No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
A Mathematical Model of the Heat Loss of Steel in a Metallurgical Ladle
Abstract
A mathematical model suitable as a tool for improving temperature control in the steel plant is presented. With this tool, a number of variables such as holding time, material choice and refractory layer thicknesses can be studied with regard to their influence on the steel temperature evolution during casting. In addition, the model can be used as a decision support and forms a basis for automation of temperature control.
... See, e.g. (Pfeifer et al. , 1983;Morrow and Russell , 1985;Tomazin et al., 1986;Barber et al., 1994;Fredman et al. , 1997;. The influence of alterations to practice, such as stirring and preheating, have also been studied (Omotani et al. , 1983;Pfeifer et al., 1985;Tomazin et al., 1986;Koo et al., 1989;Austin et al., 1992;Fredman et al. , 1997; using results from 369 modeling as decision support . ...
... (Pfeifer et al. , 1983;Morrow and Russell , 1985;Tomazin et al., 1986;Barber et al., 1994;Fredman et al. , 1997;. The influence of alterations to practice, such as stirring and preheating, have also been studied (Omotani et al. , 1983;Pfeifer et al., 1985;Tomazin et al., 1986;Koo et al., 1989;Austin et al., 1992;Fredman et al. , 1997; using results from 369 modeling as decision support . However , perhaps the most important application area for thermal modeling has grown out of automation of the continuous casting process , in particular temperature control of the molten steel. ...
The heat conduction in the multilayer lining of a steelmaking ladle is treated by a semi-analytical solution method for composite layer heat conduction in cylindrical geometry. The technique is based on local analytical solutions for the single material layers combined with a numerical solution scheme for the material boundary temperatures. Developed from previously presented quasi steady-state models involving only one dynamic material layer, the model now describes a fully dynamic lining setup. The approach makes it possible to obtain rapid estimates of the temperature profile over the lining and a reliable picture of the thermal state of the ladle. Accurate knowledge of the lining thermal state is a prerequisite for efficient temperature control of the molten steel and an important part in automation of the continuous casting process. The model was evaluated by simulating two representative ladle cycles of a thermocouple measurement campaign carried out at the facilities of a Finnish steel producer. The agreement between model output and measurements was satisfactory, illustrating the feasiblity of the adopted, simplified, modeling strategy.
... A critical factor for its definition concerns the estimation in advance of the thermal losses of the steel between both equipments the ladle furnace and the casting machine (Duarte, 2009;Murata et al., 2012). Duarte et al. (2015), Zimmer et al. (2008), Gupta and Chandra (2004) and Fredman et al. (1997) used the process-driven approach considering basically the losses in the ladle furnace, which are mainly associated to the refractory linings at the side walls, its bottom and to the slag layer at the top. Besides, heat losses also occur during the transport time of the steel from the ladle until the casting unit, and the waiting time until the begining of its processing on the caster (He et al., 2014). ...
A critical factor in steelworks concerns setting the steel release temperature from the ladle furnace. The challenge resides in estimating in advance the reduction the steel temperature will undergo during its non-processing time until the subsequent casting process. A poor estimation results in productivity and yield losses in casting and unnecessary energy consumption in the ladle. Given process complexity, a pure mathematical description is not available. This work develops a predictive neural model for the reduction in steel temperature between the ladle and the caster considering the main sources of heat losses. The case study refers to a steelmaking plant in Brazil. After model identification and validation, and a sensitivity analysis study, thirty troublesome steel runs that resulted in unplanned shutdowns during casting were investigated. The neural approach provided a correlation between factory-collected values and model estimates of 0.895, with a satisfactory Mean Absolute Error (MAE) of 3.03 °C , against 0.308 and 4.97 °C, respectively, given by the experimental plant model used by the process team, and ‒0.087 and 8.53 °C, respectively, obtained with a linear regression analysis used for comparison purposes. More reliable estimation of the reduction in steel temperature leads to more efficient and economic operations.
A fully transient 3D CFD model of an industrial argon bottom-stirred ladle with two eccentric porous plugs was developed. The computational domain included molten steel, slag, air and refractory phases. The slag-air interface was set as a free surface to ensure that the influence of the flow and the heat dissipation at the slag free surface on the temperature of the molten steel can be considered simultaneously. As a result, the model reasonably predicted the velocity and temperature distribution of molten steel, heat losses from the top slag layer and the temperature distribution in the refractory walls due to bottom gas injection. Previous numerical models on heat transfer in ladles have either neglected bottom gas injection, assumed a constant heat flux through the top slag layer or assumed a flat surface. The current mathematical model overcomes the previous limitations, it is capable to predict fluid flow and temperature distribution under transient conditions comparing a flat and a free surface. It is shown that the assumption of a flat surface leads to errors in the numerical predictions, it also predicts heat losses by the top slag surface and the refractory walls.
