Alexandre Furtado Ferreira

Simulation of the solidification of pure nickel via the phase-field method

The Phase-Field method was applied to simulate the solidification of pure nickel dendrites and the results compared with those predicted by the solidification theory and with experimental data reported in the literature. The models behavior was tested with respect to some initial and boundary conditions. For an initial condition without supercooling, the smooth interface of the solid phase nucleated at the edges of the domain grew uniformly into the liquid region, without branching. In an initially supercooled melt, the interface became unstable under 260 K supercooling, generating ramifications into the liquid region. The phase-field results for dendrite tip velocity were close to experimental results reported in the literature for supercooling above 50 K, but they failed to describe correctly the nonlinear behavior predicted by the collision-limited growth theory and confirmed by experimental data for low supercooling levels.

Microsegregation in Fe-C-P ternary alloys using a phase-field model

A phase-field model is proposed for the simulation of microstructure and solute concentration during the solidification process of Fe-C-P ternary alloys. A relation between material properties and model parameters is presented. Two-dimensional computation results exhibit dendrites in Fe-C-P alloys for different phosphorus concentrations. Alterations in the phosphorus concentration appear to affect the advance speed of the solid-liquid interface. Such an alteration is due to the small diffusivity of phosphorus during the solidification process.

Numerical Predictions for the Thermal History, Microstructure and Hardness Distributions at the HAZ during Welding of Low Alloy Steels

A phenomenological model to predict the multiphase diffusional decomposition of the austenite in low-alloy hypoeutectoid steels was adapted for welding conditions. The kinetics of phase transformations coupled with the heat transfer phenomena was numerically implemented using the Finite Volume Method (FVM) in a computational code. The model was applied to simulate the welding of a commercial type of low-alloy hypoeutectoid steel, making it possible to track the phase formations and to predict the volume fractions of ferrite, pearlite and bainite at the heat-affected zone (HAZ). The volume fraction of martensite was calculated using a novel kinetic model based on the optimization of the well-known Koistinen-Marburger model. Results were confronted with the predictions provided by the continuous cooling transformation (CCT) diagram for the investigated steel, allowing the use of the proposed methodology for the microstructure and hardness predictions at the HAZ of low-alloy hypoeutectoid steels.

Numerical simulation of the solidification of pure melt by a phase-field model using an adaptive computation domain

In this paper, we present a phase-field model with a grid based on the Finite-Difference Method, for improvement of computational efficiency and reducing the memory size requirement. The numerical technique, which is based on the temperature change of the pure material, enables us to use, in the initial steps of the computation, a very small computational domain. Subsequently, in the course of the simulation of the solidification process, the computation domain expands around the dendrite. The computation showed that the dendrite with well-developed secondary arms can be obtained with low computation time and moderate memory demand. The computational efficiency of this numerical technique, the microstructural evolution during the solidification, and competitive growth between side-branches are discussed.

2D Phase-Field Simulation of the Directional Solidification Process

The microstructure evolution during the directional solidification of Al-Cu alloy is simulated using a phase field model. The transformation from liquid to solid phase is a non-equilibrium process with three regions (liquid, solid and interface) involved. Phase field model is defined for each of the three regions. The evolution of each phase is calculated by a set of phase field equations, whereas the solute in those regions is calculated by a concentration equation. In this work, the phase field model which is generally valid for most kinds of transitions between phases, it is applied to the directional solidification problem. Numerical results for the morphological evolution of columnar dendrite in Al-Cu alloy are in agreement with experimental observations found in the literature. The growth velocity of the dendrite tip and the concentration profile in the solid, interface and liquid region were calculated.

Application of Computational Thermodynamics to the Evolution of Surface Tension and Gibbs-Thomson Coefficient during Multicomponent Aluminum Alloy Solidification

Numerical simulation of multicomponent alloy solidification demands accuracy of thermophysical properties in order to obtain a numerical representation as close as possible to the physical reality. Some alloy properties are only seldom found in the literature. In this paper, a solution of Butler’s formulation for surface tension is presented for Al-Cu-Si ternary alloys, allowing the Gibbs-Thomson coefficient to be calculated as a function of Cu and Si contents. The importance of the Gibbs-Thomson coefficient is related to the reliability of predictions furnished by predictive microstructure growth models and of numerical computations of solidification thermal variables that will be strongly dependent on the values of the thermophysical properties adopted in the calculations. A numerical model based on Powell hybrid algorithm and a finite difference Jacobian approximation was coupled with a ThermoCalc TCAPI interface to assess the excess Gibbs energy of the liquid phase, permitting the surface tension and Gibbs-Thomson coefficient for Al-Cu-Si hypoeutectic alloys to be calculated. The computed results are presented as a function of the alloy composition.

