A mathematical model of the heat and fluid flows in direct-chill casting of aluminum sheet ingots and billets

A finite-element method model for the time-dependent heat and fluid flows t hat develop during direct-chill (DC) semicontinuous casting of aluminium in gots is presented. Thermal convection and turbulence are included in the mo del formulation and, in the mushy zone, the momentum equations are modified with a Darcy-type source term dependent on the liquid fraction. The bounda ry conditions involve calculations of the air gap along the mold wall as we ll as the heat transfer to the falling water film with forced convection, n ucleate boiling, and film boiling. The mold wall and the starting block are included in the computational domain. In the start-up period of the castin g, the ingot domain expands over the starting-block level. The numerical me thod applies a fractional-step method for the dynamic Navier-Stokes equatio ns and the "streamline upwind Petrov-Galerkin" (SUPG) method for mixed diff usion and convection in the momentum and energy equations. The modeling of the start-up period of the casting is demonstrated and compared to temperat ure measurements in an AA1050 200 X 600 mm sheet ingot.