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.
Abstract A two-phase Mixture model is proposed to simulate the liquid-solid phase transition of a Fe-0.82wt%C steel alloy under the effect of Marangoni flow. This model simplifies computations by ...solving a single momentum and enthalpy equation for the mixture phase using a three-dimensional finite volume method. The simulation involves solidifying a rectangular ingot (100 × 10 × 100 mm 3 ) from the cold bottom surface towards the hot-free surface at the top. To facilitate heat exchange with the surrounding environment, a high heat transfer coefficient of h = 600 W/m 2 /K was applied on the bottom surface to establish an upward solidification direction. However, a lower heat transfer coefficient of 20 W/m 2 /K was applied on the top free surface, which was considered flat. This study aims to examine the effect of Marangoni flow generated by surface tension on flow and segregation patterns. The results show that the Marangoni flow emerges at the free surface and penetrates into the liquid depth, leading to the formation of hexagonal patterns along the liquid thickness. Upon full solidification, macro-segregation also exhibits hexagonal structures, mirroring the stationary hexagonal shapes generated by Marangoni flow.
The clogging of the submerged entry nozzle (SEN) during the continuous casting of steel can be divided into two stages: the “early stage,” when the initial layer of the clog covers the SEN refractory ...surface owing to chemical reactions, and the “late stage,” when the clog layer continues to grow because of the deposition of non-metallic inclusions (NMIs). In this paper, a mathematical formulation is proposed for the build-up of the initial oxide. The chemical reaction mechanism is based on the work of Lee and Kang (Lee
et al.
in ISIJ Int 58:1257–1266, 2018): a reaction among SEN refractory constituents produces CO gas, which can re-oxidize the steel melt and consequently form an oxide layer on the SEN surface. The proposed formulation was further incorporated as a sub-model in a transient clogging model, which was previously developed by the current authors to track the late stage of clogging. The thermodynamics and kinetics of CO production, depending on the local pressure and temperature, must be considered for the sub-model of early-stage clogging. Test simulations based on a section of an actual industrial SEN were conducted, and it was verified that the clogging phenomenon is related to the SEN refractory, the chemical reaction with the steel melt, the local temperature and pressure, and the transport of NMIs by the turbulent melt flow in the SEN. The model was qualitatively validated through laboratory experiments. The uncertainty of some parameters that govern the reaction kinetics and permeability of the oxide layer is discussed.
A three-phase model for mixed columnar-equiaxed solidification is presented in this article. The three phases are the parent melt as the primary phase, as well as the solidifying columnar dendrites ...and globular equiaxed grains as two different secondary phases. With an Eulerian approach, the three phases are considered as spatially coupled and interpenetrating continua. The conservation equations of mass, momentum, species, and enthalpy are solved for all three phases. An additional conservation equation for the number density of the equiaxed grains is defined and solved. Nucleation of the equiaxed grains, diffusion-controlled growth of both columnar and equiaxed phases, interphase exchanges, and interactions such as mass transfer during solidification, drag force, solute partitioning at the liquid/solid interface, and release of latent heat are taken into account. Binary steel ingots (Fe0.34 wt pct C) with two-dimensional (2-D) axis symmetrical and three-dimensional (3-D) geometries as a benchmark were simulated. It is demonstrated that the model can be used to simulate the mixed columnar-equiaxed solidification, including melt convection and grain sedimentation, macrosegregation, columnar-to-equiaxed-transition (CET), and macrostructure distribution. The model was evaluated by comparing it to classical analytical models based on limited one-dimensional (1-D) cases. Satisfactory results were obtained. It is also shown that in order to apply this model for industrial castings, further improvements are still necessary concerning some details.
