Phase-field lattice Boltzmann simulations of multiple dendrite growth with motion, collision, and coalescence and subsequent grain growth

Phase-field lattice Boltzmann model for dendrites growing and moving in melt flow

“…As the main goal of the present paper is to demonstrate that multiphase flow of growing particles can be handled with our approach, we performed our simulations in two dimensions with free energies of the bulk solid (β(Ti) of bcc structure) and bulk liquid phases taken from the CALPHAD-type assessment in ref., 46 and with reasonable estimates for the other input data. To keep the solution of the dynamical equations numerically tractable, as in the work of Takaki et al, 26 we set the viscosity about three orders of magnitude smaller than the experimental value. The parameter sets used in the simulations are compiled in Table 1.…”

“…[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] While the majority of the earlier studies refer to solidification of static particles in fluid flow, the motion of growing solid particles in the melt was addressed by more recent investigations. Solutions for the latter problem were presented by Do-Quang and Amberg, 21 Steinbach,22,23 Qi et al, 25 and Takaki and coworkers, 24,26,27 who coupled the phase-field approach to the Navier-Stokes equations 21,25 or to lattice Boltzmann hydrodynamics. [22][23][24]26,27 To describe a single dendritic particle that descends in a viscous fluid in two dimensions, Do-Quang and Amberg used a semi-sharp phase-field model combined with the distributed Lagrangian method to realize rigid body motion of the solid domain.…”

“…Solutions for the latter problem were presented by Do-Quang and Amberg, 21 Steinbach,22,23 Qi et al, 25 and Takaki and coworkers, 24,26,27 who coupled the phase-field approach to the Navier-Stokes equations 21,25 or to lattice Boltzmann hydrodynamics. [22][23][24]26,27 To describe a single dendritic particle that descends in a viscous fluid in two dimensions, Do-Quang and Amberg used a semi-sharp phase-field model combined with the distributed Lagrangian method to realize rigid body motion of the solid domain. 21 The phase-field approach by Steinbach and coworkers was used to describe the formation and motion of a single dendritic particle in shear flow in two and three dimensions, 22,23 whereas Takaki et al performed simulations in two dimensions for a descending single dendritic particle and the motion of several dendritic particles in shear flow.…”

“…21 The phase-field approach by Steinbach and coworkers was used to describe the formation and motion of a single dendritic particle in shear flow in two and three dimensions, 22,23 whereas Takaki et al performed simulations in two dimensions for a descending single dendritic particle and the motion of several dendritic particles in shear flow. 24,26 In the latter case a specific dendrite-dendrite interaction, "collision-coalescence" was assumed: the solid particles that touch each other stick together forming a single solid body that moves accordingly. In a recent work Qi et al 25 addressed the buoyancy induced motion of several dendrites, performing the simulations at relatively small viscosity contrast (up to 100) and a large density contrast (1000), however, retaining exclusively hydrodynamic interaction between the dendritic particles.…”

Multiscale dendritic needle network model of alloy solidification with fluid flow

“…Alleviating the high computational cost of explicit interface tracking, most computational studies over the past couple of decades have used the phase-field method [18,[29][30][31][32][33][34]. Still, even combining the most advanced state-of-the-art numerical methods and hardware, simulations remain limited to the scale of a handful of dendritic grains [35,36].…”