This work introduces a 0.6-scale water model of the continuous slab-casting process and a MATLAB-based model to study the effects of non-primed and multiphase flow on pressure and flow rate. The water model uses stopper-rod flow control and features pressure and velocity measurements at multiple locations. The new computational model, PFSR V4 (Pressure-drop Flow-rate model of Stopper Rod metal delivery systems, Version 4), improves upon a prior one-dimensional Bernoulli-based framework by incorporating a bubble accumulation zone. This zone represents a region of bubbly flow with an intermediate gas fraction between constant-pressure gas pockets below the stopper tip and the downstream bubbly flow regime. Parametric studies with the water model show that flow remains fully primed at low gas flow rates but transitions to non-primed flow as the gas flow rate exceeds 10–16 SLPM. Three different flow regions are observed inside the water model nozzle: air pocket, bubble accumulation, and bubbly flow, which are also captured by the new computational model. Above a critical gas flow rate, the flow becomes unstable and difficult to control, though higher hot gas flow rates are expected for similar transitions in a real steel caster due to gas expansion at high temperatures. Pressure changes are minimal in the air pocket region and increase significantly in the upper bubble accumulation zone, where liquid velocity is much higher than in the classic bubbly-flow region, found lower in the nozzle. The new model was successfully calibrated to match the observed flow regimes and shows good agreement with the water-model measurements.

Transverse corner cracks on the slab surface occur most frequently, particularly in hypo-peritectic steel cast by the vertical-bending casters. These defects require additional surface machining before rolling, along with compensating for temperature drops in the reheating furnace, which significantly increases steel production cost. To address this issue, POSCO developed a chamfered mold, which effectively reduced transverse corner cracks when operating at casting speeds below 1.0 m/min. At higher speeds, however, the chamfered mold exacerbated side effects such as longitudinal cracks on chamfered faces. With insights gained from a multiphysics model, it is revealed in this work that these longitudinal cracks are caused by uneven solidification due to excessive gap formation from insufficient taper at the corner in the mold top region. Consequently, a better chamfered mold has been designed to improve taper on both the wide and narrow faces, leading to a reduction in the gap size and associated problems. This new mold is currently being applied to specific high-speed casters with higher cracking rates, and is found to be effective in reducing transverse corner cracks without side effects of longitudinal cracks or excessive mold wear.

The continuous casting of Ti-Nb microalloyed steel was simulated with high temperature confocal laser scanning microscopy (HTCLSM). Evolution of the sample surface morphology was observed in-situ, during cooling conditions chosen to represent different locations in a cast slab. Calculations with a thermodynamics model of carbonitride precipitate formation agreed with the transmission electron microscopy (TEM) analysis that fine reliefs observed on the sample surface were actually caused by interior precipitation of (Ti,Nb)(C,N). Precipitation and the resulting reliefs changed with location beneath the slab surface, simulated casting speed, and steel composition. With the same casting speed and steel composition, reliefs in the simulated slab surface sample appeared earlier and were larger than in the slab center. With increased casting speed, reliefs were observed later and decreased in size. With increased titanium or niobium content, reliefs appeared earlier and increased in number. TEM measurement showed that the precipitate diameters were mainly smaller than 4 nm, with a few between 4 and 8 nm. The property of surface reliefs observed via HTCLSM correlated qualitatively with the number and size of internal precipitates measured with TEM, showing this to be an effective tool for indirectly characterizing nanoscale secondary phase precipitation inside the sample.

Computational models are powerful tools to quantify physical phenomena to gain valuable insights into a manufacturing process. Their accuracy is hindered, however, by uncertainty in the input data. Furthermore, when calibrating models with plant measurements, it helps to understand which variables have greatest effect on the critical model outputs. This work applies uncertainty quantification and sensitivity analysis to determine the most influential input parameters in the CON1D model of heat transfer and solidification in steel continuous casting with slag. Results show that the slag rim greatly affects heat flux near the meniscus, so control of its size is important. Heat flux and temperature down the mold depend greatly on velocity of the solid slag layer, and slag solidification temperature, which control the slag layer thickness, which in turn affects the interfacial resistance that controls heat transfer in the process. Scale formation on the mold coldface greatly increases mold temperatures. Based on the results presented here, models of heat transfer in continuous casting such as CON1D would benefit from plant measurements such as slag rim size and solid slag velocity, and lab measurements such as slag viscosity at lower temperatures, to better characterize this important slag property.

