A level set simulation of dendritic solidification of multi-component alloys

A level set method combining features of front tracking methods and fixed domain methods is presented to model microstructure evolution in the solidification of multi-component alloys. Phase boundaries are tracked by solving the multi-phase level set equations. Diffused interfaces are constructed from these tracked phase boundaries using the level set functions. Based on the assumed diffused interfaces, volume-averaging techniques are applied for energy, species and momentum transport. Microstructure evolution in multi-component alloy systems is predicted using realistic material parameters. The methodology avoids the difficulty of parameter identification needed in other diffused interface models, and allows easy application to various practical alloy systems. Techniques including fast marching, narrow band computing and adaptive meshing are utilized to speed up computations. Several numerical examples are considered to validate the method and examine its potential for modeling solidification of practical alloy systems. These examples include two- and three-dimensional solidification of a binary alloy in an undercooled melt, a study of planar/cellular/dendritic transition in the solidification of a Ni-Cu alloy, and eutectic and peritectic solidification of an Fe-C system. Adaptive mesh refinement in the rapidly varying interface region makes the method practical for coupling the microstructure evolution at the meso-scale with buoyancy driven flow in the macro-scale, which is shown in the solidification of a Ni-Al-Ta ternary alloy.

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