Binary Alloy Solidification Process Research Articles

A Monte Carlo approach to simulate dendritic microstructures during binary alloy solidification

A Monte Carlo (MC) approach to model the evolution of microstructures during the binary alloy solidification process has been presented. The evolution of these microstructures is comprehensively modelled by ensuring a local minimization of free energy taking into account the contributions of the free energy change during phase transformation, solid-liquid interfacial energy, interfacial energy anisotropy and grain boundary energy, which are some of the ignored aspects of the existing MC models. Further, the effect of imposed orientation is also represented in this model. The proposed method is able to simulate the preferential growth of cubic structures in ⟨100⟩ direction, growth of large number of grains and competition among them, and also incorporates the grain boundary energetics. The model is applied to simulate the growth of free and constrained dendrites, the transition from stable to cellular and dendritic growth under different growth conditions. Growth of multiple grains, the competition during columnar growth, columnar to equiaxed transition by seeding the undercooled melt with solid phase and the impingement of equiaxed grains has also been simulated using this model.

Numerical modeling of solidification process taking into account the effect of air gap

The paper presents a method of numerical modeling of binary alloy solidification process in a permanent mold in a two-dimensional area. The model takes into account the influence of the gas gap of variable width existing between the mold and the casting on the rate of solidification process. The numerical model is based on the finite element method (FEM) with independent spatial discretization of the casting and the mold. The displacements of these regions resulting from a thermally dependent changes of their volumes are also taken into account. The adopted approach involves the use of two separated meshes, where the temporary temperature fields are obtained. The thermal interaction between the casting and the mold is described by the appropriate boundary condition. The solution is obtained sequentially in each time step independently for the each region.

The correlation between the eigenvalues of global FEM matrix and the size of time step in the numerical solutions of solidification equation

In the paper the influence of the eigenvalues of the matrix on the stability of the numerical simulations of binary alloy solidification process was analyzed. One step � scheme time integration for the modeling was used. The occurrence of the equation clotting full, diagonal and lumped capacitance matrix was considered. In the explicit schema (conditionally stable) the major influence on the proper selection of the size of the critical time step was proved. The physically incorrect results are given when the maximum allowable time step is exceeded.

On the problem of control the composition of material in the binary alloy solidification process

Abstract In a framework of classical one-dimensional binary alloy solidification problem with zero diffusion coefficient in the solid phase the inverse problem is posed and considered. The problem consists in finding of the temperature regime at the outer boundary of domain when the final distribution of admixture in solidified part is known. In the cases when the desired concentration is linear function of space coordinate the boundary-value problem for the system of equations can be disjoin and the inverse problem can be reduced to the successive solving of three problems. First one is a “supercooled” Stefan problem [Fasano, Primicherio, Quart. Appl. Math. 38: 439–460, 1981,Petrova, Tarzia, Turner, Advances in Math. Sciences and Applications, Gakkotosho 4: 35–50, 1994], the second one is an initial-boundary problem for heat equation in the domain with known moving boundary, and the last one is a non-characteristic Cauchy problem [Alifanov, Inverse Problems of Heat Exchange (in Russian), Nauka, 1988]. We investigate this last problem in two aspects – classical “exact” and extremal, as a problem of minimizing a functional. Besides, we consider the self-similar version of the inverse problem and construct the exact solution to the inverse problem.

サクシノニトリル‐アセトン系有機モデル合金のデンドライト成長

Unidirectional solidification experiments of a model alloy of succinonitrile (SCN)-acetone that is a transparent organic compound and is available for a direct observation were performed in order to clarify the solidification process of binary alloy. The dependences of primary arm spacing (DAS1) of dendrite and secondary arm spacing (DAS2) on the growth speed of a crystal were studied. The sample, heareafter called as the cell, was inserted into the gap of the two slides (26 mm×76 mm×1.3 mm each), of which distance was 200 μm. The cell was pulled at a constant speed V toward the low temperature side under the fixed temperature gradient (1 K/mm). Changing pulling speed of the cell controlled the growth speed of the crystal. The composition of the examined samples is SCN-1.9 mass% acetone and SCN-6.0 mass% acetone. DAS1-V relationship was studied for the 1.9 mass% case only and found to be in proportional with the growth speed V-1/2. This is almost the same as that of unidirectional solidification of aluminum-(0.1-6.9) mass%Si alloy. DAS2 of 1.9 mass% and 6.0 mass% changed with growth speed as V-1/3. However, when growth speed increased, DAS2 of 1.9 mass% and 6.0 mass% decreased more than the V-1/3 relationship. DAS2 of 6.0 mass% separated from the curve of V-1/3 earlier than that of 1.9 mass%.

Evaluation of enthalpy and entropy changes for binary alloy solidification process

Analytical expression of the entropy and enthalpy changes and apparent specific heat capacity of binary alloys in the solidification process are derived. The non-equilibrium lever rule is employed in the assessments of the relative concentration of binary alloys during solidification. The effect of the partial ordering of alloys in the liquid state is ignored and the alloy solidification process is divided into steps in the evaluations. Furthermore, experimental data from the available literature for Al−Cu alloys are employed to check the predictions of the current approaches, which indicates the reasonability of the current expressions.