Gas injection through the submerged entry nozzle (SEN) into the continuous casting mold can be an effective approach for preventing SEN clogging and promoting the floatation of the non‐metallic ...inclusions. However, sometimes the exposed slag eyes due to gas injection appear on the top surface of the liquid slag layer, resulting in heat losses, re‐oxidation, and nitrogen pickup in the molten steel. An Eulerian multiphase‐flow model is developed to predict the argon‐steel‐slag three‐phase flow in a slab continuous casting mold. All the phases are treated based on Eulerian approach. The mathematical model is compared with the industrial observations and the water model experiments. Both of physical and numerical results reproduce the phenomenon of the high gas concentration at the SEN exit port. Most of the argon bubbles stay below the slag layer for quite long time because the slag blocks their floatation. Furthermore, the argon bubbles would gradually gather in a dense plume while escaping through the slag layer. Scattered argon exit spots are found at the top surface of slag layer. Two main locations of the exposed slag eye are found: 1) adjacent to the SEN; 2) at the mold's mid‐section at the position where a concentrated argon plume breaches through the slag layer. The near‐SEN exposed eye occurs under any of considered conditions. The one at the mid‐section is formed when the meniscus convex reaches a critical level, been dependent on the casting conditions.
The exposed slag eyes due to gas injection appear on the top surface of the mold are studied by an Eulerian multiphase‐flow model. Two main locations of exposed slag eye are found: 1) adjacent to the SEN; 2) at the mold's mid‐section at the position where a concentrated argon plume breaches through the slag layer.
The Electroslag Remelting (ESR) is an advanced technology for the production of high quality materials, for example, hot work tool steels or nickel base alloys. In the past years, several models are ...developed aiming to predict the way in which the operational parameters affect the structure and chemical composition of the final ESR ingot. Proper modeling of this process depends on the ability of the model to predict the Multiphysics resulting from the complex coupling between many physical phenomena. This review includes the main findings starting from the 1970's, with a special focus on the results obtained in the period of 1999–2017. The difficulties related to the poorly known physical properties of ESR slags are discussed. Then, the main achievements in the field of electromagnetism, fluid flow, heat transfer, and solidification are also summarized. The review finishes by presenting the special topics representing the actual scientific frontiers, such as the physics of mold current, the importance of multiphase phenomena, and the difficulties in predicting the electrode melting rate.
The Electroslag Remelting (ESR) is an advanced technology for the production of high quality materials, such as hot work tool steels or nickel base alloys. This study presents a re‐view on modeling and simulation of the ESR including the main findings starting from the 1970's, with a special focus on the results obtained in the period of 1999–2017.
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 mm
) from the bottom cold surface to the top hot free surface by applying a heat transfer coefficient of h = 600 W/m
/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.
In this paper a numerical investigations on the thermal state and on the tip shape of a melting electrode during electro-slag remelting are presented. In the first part the heat necessary to melt an ...electrode with a flat tip shape is calculated. It is shown that to keep a constant melting rate, the heat supplied to the electrode must be continuously changed. The results for different electrode descend rates, corresponding to different melting rates, are presented. In the second part the melting process was simulated with the help of a numerical model which takes into account simultaneous action of magneto-hydrodynamics, and thermal and phase changes phenomena. The model assumes no mould current. Simulations were performed with constant applied current and electrode descend velocity. The simulations have shown that the coupling between the melting rate and the Joule heat release process is very unstable. One result showing a stable electrode tip is presented and discussed in details.
The most recent developments and applications in volume-averaged modeling of solidification processes have been reviewed. Since the last reviews of this topic by Beckermann and co-workers Applied ...Mech. Rev. 1993, p. 1; Annual Rev. Heat Transfer 1995, p. 115, major progress in this area has included (i) the development of a mixed columnar-equiaxed solidification model; (ii) further consideration of moving crystals and crystal dendritic morphology; and (iii) the model applications to analyze the formation mechanisms of macrosegregation, as-cast structure, shrinkage cavity and porosity in different casting processes. The capacity of computer hardware is still a limiting factor. However, many calculation examples, as verified by the laboratory casting experiments, or even by the casting processes at a small industrial scale, show great application potential. Following the trend of developments in computer hardware (projection according to Moore’s law), a full 3D calculation of casting at the industry scale with the multiphase volume-averaged solidification models will become practically feasible in the foreseeable future.
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.
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