Mesoscopic modeling of equiaxed and columnar solidification microstructures under forced flow and buoyancy-driven flow in hypergravity: Envelope versus phase-field model

Abstract

Quantitative modeling of solidification microstructures growing under the influence of convection is a challenging multiscale problem. It is of particular interest in processes where strong flow is present, such as centrifugal casting of Ti–Al alloys, where hypergravity strongly reinforces the buoyancy-driven flow. We present the coupling of the mesoscopic envelope model for dendritic solidification with fluid flow. We use the model to investigate columnar and equiaxed dendritic growth of the β-solidifying Ti–45 at.%Al under the influence of flow. The calculations are compared to phase-field results in 2D. For equiaxed growth the case of forced flow is treated. For columnar growth, the influence of buoyancy-driven flow on the growing structure and on the primary dendrite arm spacing is characterized for gravity levels ranging from 0 to ± 15 g. The computational cost of the mesoscopic simulations is around two orders of magnitude lower than that of phase field. We show that the mesoscopic model can accurately reproduce the microstructure characteristics, such as grain shape and primary arm spacing (PDAS), as long as the dendrite tip remains parabolic. When flow effects in columnar growth are strong enough to change the tip shape and induce tip splitting events, the mesoscopic envelope model does not reproduce the resulting branched microstructures. It does however predict the corresponding PDAS reduction at the correct gravity level.