A new simple model of pressure and flow in the liquid-metal delivery system of continuous casting operations with stopper-rod flow control, PFSR, is introduced. This one-dimensional model calculates the gauge pressure distribution and flow rate in the complete tundish, stopper-rod, and nozzle system by solving a set of pressure-energy balance Bernoulli-type equations. It includes the effects of argon gas injection and its expansion according to the local pressure. PFSR is a MATLAB-based software package with a user-friendly graphical user interface (GUI). It employs an inverse model to solve the system of governing equations for any unknown chosen by the user. This enables fast and efficient parametric studies to investigate the effects of casting conditions and nozzle geometry under realistic conditions. The model is verified with three-dimensional computational fluid dynamics (CFD) simulations and validated with both water model and plant measurements. To overcome unrealistically low minimum pressure predictions in steel casters, two other physical phenomena should be considered: cavitation and non-primed annular/slug (waterfall-type) flow with large gas pockets. Preliminary results that include these two new phenomena into the PFSR model show that cavitation and air pockets (non-primed flow) can explain steel plant measurements and likely occur for most casting conditions in real casters with stopper-rod control systems.

A new model of particle entrapment during continuous casting of steel is presented, which includes the effects of multiphase flow from argon gas injection and thermal buoyancy from superheat in the strand. The model simulates three different capture mechanisms, including capture by solidified hooks at the meniscus, entrapment between dendrites, and engulfment by the surrounding of large particles. The fluid flow and bubble capture results are validated with plant measurements, including nail board dipping tests and ultrasonic tests, respectively, and good agreement is seen. Results suggest that the superheat has a negligible effect on the flow in the mold region. However, higher (30 K) superheat causes a more complex flow in the lower strand by creating multiple recirculation zones due to the thermal buoyancy effects. This causes less penetration deep into the strand, which leads to fewer and shallower particle captures. Lower (10 K) superheat may enable significant top surface freezing, leading to very large internal defect clusters. Lower superheat also leads to deeper meniscus hooks, which sometimes (0.003%) capture large (1 mm) bubbles. Capture bands occur near the transition line from vertical to curved, due to the downward fluid velocity balancing the particle terminal velocity, enabling capture in the relative stagnation region beneath the longitudinal recirculation zone. These findings agree with plant observations.

Thermal distortion during the initial stages of solidification is an important cause of surface quality problems in cast products. In this work, a finite element model including non-linear temperature-, phase-, and carbon-content-dependent elastic–viscoplastic constitutive equations is applied to study the effect of steel grade and interfacial heat flux on thermal distortion of a solidifying steel droplet. Due to thermal contraction, the bottom surface of the droplet bends away from the chill plate and a gap forms. It is shown that, regardless of the nature of the heat flux, the gap forms and grows the most very early during solidification (~0.1 s) and remains almost unchanged afterward. Increasing the heat flux decreases the time for evolution of the gap and increases its depth. When the carbon content is less than 0.10%C, the gap depth is very sensitive to the heat flux, but for higher carbon contents, this sensitivity is much weaker. The highest gap depths are predicted in ultra-low carbon (0.003%C) and peritectic steels (0.12%C), and agree both qualitatively and quantitatively with the experimental measurements. Thus, the current thermal-mechanical model, including its phase-dependent properties, captures the mechanism responsible for nonuniform solidification, depression sensitivity and surface defects affecting these steels.

