The need to achieve increased efficiency and performance in aerospace gas turbines requires advanced single crystal Ni-based superalloys to exhibit increased temperature capabilities. High temperature creep resistance of the turbine blades is one of the major limitations to meet increased performance goals of gas turbines. The ultimate creep resistance of the Ni-based superalloys is dependent on solidification structures formed during casting.\ud In this study, multi-scale modelling method was used to study the solidification structure evolution occurring at various scales during investment casting. Modelling of solidification on the macroscopic scale of the process was implemented using a macroscopic Finite Element casting model, ProCAST, to predict thermal and flow profiles. The predicted thermal and flow data were then used as input in a meso-scale model Cellular Automaton Finite Element (CAFE) to predict grain structure and grain orientations during solidification. At the micro-level, detailed dendritic morphology and solutal interaction were investigated using a μMatIC model. Using the multi-scale approach, grain selection in spiral grain selector, formation of new grains ahead of solidification interface and the effect of dendrite packing patterns on primary dendrite spacing were investigated.\ud The effect of spiral shape on grain selection in single crystal grain selector has been systematically studied. It was found that the efficiency of the spiral selector significantly depends on its geometry and dimensions. The spiral becomes more efficient with a smaller wax wire diameter, larger spiral diameter and smaller take-off angle.\ud Formation of new grains ahead of solid/liquid growth front was simulated. Stray grain formation in the platform region of turbine blades was investigated, indicating that the alloy with greater susceptibility to the formation of stray grains has lower critical nucleation undercooling. The columnar-to-equiaxed transition (CET) during solidification was predicted and the effect of material properties on the CET was analyzed. The analysis results revealed that the CET can be promoted by: (1) decreasing the critical nucleation undercooling; (2) increasing the nuclei density of the melt; and (3) extending the solidification range.\ud Dendrites with different packing patterns were used to simulate dendrite spacing adjustment during solidification. It was found that the branching of secondary and tertiary arms in the hexahedral packing is easier than that in the cuboidal packing, leading to a smaller average spacing
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