A Study on Ammonium Chloride Dendrite Tip Kinetics: The Importance of the Solid-Liquid Density Change and Interfacial Kinetics.

Ammonium chloride (NH4Cl) has been extensively studied as a transparent analogue for investigating the solidification of metals due to its distinctive properties and the simplicity of the experimentation. Furthermore, NH4Cl exhibits a striking resemblance in solidification behavior to the majority of binary eutectic alloy systems, rendering it a valuable model for studying phase transition phenomena. Experiments conducted on ammonium chloride are frequently employed to validate numerical models for predicting grain structures, macrosegregation, and the columnar-to-equiaxed transition (CET). This latter phenomenon arises due to differences in the velocities of columnar dendrite tips and the liquidus isosurface. However, the kinetics of dendrite tip growth, as a function of supersaturation, remains poorly understood for this commonly used alloy. The objective of this study was to utilize the available experimental data in conjunction with Ivantsov correlations to shed light on the ambiguous kinetics. The results indicate that when considering the crystal-melt density ratio, the Ivantsov solution offers a good correlation. Furthermore, incorporating a moderate interfacial kinetic coefficient enhances the correlations further. This correlation can be implemented in numerical models, which will aid in the determination of the columnar front, the columnar-to-equiaxed transition, and the equiaxed growth velocities.

The Impact of Marangoni and Buoyancy Convections on Flow and Segregation Patterns during the Solidification of Fe-0.82wt%C Steel.

Due to the high computational costs of the Eulerian multiphase model, which solves the conservation equations for each considered phase, a two-phase mixture model is proposed to reduce these costs in the current study. Only one single equation for each the momentum and enthalpy equations has to be solved for the mixture phase. The Navier-Stokes and energy equations were solved using the 3D finite volume method. The model was used to simulate the liquid-solid phase transformation of a Fe-0.82wt%C steel alloy under the effect of both thermocapillary and buoyancy convections. The alloy was cooled in a rectangular ingot (100 × 100 × 10 mm3) from the bottom cold surface to the top hot free surface by applying a heat transfer coefficient of h = 600 W/m2/K, which allows for heat exchange with the outer medium. The purpose of this work is to study the effect of the surface tension on the flow and segregation patterns. The results before solidification show that Marangoni flow was formed at the free surface of the molten alloy, extending into the liquid depth and creating polygonized hexagonal patterns. The size and the number of these hexagons were found to be dependent on the Marangoni number, where the number of convective cells increases with the increase in the Marangoni number. During solidification, the solid front grew in a concave morphology, as the centers of the cells were hotter; a macro-segregation pattern with hexagonal cells was formed, which was analogous to the hexagonal flow cells generated by the Marangoni effect. After full solidification, the segregation was found to be in perfect hexagonal shapes with a strong compositional variation at the free surface. This study illuminates the crucial role of surface-tension-driven Marangoni flow in producing hexagonal patterns before and during the solidification process and provides valuable insights into the complex interplay between the Marangoni flow, buoyancy convection, and solidification phenomena.

Prediction of the Secondary Arms Spacing Based on Dendrite Tip Kinetics and Cooling Rate.

Secondary dendrite arm spacing (SDAS) is one of the most important factors affecting macrosegregation and mechanical properties in solidification processes. Predicting SDAS is one of the major parameters in foundry technology. In order to predict the evolution of microstructures during the solidification process, we proposed a simple model which predicted the secondary dendrite arm spacing based solely on the tip velocity (related to the tip supersaturation) and cooling rate. The model consisted of a growing cylinder inside a liquid cylindrical envelope. Two important hypotheses were made: (1) Initially the cylinder radius was assumed to equal the dendrite tip radius and (2) the cylindrical envelope had a fixed radius in the order of the dendrite tip diffusion length. The numerical model was tested against experiments using various Pb-Sn alloys for a fixed temperature gradient. The results were found to be in excellent agreement with experimental measurements in terms of SDAS and dendrite tip velocity prediction. This simple model is naturally destined to be implemented as a sub-grid model in volume-averaging models to predict the local microstructure, which in turn directly controls the mushy zone permeability and macrosegregation phenomena.