Quantifying the pressure distribution and flow rate in the metal delivery system from the tundish to the mold is important to understand nozzle clogging due to air aspiration, argon bubble size, and other important phenomena in continuous casting of steel. A one-dimensional pressure energy model, PFSG, is presented here to calculate pressure distribution and flow rate in slide-gate nozzle systems for argon-molten steel flow systems including argon gas expansion by solving a system of Bernoulli equations. PFSG is a user-friendly MATLAB-based software package with an intuitive Graphical User Interface capable of inverse solutions that enables users to conduct parametric studies in seconds. The model predictions is verified with computational fluid dynamics simulations and validated with plant measurements and water model measurements, with errors of less than 6 pct. The verified and validated PFSG model is then applied to investigate the effect of different casting conditions on the flow rate and pressure distribution. For a given slide gate opening, the flow rate increases with increasing distance from the tundish level to the mold level, increasing SEN diameter, and decreasing argon gas injection rate. The slide-gate opening fraction that produces the minimum pressure is almost independent of casting conditions, except for SEN bore diameter. This critical opening fraction, which is most detrimental for air aspiration, increases from 50 to 70 pct with increasing SEN diameter by 13 pct for the system studied. The minimum pressure worsens (decreases) with increasing tundish height and/or nozzle bore diameter.

This paper presents an enthalpy based full-state feedback control law with respect to a reference solution for a one-phase Stefan problem under unknown boundary input hysteresis. The one-phase Stefan problem describes the evolution of the temperature and the liquid-solid interface location in a solidifying material. In this paper, this setting is used to model an industrial continuous casting process, which produces nearly all steel currently used worldwide. Regulation of both the steel temperature and the liquid-solid interface location history is the key to the steel quality. Experiments have revealed the existence of hysteresis due to boiling of the cooling water at the surface of the outer (solid) boundary of the solidifying steal shell. This work addresses this difficulty by considering control of the Stefan problem with unknown boundary hysteresis. To reduce the problem complexity, the hysteresis effect uncertainty is represented through the changing parameters. Then, the hysteresis inverse is designed and the recalibration method for the hysteresis inverse is proposed. Simulation results are provided, showing that under this setting, both the temperature and the interface location converge to the reference states.

Particles in molten steel, including argon-gas bubbles, slag droplets, and non-metallic inclusions, are removed into the surface-slag layer or captured by the solidifying steel-shell during continuous steel casting. Captured particles often become serious defects in the final steel product, so understanding particle-capture mechanisms is important for steel quality. Slab casters often have a straight mold and upper-strand prior to a curved lower-strand. The present work investigates particle capture in such a caster using computational modeling with a standard k-ε model for molten-steel flow, a discrete phase model for inclusion transport, and an advanced capture criterion for inclusion entrapment and engulfment into the steel shell. A new postprocessing methodology is presented and applied to predict inclusion-capture rates in commercial cast product. The locations and size distributions of particles captured into the shell, and actual capture rates are quantified. The model predictions are validated with ultrasonic-test plant measurements of the locations of large particles captured in a steel slab. The results reveal how large-inclusion capture accumulates in the beginning of the curved strand, leading to a capture band in the slab inside radius. Finally, the capture fractions and locations due to all capture mechanisms are compared for different inclusion sizes, and the implications are discussed.

Air gap formation during solidification greatly affects interfacial heat transfer and both must be understood quantitatively for accurate numerical simulation of casting processes, which are needed for fundamental understanding to enable quality improvements. Displacement and temperature in a 23 kg steel ingot and mold were measured simultaneously during solidification using a new experimental system. Interfacial heat transfer coefficients were extracted from the measurement results using an inverse heat conduction model. The evolution of temperature, air gap thickness, and interfacial heat transfer coefficients (IHTC) were quantified during this ingot casting process. The air gap forms earlier and grows larger on the narrow side than on the width side of the ingot. Interfacial heat transfer can be divided into four stages. In the first stage, there is good contact between the steel shell and the mold, so there is no air gap, and IHTC is high: 2700 to 3000 W m−2 °C−1. In the second stage, an air gap starts to form, so heat transfer decreases sharply. In the third stage, as the air gap thickness continues to grow, its effect weakens. In the fourth stage, even as the air gap continues to grow, IHTC remains almost constant at about 600 W m−2 °C−1. The IHTC can be predicted reasonably well with a simple equation based on conduction across the measured gap thickness, radiation, and contact resistance based on the measured roughness of the cast surface. Conduction is more important than radiation across the gap, accounting for about seventy percent of the effective IHTC at later times when the gap is large.

