either toward an equilibrium height away from the middle between two walls or back to the middle depending on the confined ratio and particle Reynolds number.