Studies on turbulent momentum, heat and species transport during binary alloy solidification in a top-cooled rectangular cavity

A two-dimensional transient fixed-grid enthalpy-based numerical method is developed to analyze the effects of turbulent transport during a binary alloy solidification process. Turbulence effects are introduced through standard k– ε equations, where coefficients are appropriately modified to account for phase-change. Microscopically-consistent estimates are made regarding temperature-solute coupling in a non-equilibrium solidification situation. The model is tested against laboratory experiments performed using an NH 4Cl–H 2O system in a rectangular cavity cooled and solidified from the top. Particular emphasis is laid on studying the interaction between Rayleigh–Benard type convection and directional solidification in the presence of turbulent transport. Numerical predictions are subsequently compared with experimental results regarding flow patterns, interface growth and evolution of the temperature field, and the agreement is found to be good.

Effects of dendritic arm coarsening on macroscopic modelling of solidification of binary alloys

A pure macroscopic two-dimensional numerical model has been developed, capable of capturing the effects of dendritic arm coarsening on the transport phenomena occurring during a binary alloy solidification process. The general continuum conservation equations are aptly modified to take into account shrinkage induced fluid flow. Simultaneously, the effective permeability of the mushy zone is numerically modelled according to the microscopic coarsening kinetics. Moreover, a new nodal latent heat updating algorithm is proposed that takes into account dendritic arm coarsening considerations. The numerical results are first tested against experimental results reported in the literature, corresponding to the solidification of an Al-Cu alloy in a bottom cooled cavity. It is concluded that dendritic arm coarsening leads to an increased effective permeability of the mushy region as well as an enhanced eutectic fraction of the solidified ingot. Consequently, an enhanced macrosegregation is predicted, compared with that dictated by shrinkage induced fluid flow alone. Physical insights are also developed regarding the effects of various parameters on the overall macrosegregation.

Solidification of aqueous ammonium chloride in a rectangular cell under constant wall temperature - an experimental study

The effect of a binary alloy solidification process was investigated for four different initial ammonium chloride concentrations (5%, 10%, 15% and 25%) and for four different constant wall temperature conditions (−13°C, −20°C, −25°C and −30°C). The solidification process inside the test cell was interrupted at various time steps to capture the phase front profile. Results show that a higher initial concentration and a lower constant wall temperature tend to increase the strength of thermal-driven buoyancy flow and solute-driven buoyancy flow respectively. The shape of both the solid and mushy phase front profiles are affected by the strength of these two flows. Isotherm plots and superimposed images are used to determine the location of solid-must interface and must-liquid interface respectively, inside the test cell at any time interval.

Experimental and numerical comparison of extractive and in situ laser measurements of non-equillibrium carbon monoxide in lean-premixed natural gas combustion

A two-dimensional transient fixed-grid enthalpy-based numerical method is developed to analyze the effects of turbulent transport during a binary alloy solidification process. Turbulence effects are introduced through standard k–ε equations, where coefficients are appropriately modified to account for phase-change. Microscopically-consistent estimates are made regarding temperature-solute coupling in a non-equilibrium solidification situation. The model is tested against laboratory experiments performed using an NH4Cl–H2O system in a rectangular cavity cooled and solidified from the top. Particular emphasis is laid on studying the interaction between Rayleigh–Benard type convection and directional solidification in the presence of turbulent transport. Numerical predictions are subsequently compared with experimental results regarding flow patterns, interface growth and evolution of the temperature field, and the agreement is found to be good.

GRAVITY- AND SOLIDIFICATION-SHRINKAGE-INDUCED LIQUID FLOW IN A HORIZONTALLY SOLIDIFIED ALLOY INGOT

A basic-variable, explicit finite difference scheme is used to solve the unsteady and strongly pressure-coupled velocity problems of liquid flows induced both by thermosolutal buoyancies and solidification shrinkage in a binary alloy solidification process. A sample calculation, performed on an IBM personal computer, for a horizontally solidified Al-4.5%Cu alloy in a high-H/L ratio cavity with a top riser shows that the shrinkage established pressure gradient in the mushy region can be several hundred, even several thousand, times larger than that in the bulk liquid region.

A Numerical Simulation of a Binary Alloy Solidification Process

We describe the numerical implementation of a mathematical model of a binary alloy solidification process introduced in [1]. The model takes into account the “mushy” zone of dendritic growth between liquid and solid phase regions.

2元合金鋳物の凝固過程に対する非平衡熱力学的取扱い

The purpose of the present paper is to theoretically calculate the solidification process of alloy castings. The equations of the rate of the reactions and the conservations of mass and energy have been derived by expressing the solidification process of binary alloy, in which only primary crystals are solidified, in terms of two reactions, A (in liq.) =A(in sol.) and B(in liq.)=B(in sol.), and also by regarding it as a process of growth of crystals dispersed in the melt. These equations transform into the foundamental equations which describe the solidification process of a binary alloy casting when the related properties are given as known functions of temperature and concentration. In the present paper most of the properties are regarded to be constant. But, the activities and partial enthalpies of the components are estimated from the phase diagram on the assumption that Raoult’s law is valid in solid and Henry’s law in liquid. The foundamental equations consisting of four simultaneous non-linear partial differential equations have four unknown functions, that is, temperature, concentrations in solid and in liquid and fraction of solidification.As an example of the calculation, a solidification process of an Al-4.5% Cu plate in the metal mold has been calculated by the finite difference method, and distributions of temperature, concentration and fraction of solidification, and their variations with time have been obtained. These data indicate a mush mode of the solidification, the near-equilibrium condition of concentration and temperature, and less segregation than expected. The motion of the liquid phase and the behavior of the nucleus, which are neglected in the present calculation, may have a great influence on the mode of solidification and on the segregation.