The development of mathematical models for the heat balance and for the stratification phenomenon of the steel in the ladle is described. Measurements are made of the steel temperature in the converter, in the ladle and in the teeming jet, of temperature profiles in the ladle refractories and of the flow rate of the steel during tapping and teeming. The results from the calculations of the heat balance model agree with the measured values within the accuracy of the measurements. The stratification model is also in agreement with experiments. The possibilities of using the two models combined are illustrated.
The requirement for better temperature control of molten steel during teeming or casting necessitates an improved means to evaluate the thermal effects of different refractory materials and melt shop operations. Both steady- and unsteady-state heat transfer models are used to evaluate changes in ladle refractories and the effects on steel temperatures. Parameters evaluated include refractory type, the use of insulation, and the use of ladle covers. 10 refs.
In the initial planning for the installation of a new horizontal caster at Avesta Panteg, it was decided to utilise the existing ingot teeming ladles for liquid steel supply. However, with long casting times and a small ladle size, indications were that high superheats would be required with a risk of breakout and poor billet quality. Therefore, an extensive programme of work was undertaken to redesign the ladle refractory lining for heat retention and thereby minimise superheat during horizontal casting. To enable accurate predictions of liquid steel temperature loss in the ladle and tundish to be made for horizontal casting, mathematical models of the ladle and tundish were calibrated via instrumented ladle trials. These trials showed that the expected temperature loss in the ladle during casting with the original refractory configuration would be 87 K with a corresponding 92 K loss in the tundish. Further trials with ladle insulation and mathematical modelling of the ladle have resulted in an insulated ladle design which reduced the temperature loss in the ladle to 46 K. With increasing use of the caster, this has now been reduced to 20-30 K.
A mathematical model is established to calculate the temperature variation of steel melts in the ladle by heat flows in the ladle wall, the ladle bottom and the slag. The model permits the definition of the melt temperature, from tapping to the end of the pouring process, taking due account of larger quantities of alloys and additions as well as scavenging of the melt. The temperature profiles in the refractory lining can be computed. 12 refs.
Inert gas stirring of the melt in the ladle is a proven engineering process measure in secondary steelmaking. It is employed to ensure the specified homogeneity of the melt in terms of composition and temperature. The achievement of these objectives is essentially contingent on the flow conditions in the melt. The present paper deals with the results of numerical computations of the bubble movement and velocity field generated by such a gas stirring process. The distribution of alloy elements and the temperature field in the melt are computed on the basis of real temperature-dependent fluid properties. The results of the numerical computations are compared with corresponding results of model trials and expressed in a form usable for operating plants. In addition, recommendations are made with regard to the scale-up of model trial results to full size ladles under actual operating conditions.
Plant measurements were done for selected parameters, influencing the heat content in ladle lining and the steel in ladle, from tapping time to the start of casting. Temperature profiles in ladle lining were measured throughout the ladle cycle by thermocouples installed in the lining. Measured parameters, such as molten steel temperature and ladle lining temperature profiles at the start of the ladle cycle, were used as initial input to the heat balance simulation model TempSim. Calculated and measured temperatures were compared and the possibility of using the heat balance model TempSim for prediction of steel temperature was demonstrated. The results obtained show that it is possible to predict steel temperatures in ladle at arrival to the casting station with a standard deviation of ±3°. The agreement between measured and calculated lining sublayer temperatures is also good. Effects on the melt temperature in ladle of lining wear, length of tapping time, amount of slag tapped from the primary furnace and lining temperature profile were also highlighted in this work. In particular, ladle lining wear and the length of the tapping influence the steel temperature in the ladle considerably.
A unique computer system for on-line ladle thermal tracking and the calculation and prediction of the temperature of liquid steel in the ladle and tundish has been successfully commissioned at the Scunthorpe Works of British Steel.
A mathematical formulation has been developed, and computed results are presented describing the evolution of the temperature and the velocity profiles in ladles holding molten steel. The calculations, which have been carried out using the PHOE, NICS computational package, have shown that, notwithstanding the strong turbulent recirculating flows, significant stratification may take place. However, this stratification may be greatly minimized by a relatively gentle agitation.
