Limiting casting expression speed was obtained and the flow redistribution and thermal history in a horizontal direct-chill (HDC) casting was predicted using the numerical modeling approach. The governing solidification equations were non-dimensionalized to understand the relevant contribution of each term in the solidification processes in the HDC system. The effect of an increase in the casting speed on the flow characteristics and sump length was represented by the Péclet number Pe. Details of the simulation reveal that at a low Pe, the natural convective flow creates minor counter-clockwise recirculating cells in the lower half of the HDC domain. However, at a Pe above 82.75, the minor recirculating cells disappear due to the strong forced convective flow from the upstream. Additionally, an increase in the Pe increases the sump length, strength, and spread of the turbulence field within and beyond the mold region. The limiting casting conditions are computed by predicting the sump length over which the alloy temperature is above the solidus temperature. This gives a simple relation for the casting speed as a function of the geometrical data and the alloy properties. The current work is useful to casting engineers who always rely on trial and error in choosing a new casting speed whenever a new alloy is to be produced. Hence, with the new information and the casting speed relations, it is possible and easy to predict the operating window over which melt break-out can occur during HDC.

A numerical modeling of diffusion-controlled heat and specie transfer using a source base method to determine evolution of liquid/solid fraction from energy equation both for constant densities in the phases and variable densities as a function of temperature and concentration was developed to predict macro-solute redistribution in binary alloy system. From the results, it is observed that there was a solute depleted zone near the chill surface and that, the source base method can be effectively implemented without the need for setting a large arbitrary value in determining the derivative of liquid fraction-temperature function . The cooling curve and the liquid volume fraction versus temperature profile shows a smooth transition from fully liquid to mushy zone and then to fully solid state, hence, adequate handling of the jump discontinuity was ensured. The liquid fraction-temperature relation outlined in this work is suitable for tracking the liquid/solid interface.

A comprehensive modelling of globular equiaxed eutectic solidification in a direct chill casting of aluminium binary alloy systems has been presented. The modelling applies the finite volume method in a diffusion dominated 2D axisymetric domain. The model couples the macroscopic heat transfer equation with solidification kinetics model to predict total solidification time, actual solidification time, grain size, undercooling, and grain growth rate in the two binary aluminium alloy systems namely; Al-Cu system and Al-Si system. The linearization of the solidification kinetics source term coupled to the heat transfer equation ensures robust and converged computation of the numerical model. The results obtained show that under the same cooling conditions at the billet surface, Al-Cu alloy system solidifies faster than Al-Si alloy system. In addition higher undercooling, grain size and growth rate are evident in the former than the later.