Modeling of coupled motion and growth interaction of equiaxed dendritic crystals in a binary alloy during solidification

Xin Bo Qi,Tong Zhao Gong,Xiu Hong Kang,Yun Chen,Dian Zhong Li

doi:10.1038/srep45770

Abstract

Motion of growing dendrites is a common phenomenon during solidification but often neglected in numerical simulations because of the complicate underlying multiphysics. Here a phase-field model incorporating dendrite-melt two-phase flow is proposed for simulating the dynamically interacted process. The proposed model circumvents complexity to resolve dendritic growth, natural convection and solid motion simultaneously. Simulations are performed for single and multiple dendritic growth of an Al-based alloy in a gravity environment. Computing results of an isolated dendrite settling down in the convective supersaturated melt shows that solid motion is able to overwhelm solutal convection and causes a rather different growth morphology from the stationary dendrite that considers natural convection alone. The simulated tip growth dynamics are correlated with a modified boundary layer model in the presence of melt flow, which well accounts for the variation of tip velocity with flow direction. Polycrystalline simulations reveal that the motion of dendrites accelerates the occurrence of growth impingement which causes the behaviors of multiple dendrites are distinct from that of single dendrite, including growth dynamics, morphology evolution and movement path. These polycrystalline simulations provide a primary understanding of the sedimentation of crystals and resulting chemical homogeneity in industrial ingots.

Highlights

Experiments to measure tip velocities of six primary dendrite arms of cubic SCN-acetone alloy and investigated the effects of settling speed and inclination angle on growth dynamic in details[9]
Rojas et al and Takaki et al used the PFLB method to simulate motion and growth of a dendrite[14,15]. Both methods consist of two parts: the phase-field model is implemented to calculate the growth of dendrites, while the fictitious domain method or Lattice Boltzmann method is employed to compute the motion of liquid and solid
Compared to previously used phase-field Lattice Boltzmann method, it is not necessary to track explicitly the interfaces between different phases or different grains to resolve the motion of crystals, but still able to predict the rotational and translational motion of a solid with complex morphology in the proposed method

Summary

Model Description

The phase-field model proposed by Karma for alloy solidification[23] and the procedures by Warren et al for polycrystalline materials[24] are combined to simulate dendritic alloy solidification from a supersaturated liquid melt. This assumption refers to the schemes of conventional diffusive interface model for two incompressible viscosity-matched fluids[17,18] The advantage of this method is that the motion of liquid and solid can be calculated simultaneously within one set of governing equations. A series of numerical tests are presented in the Supplementary Materials, including the rising of a circular particle, rotation of a growing dendrite at a constant angular velocity and single crystal in a forced shear flow These numerical tests verify the accuracy of the proposed model in handling dendrite-melt two phase flow and the choice of interface width parameter, W0 (see Figs S1–S5 and corresponding analysis in the Supplementary Note)

Results and Discussion

Here in the calculation of

Conclusion

Author Contributions

Additional Information