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In this study, the Euler-Euler and Euler-Lagrange modeling approaches were applied to simulate the multiphase flow in the water model and gas-stirred ladle systems. Detailed comparisons of the computational and experimental results were performed to establish which approach is more accurate for predicting the gas-liquid multiphase flow phenomena. It was demonstrated that the Euler-Lagrange approach is more accurate than the Euler-Euler approach. The Euler-Lagrange approach was applied to study the effects of the free surface setup, injected bubble size, gas flow rate, and slag layer thickness on the slag-steel interaction and mass transfer behavior. Detailed discussions on the flat/non-flat free surface assumption were provided. Significant inaccuracies in the prediction of the surface fluid flow characteristics were found when the flat free surface was assumed. The variations in the main controlling parameters (bubble size, gas flow rate, and slag layer thickness) and their potential impact on the multiphase fluid flow and mass transfer characteristics (turbulent intensity, mass transfer rate, slag-steel interfacial area, flow patterns, etc.,) in gas-stirred ladles were quantitatively determined to ensure the proper increase in the ladle refining efficiency. It was revealed that by injecting finer bubbles as well as by properly increasing the gas flow rate and the slag layer thickness, the ladle refining efficiency can be enhanced significantly.

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To relax many of the assumptions used in continuum approaches, a general stochastic model has been developed. The stochastic model can be used not only for an accurate description of the fraction of solid evolution, and therefore accurate cooling curves, but also for simulation of microstructure formation in castings. The advantage of using the stochastic approach is to give a time- and space-dependent description of solidification processes. Time- and space-dependent processes can also be described by partial differential equations. Unlike a differential formulation which, in most cases, has to be transformed into a difference equation and solved numerically, the stochastic approach is essentially a direct numerical algorithm. The stochastic model is comprehensive, since the competition between various phases is considered. Furthermore, grain impingement is directly included through the structure of the model. In the present research, all grain morphologies are simulated with this procedure. The relevance of the stochastic approach is that the simulated microstructures can be directly compared with microstructures obtained from experiments. The computer becomes a `dynamic metallographic microscope'. A comparison between deterministic and stochastic approaches has been performed. An important objective of this research was to answer the following general questions: (1) `Would fully deterministic approaches continue to be useful in solidification modelling?' and (2) `Would stochastic algorithms be capable of entirely replacing purely deterministic models?'

LAURENTIU NASTACUltrasonic treatment (UST) was studied in this work to improve the quality of the cast ingots as well as to control the solidification structure evolution. Ultrasonically induced cavitation consists of the formation of small cavities (bubbles) in the molten metal followed by their growth, pulsation, and collapse. These cavities are created by the tensile stresses that are produced by acoustic waves in the rarefaction phase. The pressure for nucleation of the bubbles (e.g., cavitation threshold pressure) may decrease with increasing the amount of dissolved gases and especially with the amount of inclusions in the melt. Modeling and simulation of casting solidification of alloys with UST requires complex multiscale computations, from computational fluid dynamics (CFD) macroscopic modeling through mesoscopic to microscopic modeling, as well as strategies to link various length-scales emerged in modeling of microstructural evolution. The developed UST modeling approach is based on the numerical solution of the Lilley model (that is founded on Lighthills's acoustic analogy), fluid flow, heat transfer equations, and mesoscopic modeling of the grain structure. The CFD analysis tool is capable of modeling acoustic streaming and ultrasonic cavitation. It is used in this work to study ingot solidification under the presence of ultrasound. The UST model was applied to low-temperature alloys including Al-and Mg-based alloys. Although the predicted ultrasonic cavitation region is relatively small, the acoustic streaming is strong and, thus, the created/survived bubbles/nuclei are transported into the bulk liquid quickly. The predicted grain size under UST condition is at least one order of magnitude lower than that without UST.