A numerical model based on the shallow water equations (SWE) was proposed to simulate the two-dimensional (2D) average flow dynamics of the liquid metal spreading inside a horizontally rotating mold. The SWE were modified to account for the forces, such as the centrifugal force, Coriolis force, shear force with the mold wall, and gravity. In addition, inherent vibrations caused by a poor roundness of the mold and the mold deformation due to temperature gradients were applied explicitly by perturbing the gravity and the axis bending, respectively. Several cases were studied with the following initial conditions: a constant average height of the liquid metal (5, 10, 20, 30, and 40 mm) patched as a flat or a perturbed surface. The angular frequency Ω of the mold (∅1150–3200) was 71.2 (or 30) rad/s. Results showed various wave patterns propagating on the free surface. In early stages, a single longitudinal wave moved around the circumference. As the time proceeded, it slowly diminished and waves traveled mainly in the axial direction. It was found that the mean amplitude of the oscillations grows with the increasing liquid height.
Stability and Numerical Simulation of the Liquid Metal Pinch Using the Shallow Water Approximation
