Phase-field Simulation Of Dendritic Growth Research Articles

Parallel-GPU-accelerated adaptive mesh refinement for three-dimensional phase-field simulation of dendritic growth during solidification of binary alloy

In the phase-field simulation of dendrite growth during the solidification of an alloy, the computational cost becomes extremely high when the diffusion length is significantly larger than the curvature radius of a dendrite tip. In such cases, the adaptive mesh refinement (AMR) method is effective for improving the computational performance. In this study, we perform a three-dimensional dendrite growth phase-field simulation in which AMR is implemented via parallel computing using multiple graphics processing units (GPUs), which provide high parallel computation performance. In the parallel GPU computation, we apply dynamic load balancing to parallel computing to equalize the computational cost per GPU. The accuracy of an AMR refinement condition is confirmed through the single-GPU computations of columnar dendrite growth during the directional solidification of a binary alloy. Next, we evaluate the efficiency of dynamic load balancing by performing multiple-GPU parallel computations for three different directional solidification simulations using a moving frame algorithm. Finally, weak scaling tests are performed to confirm the parallel efficiency of the developed code.

Multi-GPUs parallel computation for AMR phase-field simulation of dendrite growth with liquid flow and solid motion

Multi-GPUs parallel computation for AMR phase-field simulation of dendrite growth with liquid flow and solid motion

GPU-accelerated three-dimensional phase-field simulation of dendrite growth in a nickel-based superalloy

The microstructure formation of a nickel-based superalloy during solidification in three dimensions was investigated using the phase-field method. To accelerate the large-scale phase-field simulation, a parallel computing approach was developed using the graphic processing unit (GPU), and the limitation of insufficient GPU memory was circumvented by employing an asynchronous concurrent algorithm. The performance of the GPU-based parallel computing method was tested and the results demonstrate that a maximum performance of 774.292 GFLOPS (giga floating-point operations per second) can be obtained using a single NVIDIA GTX1080 GPU. In simulations of isothermal solidification, the microstructure evolution of a single and multiple dendrites under different undercooling levels was shown in detail. During the solidification, the dendrite tip growth velocity and fraction solid were recorded and then analyzed. In simulations of directional solidification, the formation of primary dendrite arms under different temperature gradients was investigated, and the simulated microstructure was in good agreement with experimental observations. Additionally, the distribution of primary dendrite arm spacing was quantitatively analyzed by Voronoi tessellation. Finally, simulation of polycrystalline growth in directional solidification was conducted to study the dendrite competitive growth. The unusual overgrowth phenomenon was observed in the initial growth stage, while as the solidification process proceeded, the dendrites with small inclination angles were more likely to overgrow the dendrites with large inclination angles.

Phase-field simulation of dendrite growth in the presence of lateral constraints

The effect of a sudden change in the crossing section on the microstructural evolution as well as solute and heat diffusions during solidification of the Ni-40.8% Cu alloy was investigated by implementing a non-isothermal phase-field model. Simulations with lateral constraints of different sizes were carried out to study the changes of the dendritic growth manner. Significant changes in microstructures had been observed as the interface encountered a sharply reduced crossing section; a cellular–dendrite transition could be achieved with lateral constraints, and the tip velocity significantly changed during the development of dendrite microstructures, and also, lateral constraints of different sizes had different effects on changes of the tip positions as well as tip velocities during the dendritic growing through constraints, which agreed well with experimental results.

Phase-field simulation of dendritic growth in a forced liquid metal flow coupling with boundary heat flux

A phase-field model with forced liquid metal flow was employed to study the effect of boundary heat flux on the dendritic structure forming of a Ni-40.8%Cu alloy with liquid flow during solidification. The effect of the flow field coupling with boundary heat extractions on the morphology change and distributions of concentration and temperature fields was analyzed and discussed. The forced liquid flow could significantly affect the dendrite morphology, concentration and temperature distributions in the solidifying microstructure. And coupling with boundary heat extraction, the solute segregation and concentration diffusion were changed with different heat flux. The morphology, concentration and temperature distributions were significantly influenced by increasing the heat extraction, which could relatively make the effect of liquid flow constrained. With increasing the initial velocity of liquid flow, the lopsided rate of the primary dendrite arm was enlarged and the transition of developing manner of the secondary arms moved to the large heat extraction direction. It was the competition between heat flux and forced liquid flow that finally determined microstructure forming during solidification.

Phase-field modeling of the dendrite orientation transition in Al-Zn alloys

With a few exceptions, phase-field simulations of dendritic growth in cubic materials have been modeled using simple expressions for the interfacial energy anisotropy and with strong anisotropy. However, recent experimental results show that the Dendrite Orientation Transition (DOT) observed in Al-Zn alloys by Gonzales and Rappaz [Met. Mat. Trans. A37 (2006) 2797] occurs at weak anisotropy, and modeling these results requires at least two anisotropy parameters. In the present work, we solve the corresponding phase-field model on an adaptive grid, after measuring and compensating for the grid anisotropy. A systematic scan of equiaxed growth simulations was performed in the range of the anisotropy parameter space where the transition is expected. We find separate domains of existence of ⟨100⟩ and ⟨110⟩ dendrites, similar to those previously reported by Haxhimali et al. [Nat. Mat. 5 (2006) 660] for pure materials. In the so-called hyperbranched regime, lying between the ⟨100⟩ and ⟨110⟩ regions, we observe a competition between ⟨100⟩ and ⟨110⟩ growth directions, but no seaweed structures. Directional solidification simulations showed the stabilizing effect of the thermal gradient on the twofold splitting of ⟨110⟩ dendrites, and the importance of the choice of anisotropy parameters. We also found a strong dependence between the orientation of the crystal axes with respect to the thermal gradient and the actual growth direction. Finally, 3-dimensional seaweed microstructures were modeled for the first time, demonstrating that this pattern is a result of not only the values of anisotropy parameters, but also a consequence of directional solidification.