Transient analysis of the temperature and velocity distributions of steel during ladle standing and draining has been conducted using a mathematical model based on the PHOENICS numerical package. Parameters investigated were stand time, average steel cooling rate, drainage rate and ladle geometry. Stratification was seen to develop due to natural convection, and the rate of stratification was found to be linearly dependent on the average steel cooling rate, independent of ladle geometry. Qualitative relationships were found between the parameters and the teeming temperature during draining. Plant trials showed good agreement between simulated and actual teeming temperatures.
A theoretical model is proposed for the flow and heat transfer of molten steel in a ladle during pouring. Analytical and numerical solutions are obtained. Within the limitations of the model, agreement with plant observations is satisfactory.RésuméOn propose un modèle théorique pour l'écoulement et le transfert de chaleur d'un acier liquide durant la coulée d'une lingotière. On obtient des solutions analytique et numérique. Dans les limites du modèle, un accord satisfaisant est constaté avec les observations.ZusammenfassungFür die Strömung und den Wärmeübergang einer Stahlschmelze in der Guβpfanne während des Gieβens wird ein theoretisches Modell vorgeschlagen. Analytische und numerische Lösungen wurden gewonnen. Innerhalb der Grenzen des Modells ist die Übereinstimmung mit Betriebserfahrungen befriedigend.РефератПpeдлoжeнa тeopeтичecкaя мoдeль тeчeния и тeплoпepeнoca pacплaвлeннoй cтaли в кoвшe пpи paзливкe. Пoлyчeны aнaлитичecкиe и чиcлeнныe peшeния. B пpeдeлaч oгpaничeний мoдeли peзyльтaты pacчëтoв yдoвлeтвopитeльнo coглacyютcя c дaнными нaблюдeний, пoлyчeнными в пpoмышлeнныч ycлoвияч.
Heat losses from liquid steel in the ladle and in the tundish of a continuous-casting installation
- R Alberny
- A Leclercq
Alberny, R. and A. Leclercq (1973). Heat losses
from liquid steel in the ladle and in the tundish of a continuous-casting installation. In:
Mathematical Process Models in Iron and Steelmaking, Proceedings Amsterdam. The Metals Society. pp. 151-156.
He and A Thermal modelling of steel ladles
- P R Austin
- S L O 'rourke
Austin, P. R., S. L. O 'Rourke, Q. 1. He and
A. J. Rex (1992b). Thermal modelling of
steel ladles. In : 75th Steelmaking Conference
Proceedings. Vol. 75. Iron & Steel Society.
pp. 317-323.
Transport Phenomena. JohnWiley & Sons
- R B Bird
- W E Stewart
- E N Lightfoot
Bird, R. B., W. E. Stewart and E. N. Lightfoot
(1960 ). Transport Phenomena. JohnWiley &
Sons. New York.
Konzept eines On-line-Model.ls zur Uberwachung der Stahltemperatur ill der Sekundarmetallurgie
- W Hoppmann
- F N Fett
- G Hsu
- L Fiege
Hoppmann, W., F. N. Fett, G. Hsu and L. Fiege U989). Konzept eines On-line-Model.ls
zur Uberwachung der Stahltemperatur ill
der Sekundarmetallurgie. Stahl tmd Eisen
109(23), 1177-1186.
Temperature drop in pouring ladles, part two
- V Paschkis
- J W Hlinka
Paschkis, V. and J. W. Hlinka (1957). Temperature drop in pouring ladles, part two. AFS
Transactions 65, 276-28l.
Improvements to liquid steel temperature control in the ladle and tundish
- A Perkins
- T Robertson
- D Smith
Perkins, A., T. Robertson and D. Smith (1986).
Improvements to liquid steel temperature
control in the ladle and tundish. FacMerichte Hiittenpraxis Metallweiterverarbeitung
24(8), 649-656.
Der Einfluss veranderlicher Pfannenbordgeometrien auf den Warmeverlust der Stahlschmelze
- H Pfeifer
- F N Fett
- H Schafer
- K .-H Heinen
Pfeifer, H., F. N. Fett, H. Schafer and K.-H.
Heinen (1983). Der Einfluss veranderlicher
Pfannenbordgeometrien auf den Warmeverlust der Stahlschmelze. Stahl und Eisen
103, 1321-1326.