Comparing mesoscopic models for dendritic growth

Abstract

We present a quantitative benchmark of multiscale models for dendritic growth simulations. We focus on approaches based on phase-field, dendritic needle network, and grain envelope dynamics. As a first step, we focus on isothermal growth of an equiaxed grain in a supersaturated liquid in three dimensions. A quantitative phase-field formulation for solidification of a dilute binary alloy is used as the reference benchmark. We study the effect of numerical and modeling parameters in both needle-based and envelope-based approaches, in terms of their capacity to quantitatively reproduce phase-field reference results. In light of this benchmark, we discuss the capabilities and limitations of each approach in quantitatively and efficiently predicting transient and steady states of dendritic growth. We identify parameters that yield a good compromise between accuracy and computational efficiency in both needle-based and envelope-based models. We expect that these results will guide further developments and utilization of these models, and ultimately pave the way to a quantitative bridging of the dendrite tip scale with that of entire experiments and solidification processes.

Multiscale prediction of microstructure length scales in metallic alloy casting

“…For the Al-1 wt%Cu alloy, the calculated values for λ min and λ max exhibit a striking agreement between PF and DNN methods, in spite of the lower undercooling predicted by DNN compared to PF (Fig. 9a), which was already observed and reported in an ongoing benchmark study [108]. Some discrepancy between DNN and PF appears at higher undercooling (i.e.…”

“…The numerical spatial discretization can be taken at the same order as the tip radius, such that the domain size can be considerably larger than in equivalent PF simulation, in particular for concentrated alloys with ρ l D . DNN simulations have been verified to reproduce analytical and phase-field predictions for steady-state and transient growth kinetics [62,63,86]. First DNN applications to the prediction of primary dendritic spacings in binary Al alloys, compared to well-controlled thin-sample directional solidification experiments [63,87,88], have shown promising results.…”

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

“…The stagnant-film thickness, , is a key parameter of the mesoscopic model. While a general calibration of has been previously established for steady-state equiaxed growth in purely diffusive conditions in 3D [23], it is not necessarily valid for growth transients [51,52], for 2D growth, and under the influence of convection. In this work we used a value for that gave the best fit to the phase-field simulations (reported in Table 2).…”

“…The influence of the stagnant-film thickness in convective conditions is yet unknown. Calibration guidelines for this model have been established only for steady-state growth [23] or for slow transients [31,52], both in diffusive conditions. This now needs to be extended to convective conditions and to fast transients, such as at the onset of equiaxed growth.…”

“…This is not linked to convection, but is also present in simulations of diffusive growth, as already shown in Refs. [23,52].…”