Modeling Dendrite Coarsening and Remelting during Directional Solidification of Al-06wt.%Cu Alloy.

Research efforts have been dedicated to predicting microstructural evolution during solidification processes. The main secondary arm spacing controls the mushy zone's permeability. The aim of the current work was to build a simple sub-grid model that describes the growth and coarsening of secondary side dendrite arms. The idea was to reduce the complexity of the curvature distribution with only two adjacent side arms in concurrence. The model was built and applied to the directional solidification of Al-06wt%Cu alloy in a Bridgman experiment. The model showed its effectiveness in predicting coarsening phenomena during the solidification of Al-06wt%Cu alloy. The results showed a rapid growth of both arms at an earlier stage of solidification, followed by the remelting of the smaller arm. In addition, the results are in good agreement with an available time-dependent expression which covers the growth and coarsening. Such model can be implemented as a sub-grid model in volume average models for the prediction of the evolution of the main secondary arms spacing during macroscopic solidification processes.

Experimental and numerical investigations of arc plasma expansion in an industrial vacuum arc remelting (VAR) process.

In the present study, we investigate arc plasma expansion in an industrial vacuum arc remelting (VAR) process using experimental and numerical tools. Stainless steel is the alloy of interest for the electrode (cathode) and ingot (anode). During the operation of the VAR process, behaviors of cathode spots and plasma arc were captured using the high-speed camera (Phantom v2512). We found that spots prefer to onset and remain within the partially melted surface at the center of the electrode tip. Existing spots outside the melting zone accelerate toward the edge of the electrode to extinguish. We observed a fairly symmetrical and centric plasma column during the operation. For further investigation of the observed arc column in our experiment, we used the two-fluid magnetohydrodynamics (MHD) model of plasma proposed by Braginskii. Thus, we modeled the arc column as a mixture of two continuous interpenetrating compressible fluids involving ions and electrons. Through numerical simulations, we calculated plasma parameters such as number density of ions/electrons, electric current density, flow of ions/electrons, temperature of ions/electrons, and light intensity for the observed arc column in our experiment. The calculated light intensity of plasma was compared with images captured by the camera to verify the model. The distribution of electric current density along the surface of the anode, namely ingot, is a decisive parameter that impacts the quality of the final product (ingot) in VAR process. Herein, we confirm that the traditionally used Gaussian distribution of electric current density along the surface of the ingot is viable.

Simulation of macrosegregation in a 2.45-ton steel ingot using a three-phase mixed columnar-equiaxed model.

A three-phase mixed columnar-equiaxed solidification model is used to calculate the macrosegregation in a 2.45 ton steel ingot. The main features of mixed columnar-equiaxed solidification in such an ingot can be quantitatively modelled: growth of columnar dendrite trunks; nucleation, growth and sedimentation of equiaxed crystals; thermosolutal convection of the melt; solute transport by both convection and crystal sedimentation; and the columnar-to-equiaxed transition (CET). The predicted as-cast macrostructure and the segregation pattern are in qualitative agreement with the reported experimental results. Parameter study on the numerical grid size and the nucleation of the equiaxed crystals are performed, and some segregation mechanisms are numerically analyzed. Discontinued positive-negative segregation just below the hot top is predicted because of the formation of a local mini-ingot and the subsequent sedimentation of equiaxed grains within the mini-ingot. Quasi A-segregates in the middle radius region between the casting outer surface and the centreline are also found. The quasi A-segregates originate from the flow instability, but both the appearance of equiaxed crystals and their interaction with the growing columnar dendrite tips significantly strengthen the segregates. The appearance of equiaxed phase is not a necessary condition for the formation of quasi A-segregates. The quantitative discrepancy between the predicted and experimental results is also discussed.