A simple, but comprehensive model of heat transfer and solidification of the continuous casting of steel slabs is described, including phenomena in the mold and spray regions. The model includes a one-dimensional (1-D) transient finite-difference calculation of heat conduction within the solidifying steel shell coupled with two-dimensional (2-D) steady-state heat conduction within the mold wall. The model features a detailed treatment of the interfacial gap between the shell and mold, including mass and momentum balances on the solid and liquid interfacial slag layers, and the effect of oscillation marks. The model predicts the shell thickness, temperature distributions in the mold and shell, thickness of the resolidified and liquid powder layers, heat-flux profiles down the wide and narrow faces, mold water temperature rise, ideal taper of the mold walls, and other related phenomena. The important effect of the nonuniform distribution of superheat is incorporated using the results from previous three-dimensional (3-D) turbulent fluid-flow calculations within the liquid pool. The FORTRAN program CONID has a user-friendly interface and executes in less than 1 minute on a personal computer. Calibration of the model with several different experimental measurements on operating slab casters is presented along with several example applications. In particular, the model demonstrates that the increase in heat flux throughout the mold at higher casting speeds is caused by two combined effects: a thinner interfacial gap near the top of the mold and a thinner shell toward the bottom. This modeling tool can be applied to a wide range of practical problems in continuous casters.

http://ccc.illinois.edu/pdf files/publications/03_mtb_meng_con1d_reprint_post.pdf

Heat-transfer and solidification model of continuous slab casting: CON1D

Review of non-reactive and reactive wetting of liquids on surfaces.

Hydrodynamic and hydromagnetic stability

United States. National Aeronautics and Space Administration (NASA MESSENGER Participating Scientist grant NNX07AR77G)

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/jgre.20091

The curious case of Mercury's internal structure

The latest publications regarding the development of technology to control inclusion compositions focusing on MgO·Al2O3 spinel inclusions were summarized in this review article. The problems caused by spinel inclusions, which affect practice as well as products were shown. The formation mechanism of MgO·Al2O3 spinel inclusions is secondly explained thermodynamically from the view points of chemistries of molten steels and slag compositions. Furthermore, crystallization behaviour of spinel was introduced. Countermeasures conducted in practices and laboratories were shown along with some problems still left that should be solved in the future.

https://www.jstage.jst.go.jp/article/isijinternational/50/10/50_10_1333/_pdf

Control of MgO·Al2O3 Spinel Inclusions in Stainless Steels

To overcome the limitations of differential thermal analysis (DTA) and direct casting experimentation in the measurement and understanding of the solidification phenomena of mold slags, the double and single hot thermocouple techniques (DHTT and SHTT) for the direct observation and measurement of mold slag crystallization were developed. These methods enable the solidification and melting process of transparent slags to be observed "in situ" under conditions where the temperature or temperature gradient can be measured and controlled. The SHTT allows a sample to be subjected to rapid cooling rates or to be held under isothermal conditions. The DHTT allows large temperature gradients to be developed between the two thermocouples and allows a simulation of the transient conditions which can occur in the infiltrated slag film that occurs between the mold and the solidifying shell in the mold of a continuous caster. By these techniques both isothermal and non-isothermal phenomena can be studied. A number of mold slags are optically transparent or translucent at steelmaking temperatures while the crystalline phase which precipitates upon cooling is opaque and can be clearly observed using optical microscopy. Thus the SHTT and DHTT are connected to an image capturing and analysis system that allows the onset and growth of the opaque crystals which precipitate from the slags to be documented. The development and application of these techniques to mold slag crystallization will be discussed in this paper.

/pdf/development-of-double-and-single-hot-thermocouple-technique-1a5c9jmxdq.pdf

Development of Double and Single Hot Thermocouple Technique for in Situ Observation and Measurement of Mold Slag Crystallization

The equilibrium interfacial energy between a liquid iron alloy and a liquid slag is a key physical parameter in the design of steel-refining processes as high interfacial energies are desired to avoid emulsification of slag in steel and the creation of casting defects. During a chemical reaction between a liquid iron alloy droplet and a liquid slag, it is possible to observe by X-ray photography a number of dynamic interfacial phenomena such as droplet flattening, interfacial turbulence, and spontaneous emulsification that can potentially lead to serious processing problems. These dynamic phenomena have been studied during reactions between Fe-Al and Fe-Ti alloys and silica-containing slags, and the presence of significant interfacial disturbance has been observed during the times of high reaction rate between the slag and the metal. It is suggested that interfacial chemical reactions induce Marangoni and natural convection at the slag-metal interface. This interfacial flow gives rise to interfacial waves due to a Kelvin-Helmholtz instability. The waves grow, become unstable, and lead to spontaneous emulsification of slag in steel and steel in slag. Experiments using industrial samples and controlled laboratory tests have indicated that this phenomenon may be more common than once thought and could lead to some serious problems in the processing of steel alloys containing high quantities of aluminum and/or titanium.

Dynamic and equilibrium interfacial phenomena in liquid steel-slag systems

The density of liquid Fe-C alloys at temperatures ranging from 1250 °C to 1550 °C was measured by the sessile drop profile method. An accurate method of digital image processing was de-veloped to capture, enhance, and determine the coordinates of the X-ray shadow image of the droplet. Laplace's equation was then solved to obtain the volume and density of the droplet. The density of iron-carbon alloys was then determined as a function of carbon content (from 0 to 4 wt pct) and temperature (1250 °C to 1550 °C). A least-squares analysis of our data points gives an equation for the density of liquid iron-carbon alloys as a function of temperatureT [K] and carbon content [pct C] [wt pct]: ρ[g/cm3] = (7.10 - 0.0732[pct C]) - (8.28 - 0.874[pct C]) × 10-4(T - 1823) These results will give a value to within ±1.5 pct of the data of Lucas, [3] Widawski and Sauerwald, [2] and the present work.

The density of liquid iron-carbon alloys

The conditions under which crystallization develops in a mold slag must be understood in order to select or design a mold flux for use in the continuous casting of steels. In this paper, the crystallization of an industrial mold slag was quantified using a single hot thermocouple technique which, when combined with a video camera based observation system, allowed observation of the onset and growth of the crystals which were precipitated from the melt. The beginning of crystallization was determined by direct observation and the growth rate of crystals were measured by frame by frame image analysis of recordings of the progress of crystallization. Isothermal experiments were performed at different temperatures and a Time-Temperature-Transformation (TTT) diagram was determined for this industrial mold slag. X-ray diffraction of quenched samples was used to determine the type of crystalline phases that were precipitated. The TTT diagram was divided into two separate regions which corresponded to the precipitation of dicalcium silicate (Ca 2 SiO 4 ) at temperatures over 1 050 °C and of Cuspidine (Ca 4 Si 2 O 7 F 2 ) at temperatures below 1 050°C. The evolution crystal fraction was described by Avrami's equation. This work indicates that industrial mold slags are easily undercooled, that crystallization occurs throughout the melt, that crystals grow initially as equiaxed dendrites and that the onset of crystallization is a function of cooling rate and must be described by either TTT or CCT curves.

https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/75701/1/ISIJ%20Int.%2038%284%29_%20357.pdf

Alan W. Cramb

Papers

Development of Double and Single Hot Thermocouple Technique for in Situ Observation and Measurement of Mold Slag Crystallization

Dynamic and equilibrium interfacial phenomena in liquid steel-slag systems

The density of liquid iron-carbon alloys

An investigation of the crystallization of a continuous casting mold slag using the single hot thermocouple technique

Kinetics of Al2O3 dissolution in CaO-MgO-SiO2-Al2O3 slags: In Situ observations and analysis