ISIJ Int Research Articles

Mathematical Modeling of the Early Stage of Clogging of the SEN During Continuous Casting of Ti-ULC Steel

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.

Physical Simulation Behavior of the Slag in Gas Injection with Non-consumable Lance and Porous Plug for Secondary Refining Operations

In secondary refining operations, injection of inert gases into the metal bath is required to generate stirring in order to produce cleaner steels with low sulfur, ultra-low contents of nitrogen and hydrogen gases as well as improving both temperature and composition homogenization of the steel and control the inclusions and floating of them. To demonstrate the viability and competitiveness of the non-consumable lance versus porous plugs, a series of experiments in a model of secondary refining ladle were carried out in previous research (Liu et al. in ISIJ Int 57:1971, 2017). Simulation of gas injection was carried out to test the two methods: porous plug and non-consumable lance. It was found that the porous plug injection involves shorter mixing times (10–12 s) when it is positioned in an intermediate point between the center and edge of the ladle and with the increase in the airflow injected, as compared to the lance. However, one problem with this technique in the actual plant is the metal oxidation because the liquid metal is exposed to air as a result of excessive agitation. In this work, gas injection through porous plug and non-consumable lance into secondary refining ladle was simulated by the addition of oils of different densities, to simulate the behavior of the slag of different viscosities. The results show that the non-consumable lance exhibits less water surface area exposed compared with the porous plug. This means less metal is exposed to the environment and less oxidation of it, under the same agitation conditions.

Precipitation and growth of MnS inclusion in an austenitic hot-work die steel during ESR solidification process

This study follows a previous presentation of metallurgical results and operating parameters about the comparison between conventional ESR and continuous unidirectional solidification of electroslag remelting (ESR-CDS) and more precisely the effect of cooling rate on the precipitation and growth of inclusions in an austenitic hot-work die steel [Y.F. Qi, J. Li, C.B. Shi, R.M. Geng, J. Zhang, Effect of directional solidification in electroslag remelting on the microstructure and cleanliness of an austenitic hot-work die steel, ISIJ Int. 58, 1275–1284 (2018)]. A thermodynamic study, a classical solidification model and a growth model for MnS inclusions were used orderly to interpret the metallurgical results. Optical microscopy (OM) and scanning electron microscopy (SEM) were used to characterize microstructure and inclusions (i.e. number, size, morphology and distribution) in the as-cast ingots. The results showed that the as-cast microstructure was refined and the dendritic arm spacings were reduced through ESR-CDS process. The characteristics of inclusions showed that the number density and the size of inclusions in ingot were much more reduced through ESR-CDS process in comparison with ESR process. The starting time for the precipitation of MnS inclusion is retarded, which is due to the segregation of elements Mn and S lowered by higher cooling rate in ESR-CDS in comparison with that in ESR. The starting time for the precipitation of MnS inclusion in ESR was fs = 0.92, while that in ESR-CDS was fs = 0.95.

Modeling of Dendritic Evolution of Continuously Cast Steel Billet with Cellular Automaton

In order to predict the dendritic evolution during the continuous steel casting process, a simple mechanism to connect the heat transfer at the macroscopic scale and the dendritic growth at the microscopic scale was proposed in the present work. As the core of the across-scale simulation, a two-dimensional cell automaton (CA) model with a decentered square algorithm was developed and parallelized. Apart from nucleation undercooling and probability, a temperature gradient was introduced to deal with the columnar-to-equiaxed transition (CET) by considering its variation during continuous casting. Based on the thermal history, the dendritic evolution in a 4 mm × 40 mm region near the centerline of a SWRH82B steel billet was predicted. The influences of the secondary cooling intensity, superheat, and casting speed on the dendritic structure of the billet were investigated in detail. The results show that the predicted equiaxed dendritic solidification of Fe-5.3Si alloy and columnar dendritic solidification of Fe-0.45C alloy are consistent with in situ experimental results [Yasuda et al. Int J Cast Metals Res 22:15–21 (2009); Yasuda et al. ISIJ Int 51:402–408 (2011)]. Moreover, the predicted dendritic arm spacing and CET location agree well with the actual results in the billet. The primary dendrite arm spacing of columnar dendrites decreases with increasing secondary cooling intensity, or decreasing superheat and casting speed. Meanwhile, the CET is promoted as the secondary cooling intensity and superheat decrease. However, the CET is not influenced by the casting speed, owing to the adjusting of the flow rate of secondary spray water. Compared with the superheat and casting speed, the secondary cooling intensity can influence the cooling rate and temperature gradient in deeper locations, and accordingly exerts a more significant influence on the equiaxed dendritic structure.

