History of simulation of transient temperature fields of solidifying metals with phase change

Solidification and cooling of the gravitationally cast metals (technology A) or continuously cast (concast) metals, foremost steels (technology B) rank among the major technological processes. It is a rather complex problem of transient heat and mass transfer. The process in a system A casting (riser)-mould (chills)-ambient can be described by the Fourier’s equation, in a system B concasting-crystallizer or concasting-ambient (in a radial concasting machine) is described by the Fourier-Kirchoff’s equation. Analytical methods can solve only one-dimensional non-transient temperature field of the gravitationally cast casting. Analog methods allow to solve only 2D transient temperature field (in limited range 3D). The construction of the 12 types of the ingot-moulds of the steelworks and the crystallization of pure aluminium was successfully optimized via a 2D Liebmanńs analog. The solidification and cooling of the steel roller (the diameter is 1180 and height 2100 mm) of the 500×1000×500 mm ductile cast-iron block was simulated by 3D numerical model (ANSYS). Both solutions in several construction proposal brought the optimization of production. The numerical model of a continuously cast casting was developed in two variants, off-line and on-line version. Both are based on the numerical method of finite differences with explicit formula for the unknown temperature of the mesh node in the next time step. On-line version of the model works non-stop in real time, ensures continuous correction of the real process of the caster in question. Both models are original and both are applicable for any caster.