Air aspiration is an important cause of nozzle clogging and inclusions in final products of continuous casting of steel due to the presence of metal oxides (such as alumina) which occur through the reoxidation of molten steel. This problem is most likely to occur when the flow control system (slide-gate or stopper rod) causes the pressure inside the nozzle to drop below atmospheric pressure, drawing gas into the system through possible cracks or gaps in the refractory walls. In this work, a 1-D pressure-energy model of the complete metal delivery system from the tundish to the mold is developed to predict the pressure distribution and throughput under dynamic operating conditions and varying clogging conditions. The energy balance approach includes pressure losses in the slide-gate, wall friction, and nozzle geometry variations, including the effects of multiphase flow due to argon gas injection. The model also predicts air aspiration, oxide inclusion formation, and the time for clogging shutdown. The predicted pressure distribution is verified with a three-dimensional numerical simulation of multiphase turbulent flow, and is validated with plant measurements. Parametric studies with different submerged entry nozzle (SEN) designs revealed that a smaller SEN diameter may lessen negative pressure by redistributing the pressure loss from the slide-gate to the entire nozzle through increased friction losses. Under negative pressure, a submillimeter-thin gap was shown to cause considerable air aspiration. Clogging shutdown times were evaluated for several scenarios under static and dynamic operating conditions.

The “quenching and partitioning” (or Q&P) process has been developed to produce high strength steel microstructures with substantial quantities of retained austenite. Q&P is being applied industrially as one way to produce third generation advanced high strength steels (AHSS), a class of sheet steels [1] with excellent combinations of strength and formability [2]. Microstructures containing retained austenite are also of interest in wear applications, [3, 4] and so are relevant to plate steel production for construction machinery, agricultural and other earth engaging applications. The enhancement of ductility, toughness or wear resistance is intended to derive from transformation of the retained austenite to hard martensite during deformation that occurs during manufacturing or service, i.e. the TRIP (TRansformation Induced Plasticity) effect.

Due to its simplicity and efficiency, cluster dynamics modeling has been widely used to simulate microstructure evolution in materials, such as defect formation in metals. However, its computation cost becomes prohibitive when the clusters grow too large, so a particle-size-grouping method is often required. In this paper, three different size-grouping methods are compared with the exact solution of the ungrouped cluster dynamics model for Al3Sc precipitation in an Al-0.18 at.% Sc alloy. A new assumption of logarithmically-linear distribution of cluster number densities inside each size group is shown to be the most efficient way to match with all results of the ungrouped model. Finally, the calculated results are compared with the measured sizes and distributions of Al3Sc precipitates at different aging temperatures. The new size-grouping method is shown to have better accuracy for the chosen discretization and time-stepping method evaluated. This will enable significant computational savings, and the extension of time scales and cluster sizes to the ranges of realistic metallurgical systems, while preserving reasonable accuracy.

A new model, CONOFFLINE, has been developed to simulate transient thermal behavior of a longitudinal section down a continuous steel slab-casting machine. The model was first verified by comparing its predictions of shrinkage through the strand thickness with transient measurements of roll forces in a thick-slab caster during a series of speed changes. The model was then applied to investigate the evolution of temperature and shell thickness in a typical caster after sudden changes in casting speed. Simple equations are proposed to estimate the settling time of metallurgical length and surface temperature during sudden speed changes for both thin- and thick-slab casters. Finally, the influence of different spray cooling control methods on these behaviors during casting speed changes is investigated.

Surface quality and castability of steels are controlled greatly by initial solidification. Peritectic steels suffer more from surface quality problems, including deep oscillation marks and depressions, crack formation, and breakouts than other steels. This paper reviews current understanding of the fundamental mechanisms of initial solidification of peritectic steels that lead to these problems. First, different empirical relations to identify peritectic steel grades from their alloy compositions are summarized. Peritectic steels have equivalent carbon content that takes their solidification and cooling path between the point of maximum solubility in δ-ferrite and the triple point at the peritectic temperature. Surface defects are related more to the solid-state peritectic transformation (δ-ferrite → γ-austenite) which occurs after the peritectic reaction (L + δ → γ) during initial solidification. Some researchers believe that the peritectic reaction is controlled by diffusion of solute atoms from γ phase, through the liquid, to the δ phase while others believe that γ growth along the L/δ interface involves microscale heat transfer and solute mixing due to local re-melting of δ-ferrite. There is also disagreement regarding the peritectic transformation. Some believe that peritectic transformation is diffusion controlled while others believe that massive transformation is responsible for this phenomenon. Alloying elements and cooling rate greatly affect these mechanisms.