Investigation of Eccentric Open Eye Formation in a Slab Caster Tundish

Inert gas shrouding in tundish can result in the formation of a tundish open eye (TOE) due to the presence of reversed flows on the upper surface of the tundish. Prolonged presence of open eyes promotes reoxidation of liquid steel and creates harmful inclusions, which can ultimately result in clogging of SENs. In spite of its importance, not much work has been performed on TOEs. In our series of recent works (Chattopadhyay in Modelling of Transport Phenomena for Improved Steel Quality in a Delta-Shaped Four Strand Tundish, 2011; Chattopadhyay et al. in ISIJ Int 51: 573–580, 2011; Chatterjee and Chattopadhyay in ISIJ Int 55: 1416–1424, 2015; Metall Mater Trans B 41: 508–521, 2016; Metall Mater Trans B 47: 3099–3114, 2016; Chatterjee et al. in ISIJ Int 56: 1889–1892, 2016), although substantial efforts have been made to understand the basics of TOE formation process, a lot still remains to be deciphered. The current work deals with investigating a strange phenomenon observed during tundish operations: eccentric open eye formation. It is essential to gain proper insights of this matter in order to improve the operations, enhance liquid metal cleanliness, and generate more revenues. A mathematical model was developed using ANSYS-FLUENT 16.2. The standard k-e turbulence model and the discrete phase method, coupled with the discrete random walk model was employed. Three different causes for eccentric open eye formation viz., unbalanced throughput, biased argon injection, and misalignment of ladle shroud have been analyzed. The predicted results correspond to both water model experiments and real plant observations.

Retraction of “Wetting Behavior of Single Crystal TiO2 by Liquid Iron” [ISIJ Int. 56(5): 765–769 (2016)

Retraction of “Wetting Behavior of Single Crystal TiO2 by Liquid Iron” [ISIJ Int. 56(5): 765–769 (2016)

Erratum to “Multiscale Model Synthesis to Clarify the Relationship between Microstructures of Steel and Macroscopic Brittle Crack Arrest Behavior-Part I: Model Presentation” [ISIJ Int. 56(2): 341–349 (2016)

Erratum to “Multiscale Model Synthesis to Clarify the Relationship between Microstructures of Steel and Macroscopic Brittle Crack Arrest Behavior-Part I: Model Presentation” [ISIJ Int. 56(2): 341–349 (2016)

Retraction of “Microstructure and Properties of Fiber Laser Welded Joints of Ultrahigh-strength Steel 22MnB5 and its Dissimilar Combination with Q235 Steel” [ISIJ Int. 54(12): 2881–2889 (2014)

Retraction of “Microstructure and Properties of Fiber Laser Welded Joints of Ultrahigh-strength Steel 22MnB5 and its Dissimilar Combination with Q235 Steel” [ISIJ Int. 54(12): 2881–2889 (2014)

Erratum to “Desulfurization of Liquid Steel by Passing Steel Droplets through a Slag Layer” [ISIJ Int. 55(8): 1581–1590 (2015)

Erratum to “Desulfurization of Liquid Steel by Passing Steel Droplets through a Slag Layer” [ISIJ Int. 55(8): 1581–1590 (2015)

Retraction of “Gaseous Pre-reduction for the Magnetic Beneficiation of Ferruginous Low-grade Mn Ore” [ISIJ Int. 52(5): 759–763 (2012)

Retraction of “Gaseous Pre-reduction for the Magnetic Beneficiation of Ferruginous Low-grade Mn Ore” [ISIJ Int. 52(5): 759–763 (2012)

Retraction of ^|^ldquo;Representation of Dephosphorization Ability for CaO–Containing Slags Based on the Ion and Molecule Coexistence Theory^|^rdquo; [ISIJ Int. 54(3): 567–577 (2014)

Retraction of ^|^ldquo;Representation of Dephosphorization Ability for CaO–Containing Slags Based on the Ion and Molecule Coexistence Theory^|^rdquo; [ISIJ Int. 54(3): 567–577 (2014)