A fast, robust, and accurate operator splitting method for phase-field simulations of crystal growth

In this paper we propose a fast, robust, and accurate operator splitting method for phase-field simulations of dendritic growth in both two- and three-dimensional space. The proposed method is based on operator splitting techniques. We split the governing phase-field equation into three parts: the first equation is calculated by using an explicit Euler's method. The second is a heat equation with a source term and is solved by a fast solver such as a multigrid method. The third is a nonlinear equation and is evaluated using a closed form solution. We also present a set of representative numerical experiments for crystal growth simulation to demonstrate the accuracy and efficiency of the proposed method. Our simulation results are also consistent with previous numerical experiments.

Phase-field simulation of dendritic growth in a binary alloy with thermodynamics data

This paper simulates the dendrite growth process during non-isothermal solidification in the Al-Cu binary alloy by using the phase-field model. The heat transfer equation is solved simultaneously. The thermodynamic and kinetic parameters are directly obtained from existing database by using the Calculation of Phase Diagram (CALPHAD) method. The effects of the latent heat and undercooling on the dendrite growth, solute and temperature profile during the solidification of binary alloy are investigated. The results indicate that the dendrite growing morphologies could be simulated realistically by linking the phase-field method to CALPHAD. The secondary arms of solidification dendritic are better developed with the increase of undercooling. Correspondingly, the tip speed and the solute segregation in solid-liquid interface increase, but the tip radius decreases.

An Adaptive Finite Volume Method for Incompressible Heat Flow Problems in Solidification

An adaptive finite volume method is presented for solving incompressible heat flow problems with an unknown melt/solid interface, mainly in solidification applications, using primitive variables on a fixed collocated grid. A phase-field variable is introduced to treat the melt/solid interface, which is assumed to be diffusive, so that the complicated interfaces and phase change (using the enthalpy model) can be treated easily. The method is implemented through an object-oriented way based on adaptive mesh refinement and coarsening using dynamic data structures and derived data types of FORTRAN90. In addition to the refinement on the interfaces or boundaries, the mesh can be adapted to a solution based on numerical errors or gradients. Extensive tests are performed for cases with a fixed or free interface, and excellent agreement with the body-fitted or front tracking schemes is obtained. Furthermore, by gradual reduction of the interface thickness, the sharp-interface limit can be reached, which ensures the correctness of using a diffusive interface. The present approach is particularly suitable for problems having a complicated interface morphology as well as phase evolution, such as the phase-field simulation of dendritic growth. Two examples, without and with convection, are further given and good agreement with previous results are found.

A pseudo-front tracking technique for the modelling of solidification microstructures in multi-component alloys

A two-dimensional model for the simulation of microstructure formation during solidification in multi-component systems has been developed. The model is based on a new pseudo-front tracking technique for the calculation of the evolution of interfaces that are governed by solute diffusion and the Gibbs–Thomson effect. The diffusion equations are solved in the primary solid phase and in the liquid using an explicit finite volume method formulated for a regular hexagonal grid. Volume elements located in the liquid phase undergo a transition to interfacial (or mushy) cells before being incorporated in the solid phase. This layer of interfacial elements, which always separates the solid from the liquid sub-domains, permits to handle the displacement of the interface in agreement with the flux condition at the interface. The interface curvature is obtained from the field of the signed distance to the interface, as reconstructed with a PLIC (piecewise linear interface calculation) technique. The concentrations at the solid–liquid interface are calculated using thermodynamic data provided by the phase diagram software Thermo-Calc [Sundman et al. CALPHAD 1987;9:153] . Different coupling strategies between the microstructure model and Thermo-Calc have been developed, in particular a computationally-efficient direct coupling using the TQ-interface of Thermo-Calc. After testing the accuracy of the model with respect to curvature calculation, comparisons are made with predictions obtained with the marginal stability theory, a one-dimensional front-tracking method and two-dimensional phase-field simulations of dendritic growth in binary alloys. The model is then used to describe the formation of several grains in an Al–1%Mg–1%Si alloy, as a function of the heat extraction rate and inoculation conditions. It is shown that the model is capable of reproducing the transition between globular and dendritic morphologies.

Phase-field simulation of dendritic growth in a shear flow

We study how the dendritic evolution of an initially small nucleus is affected by a mean external flow. The nucleus is considered to be attached to a solid wall, and it grows away from the wall into the melt. The melt is assumed to be flowing due to an applied shear stress far away from the wall. The fluid flow alters the local heat transfer at the solidification front, and thus the shape of the dentrite. Due to the flow the nucleus evolves to an asymmetric dentrite that tilts. Another effect of the flow is that the sidebranch-growth gets promoted and inhibited on the upstream and downstream side, respectively. We use an adaptive grid and finite element applied to the phase-field method in 2D. The adaptivity results in a high local resolution at the solidification front and a much coarser mesh away from the front.