This paper presents an observer and an output feedback control with respect to a reference solution for the one-phase Stefan problem under input hysteresis. The one-phase Stefan problem describes evolution of the temperature and melting-solidification front in liquid-solid material. The setting models an industrial casting process, and experiments have revealed the existence of hysteresis due to boiling of the cooling water at the surface of the casting process. Therefore, one-phase Stefan problem with water cooling hysteresis under Neumann boundary actuation is considered. Full state feedback control law for this problem was designed and proved to provide asymptotic convergence of both temperature distribution and the solidification front. However, for the casting process, only boundary sensing is available. To address the latter problem, the present paper proposes an observer that estimates the temperature profile based on the available surface temperature measurement, taking into account boundary input hysteresis. The stability of the observer is proved with Lypanov method. Finally, an output feedback control law is proposed and proved to ensure asymptotic convergence of the temperature and the solidification front errors to zero. A numerical example presents the application of the method proposed.

Multiphase flow phenomena greatly affect the quality of continuous cast steel. Air aspiration through a nozzle, due to negative pressure distribution, can cause reoxidation and non-metallic inclusions, which may build up on the refractory walls as nozzle clogging. Asymmetric jet flow from a clogged nozzle causes excessive surface velocities and vortexing at the top surface in the mold, resulting in entrainment of the mold slag into the steel pool. In addition, instability at the interface between the molten steel and surface slag, caused by jet wobbling, results in sudden level drops and slag entrapment into the solidifying shell at the meniscus region. This surface defect formation becomes more severe with meniscus freezing and the accompanying formation of subsurface hooks. Furthermore, particles such as argon gas bubbles, alumina inclusions, and entrained slag droplets can be transported deep into the strand and captured into the steel shell, especially on the inside radius wall during curved strand casting. This causes internal defects. To quantify the above defect formation mechanisms relevant to multiphase flow phenomena, high-resolution multiphase flow models validated with plant measurements and/or laboratory-scale model experiments are required. Finally, these multiphase flow-related defects can be lessened with appropriate choice of nozzle geometry and all of the casting conditions which control the flow. The specific effects of nozzle port angle, nozzle submergence depth, casting speed, gas injection, and electromagnetic forces are discussed.

ABSTRACT The pressure distribution in the flow delivery system is very important to steel quality, since the minimum pressure in the nozzle can cause air aspiration through cracks, joints, or porous refractory. A new MATLAB-based modeling tool has been developed to predict Pressure-drop Flow-rate relations in a Slide Gate system (PFSG) that enables researchers to investigate these phenomena. This model is validated with three-dimensional finite-difference model calculations and plant measurements and is applied to conduct parametric studies. The slide gate opening at which the minimum pressure occurs depends only on the nozzle diameter and is not affected by tundish height or casting speed. Decreasing lower diameter of the Submerged Entry Nozzle requires an increase in the slide gate opening to maintain casting speed. Furthermore, changing all diameters of the nozzle together has even more effect on the slide gate opening. This effect is beneficial to increase the minimum pressure in the system and lessen air aspiration problems.

Continuous casting, a relatively recent development in the field of manufacturing process and technology, has been appropriately adopted and adapted to meet today’s consistently huge volume of demand for steel, aluminum and a number of nonferrous metals. The traditional batch production method of casting ingots could not remain attractive for long because of some inherent problems relating to stripping off every ingot from mold upon solidification, microstructural and chemical variations, and individual processing. Thus it became progressively harder for the traditional method to meet the stringent customer requirements and compete with the continuous casting process. The perceived benefits of the continuous casting particularly the improved product quality, higher productivity and efficiency, and reduction in cost acted as significant drivers for inception of the process. However, alleviation of the problems encountered in the traditional method and attainment of the state-of-the-art level of continuous casting process had to overcome many challenges relating to the design of the production system and its operation. This article illustrates the general features of the design process and technology of continuous casting including the challenges faced throughout the pathway to its current level for the solidification of various metals and alloys.