Simulation of the Microstructural Evolution of Pure Material and Alloys in an Undercooled Melts via Phase-field Method and Adaptive Computational Domain

The phase-field methods were developed mainly for studying solidification of pure materials, being then extended to the solidification of alloys. In spite of phase-field models being suitable for simulating solidification processes, they suffer from low computational efficiency. In this study, we present a numerical technique for the improvement of computational efficiency for computation of microstructural evolution for both pure metal and binary alloy during solidification process. The goal of this technique is for the computational domain to grow around the microstructure and fixed the grid spacing, while solidification advances into the liquid region. In the numerical simulations of pure metal, the phase-field model is based on the energy and phase equations, while, for binary alloy, the said model is based on the concentration and phase equations. Since the thermal diffusivity in the energy equation is much larger than the diffusivity term in phase equation in pure metal system, about twenty eight times the difference between them. The computational domain growth around the microstructure is controlled according with the thermal diffusivity for pure material in the liquid region. In the numerical simulation of dendritic evolution of Fe-C alloy, the idea is similar, i.e., the solute diffusivity in concentration equation is larger than the diffusivity term in phase equation in the liquid region, in this case eleven times the difference in Fe-C alloy system. The computational domain growth is controlled via solute diffusivity in the liquid region. Hence, phase-field model is proposed with an adaptive computational domain for efficient computational simulation of the dendritic growth in a system for both pure metal and binary alloy. The technique enables us to reduce by about an order of magnitude the run time for simulation of the solidification process. The results showed that the microstructure with well-developed secondary arms can be obtained with low computation time.

Numerical Determination of Secondary Arm Spacing of Fe-C as a Function of Cooling Rate and Local Solidiifcation Time

The phase-field model is widely used as one of the powerful computational methods to simulate the formation of complex micro structures. In this present study, the secondary arm spacing for Fe-C binary alloys are numerically predicted using a phase-field model in the two-dimensional domain. The predicted arm spacing from the present work compared with both the data by Ode et al, and the experimental data showed an excellent agreement. It is estimated at the late stage of growth. The change in the arm spacing is examined by the both changes of cooling rates and local solidification time. The relation between material properties and model parameters is presented. Two-dimensional simulations produced dendrites, which are similar to the ones found in experiments reported in the literature. Through the numerical examples, the applicability of the phase-field model to the problems of secondary dendrite arm spacing of the Fe-C alloys is demonstrated.

Modeling a Compact Sintering Process Based on Biomass Fuels

This paper is focused on the numerical simulation of a new technology of small size iron ore sintering machine using gaseous fuel and oxygen injections to produce high quality of sinter product for the blast furnace operation. The proposed methodology is to partially replace the solid fuel (coke breeze) by steelworks gases in a compact machine to enhance heat and mass transfer. A multiphase mathematical model based on transport equations of momentum, energy and chemical species coupled with chemical reaction rates and phase transformations is proposed to analyze the inner process parameters. A base case representing a possible actual industrial operation of the sintering machine is used in order to compare different scenarios of possible operations which represents advanced operations techniques. The model was used to predict four cases of fuel gas utilization: a) 3% of the wind boxes inflow from N01-N10 wind boxes of natural gas (NG) and oxygen, b) same condition with coke oven gas (COG) and c) mixture of 80% COG and 20% blast furnace gas (BFG). The model predictions indicated that for all cases, the sintering zone is enlarged and the solid fuel consumption is decreased about 12kg/t of sinter product for the best combination. In order to maximize the steelworks gas utilization it is recommended the use of mixture of COG and BFG with optimum inner temperature distribution within a compact sintering machine, which enhance the productivity and obviously, decrease the investment cost of the sintering facilities.