Numerical studies of the motion of particles in current-carrying liquid metals flowing in a circular pipe

Abstract

A mathematical model has been developed to describe the motion of particles in current-carrying liquid metals flowing through a cylindrical pipe. The fluid velocity field was obtained by solving the Navier-Stokes equations, and the trajectories of particles were calculated using equations of motion for particles. These incorporate the drag, added mass, history, electromagnetic, and fluid acceleration forces. The 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 according to the relative importance of associated force terms. In the axial direction, the particles follow the fluid velocity closely and will move further axially before reaching the wall as the fluid velocity (Re) increases. In the radial direction, the outwardly directed electromagnetic force on the particle increases with radial distance from the axis, with increasing electric current (RH), and increasing size (k) of particle. The competition between the electromagnetic force and the radial fluid acceleration force in the entrance region results in particle movement toward the central axis before moving toward the wall for small electric current (low RH) and directly toward the wall for large current (high RH). The low inertia (γ) bubbles move faster toward the wall than heavier particles do. The radial velocity of the particle movement as it approaches the wall is predicted to decrease due to wall effects. This model has been applied to the movement of inclusions within the electric sensing zone (ESZ) of the liquid metal cleanliness analyzer (LiMCA) system in molten aluminum, and it was proved that LiMCA system could be used in aluminum industries.