Retraction of ^|^ldquo;A Prediction Model of Phosphorus Distribution between CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags and Liquid Iron^|^rdquo; [ISIJ Int. 54(4): 756–765 (2014)

Retraction of ^|^ldquo;A Prediction Model of Phosphorus Distribution between CaO–SiO2–MgO–FeO–Fe2O3–P2O5 Slags and Liquid Iron^|^rdquo; [ISIJ Int. 54(4): 756–765 (2014)

Erratum to “Tensile Behavior of Ti,Mo-added Low Carbon Steels with Interphase Precipitation” [ISIJ Int. 54(1): 212-221 (2014)

Erratum to “Tensile Behavior of Ti,Mo-added Low Carbon Steels with Interphase Precipitation” [ISIJ Int. 54(1): 212-221 (2014)

Erratum to “Quantitative Determination of Free Lime Amount in Steelmaking Slag by X-ray Diffraction” [ISIJ Int. 54(6): 1334–1337 (2014)

Erratum to “Quantitative Determination of Free Lime Amount in Steelmaking Slag by X-ray Diffraction” [ISIJ Int. 54(6): 1334–1337 (2014)

Erratum to “Quantitative Evaluation for Relationship between Development of Pore Structure and Swelling of Coal in Carbonization of Single Coal Particle” [ISIJ Int. 53(10): 1739–1748 (2013)

Erratum to “Quantitative Evaluation for Relationship between Development of Pore Structure and Swelling of Coal in Carbonization of Single Coal Particle” [ISIJ Int. 53(10): 1739–1748 (2013)

Retraction of ^|^ldquo;Representation of Reaction Ability for Structural Units in Fe–Al Binary Melts^|^rdquo; [ISIJ Int. 54(6): 1185–1194 (2014)

Retraction of ^|^ldquo;Representation of Reaction Ability for Structural Units in Fe–Al Binary Melts^|^rdquo; [ISIJ Int. 54(6): 1185–1194 (2014)

Erratum to “Magnesium Non-Metallic Inclusions in Non-oriented Electrical Steel Sheets” [ISIJ Int. 51(12): 2069–2075 (2011)

Erratum to “Magnesium Non-Metallic Inclusions in Non-oriented Electrical Steel Sheets” [ISIJ Int. 51(12): 2069–2075 (2011)

Modelling the combined effect of grain size and grain shape on plastic anisotropy of metals

Within each columnar grain of a metallic film, the resistance to dislocation glide varies in function of the orientation of the slip plane with regard to the grain long axis. Plastic slip is impeded across grain boundaries and this contributes to the anisotropy of the overall mechanical response. A simplified (Taylor-type) crystal plasticity model is proposed that accounts for such effect of grain shape on the slip system selection. Assuming that dislocation density gradients are normal to the grain boundaries, backstresses developed at the onset of plasticity are estimated based on two definitions of the effective grain boundary spacing “seen” by individual slip systems. The first one reduces to the mean area-to-perimeter ratio of cross-sections of the grain cut parallel to the slip plane. Closed-form expressions of the average backstresses developed inside grains with spheroidal shapes are introduced in the crystal hardening law. The model reproduces the very high plastic anisotropy of electro-deposited pure iron with a strong γ-fiber and a refined columnar grain structure [Yoshinaga, N., Sugiura, N., Hiwatashi, S., Ushioda, K., Kada, O., 2008. Deep drawability of electro-deposited pure iron having an extremely sharp 〈111〉//ND texture. ISIJ Int. 48, 667–670]. It also provides valid estimates of the texture development and the influence of grain size on the yield strength.

Erratum: Thermodynamic Interaction between Chromium and Titanium in Liquid Fe–Cr Alloys Containing 30 mass% Cr [ISIJ Int. 50(10): 1373-1379 (2010)

Erratum: Thermodynamic Interaction between Chromium and Titanium in Liquid Fe–Cr Alloys Containing 30 mass% Cr [ISIJ Int. 50(10): 1373-1379 (2010)

Erratum: A Model for Activity Coefficient of P2O5 in BOF Slag and Phosphorus Distribution between Liquid Steel and Slag [ISIJ Int. 47(8): 1236-1238 (2007)

Equation (10) of the article published in ISIJ International, Vol. 47, No. 8, pp. 1236.1238, (2007) was not correct.Error:[Equation1]Correct:[Equation2]