Numerical studies of the motion of spheroidal particles flowing with liquid metals through an electric sensing zone

Abstract

A mathematical model has been developed to describe the motion of variously shaped and oriented spheroids entrained in liquid metals passing through a cylindrical electric sensing zone (ESZ) developed for liquid metals cleanliness analyzer (LiMCA) systems. The fluid velocity field within the ESZ was obtained by solving the Navier-Stokes equations, while the trajectories of particles within the ESZ were calculated using the equations of motion for particles. These incorporate forces resulting from drag, added mass, history, and electromagnetic and fluid acceleration balanced against the time rate of changes in a particle momentum. The effects of particle or inclusion shape and orientation were taken into account by including correction factors for drag (RD), added mass (MA), history (B), and electromagnetic force (EM). The numerical results show that particle trajectories are affected by the magnetic pressure number (RH), the Reynolds number (Re), the blockage ratio (k), and the particle-fluid density ratio (γ). In the axial direction, spheroidal particles travel further axially before hitting the wall as the fluid velocity (Re) increases. In the radial direction, the outwardly directed electromagnetic force on nonconducting spheroids increases with radial distance from the axis, with increasing electric current (RH) and with increasing size (k) of the particle. At low electric currents (low RH), the competition between the electromagnetic force and the radial fluid acceleration force in the entrance region is predicted to result in particle movements first toward the central axis, before outward motion toward the wall, but directly toward the wall at large currents (high RH). Spheroidal particles with symmetric axes perpendicular to the transverse axis of the ESZ move faster toward the sidewall as the particle aspect ratio (E) increases. The dominating increase in the added mass force over the increase in the electromagnetic force with decreasing E makes this effect much stronger for oblates (E 1). The stronger drag force on a prolate with its symmetric axis parallel to the axis of the ESZ makes it move slower toward the wall than a prolate with its axis of symmetry perpendicular to the axis of the ESZ. Low-inertia (low-γ) spheroidal particles move faster toward the sidewall than do heavier particles. This effect of γ is stronger for prolates than for oblates traversing with their symmetric axes perpendicular to the axis of the ESZ, owing to the decreased added mass effect as E increases, while the effect of γ becomes much stronger for a prolate traversing with its symmetric axis perpendicular rather than parallel to the axis of the ESZ, owing to its smaller added mass. The radial particle velocity when approaching the wall is predicted to decrease due to the wall effects. This model has been applied to the movement of spheroidal inclusions within the ESZ of a LiMCA system in molten aluminum, and it was proven from the theoretical point of view that LiMCA systems could be used in aluminum industries.