A mathematical model of a single-roll continuous strip caster based on fluid-mechanics considerations

A mathematical model based on fluid mechanics considerations has been formulated to describe a single-roll continuous strip caster. The heat transfer related phenomena are incorporated in the model through an empirical over-all parameter. The model provides useful interrelationships between the final strip thickness and the operation and design parameters, e.g. the speed of rotation of the caster drum, the stand-off distance, the nozzle passage gap and the liquid metal head in the reservoir. Simulating the process, using the model, it has been possible to predict the effect of these parameters on the final strip thickness. The model allows, though indirectly, the prediction of the conditions which would lead to choking of the liquid metal pool due to premature solidification. Comparing the results of this model with those obtained using the model based on heat balance considerations only, it is noted that the former predicts higher values of final strip thickness.     

A mathematical model of single roll strip caster based on macroscopic enthalpy balances

A mathematical model, based on the overall heat balance and the growth of solidification front, has been formulated to describe the single-roll strip-casting process for steel. The model provides useful interrelationships between the rate of growth of solidifying strip and the principal process variables such as the speed of rotation of caster drum, the system geometry, the superheat of melt and the relevant heat transfer coefficients. Using these relationships it has been possible to predict the effect of process parameters on the process performance in terms of the final strip thickness and the casting rate.     

Effect of holding time and surface cover in ladles on liquid steel flow in continuous casting tundishes

Mathematical modeling of fluid flow and heat transfer of melt in a typical two-strand slab caster tundish has been done for a complete casting sequence. The complete casting sequence consists of 1 minute of tundish emptying period during the ladle transfer operation followed by 1 minute of tundish filling period by the new ladle and pouring at the normal operating level of the tundish for 46 minutes. The effect of varying ladle stream temperature conditions on the melt flow and heat transfer in the continuous casting tundish has been studied. When the ladle stream temperature decreases appreciably over the casting period, corresponding to heat loss of the melt in the ladle from the top free surface, the incoming melt temperature becomes lower than that of the melt in the bulk of the tundish after about 30 minutes from the start of teeming. This results in melt flow along the bottom of the tundish instead of the normal free surface directed flow. The ladle melt stream temperature shows little variability when the ladle has an insulated top. Corresponding to this situation, the temperature of the incoming melt remains higher than that of the melt in the bulk of the tundish and the normal free surface directed flow is maintained throughout the casting period. The product cast under such condition is expected to have a uniformly low inclusion content. The heat loss condition from the top of the ladle has been shown to be the dominant factor in determining fluid flow and heat-transfer characteristics of the melt in the tundish rather than the holding time of the melt in the ladle. Formerly Graduate Student, Department of Materials Science and Engineering, Ohio State University     

A 3-D numerical prediction of turbulent flow,heat transfer and solidification in a continuous slab caster for steel

This study describes the numerical modeling of three-dimensional coupled turbulent flow, heat transfer, and solidification in a continuous slab caster for stainless steel. The model uses generalized transport equations which are applicable to the liquid, mushy and solid regions within the caster. The turbulent characteristics in the melt pool and mushy region are accounted for using the low-Reynolds number k–ε turbulence model by Launder and Sharma. This version of the low-Reynolds number turbulence model is found to be more easily adaptable to the coupled flow and mushy region solidification caster problem compared to the standard high-Reynolds number and other low-Reynolds number turbulence models. The macroscopic solidification process itself is based on the enthalpy-porosity scheme. The governing transport equations are solved employing the primitive variables and using the control volume based finite-difference scheme on a staggered grid. The process variables considered are the casting speed and the inlet superheat of the melt. The effects of these process variables on the velocity and temperature distributions and on the extent of the solidification and mushy regions are reported and discussed. The numerical predictions of solidification profile are compared with the limited experimental data available in the literature, and very good agreement was found.     

A three-dimensional mathematical model of electromagnetic casting and testing against a physical model: Part II. Results from a physical model and testing of the mathematical model

A physical model of an electromagnetic caster was constructed. The model was intended to provide measured data for comparison with the predictions of the three-dimensional (3-D) mathematical model described in part I. The physical model consisted of a molten Wood's metal pool (176×176 mm seen from above) on the top of an aluminum-bronze block. Probes were used to measure electric and magnetic fields, the deformation of the liquid surface, and the electromagnetically driven flow, at many positions within the melt, as a function of model geometry. Agreement between the measurements and the predictions of the mathematical model was generally good. The melt flow was 3-D and strongly influenced by the position of the electromagnetic screen interposed between the inductor and the metal pool.     

A Mathematical model of the closed mold (Watts) horizontal continuous casting process

A mathematical model is presented for the closed mold, horizontal (Watts) continuous casting system. A particular feature of the system is that molten metal is fed, from a tundish, through a pipe formed by the solidified shell, to a closed mold which is made to move away from the tundish as casting proceeds. A major practical problem in the technical assessment of the process is to estimate the maximum length that may be cast before the supply of metal to the mold is restricted by the solidification of the shell downstream from the tundish nozzle. The model described in the paper is based on a two-dimensional transient heat balance written for both the solidified shell and the molten metal (+ slurry) stream and the resultant differential equations are solved numerically. It was found that both the maximum length that may be cast and the actual location of the freezing blockage are markedly affected by the melt-shell heat transfer coefficient, the spray-shell heat transfer coefficient and the fraction of the mushy zone that is swept away by the melt. The maximum length may be cast when the melt-shell heat transfer coefficient is large and when much of the mushy zone is being swept away by the melt, which, in a physical sense would correspond to a fast casting rate. Freezing blockage would then occur some distance downstream from the inlet. For the range of operating conditions considered, for slab casting, the maximum length that could be cast corresponded to some 300 to 550 times the width of the slab. Formerly of the Department of Chemical Engineering, State University of New York at Buffalo, At this stage we shall not specify whether the thickness of the solidified shell will correspond to the solidus or the liquidus temperature at the inner surface, or to some intermediate value. This will be one of the parameters in subsequent calculations.     

A simple fluid mechanical model for planar flow casting melt-spinning

A math model for melt-spinning based on a two-dimensional steady-state condition has been developed. Because of the complexity of the processes involved, the solution of the full governing nonlinear partial differential equations and boundary conditions is not sought. Instead, the problem is analyzed using a control volume approach. In this approach, overall conservation laws for mass, momentum, and energy are satisfied for each of the zones into which the flow field can be conveniently subdivided. The zones are the reservoir, the nozzle, the liquid pool, and the solidified thin metal sheet. The conservation laws can be solved to yield the thickness of the sheet with the reservoir pressure, the ambient pressure, the nozzle/drum gap, the drum speed, and the geometry as input parameters. Because the model contains all the essential parameters, it can be used to optimize operation of the process or its dependence on any of the geometric or physical parameters.     

Transient thermal model of the continuous single-wheel thin-strip casting process

A transient heat-transfer model (STRIP1D) has been developed to simulate the single-roll continuous strip-casting process. The model predicts temperature in the solidifying strip coupled with heat transfer in the rotating wheel, using an explicit finite difference procedure. The model has been calibrated using strip thickness data from a test caster at ARMCO Inc. (Middletown, OH) and verified with a range of other available measurements. The strip/wheel interface contact resistance and heat transfer were investigated in particular, and an empirical formula to calculate this heat-transfer coefficient as a function of contact time was obtained. Wheel temperature and final strip thickness are investigated as a function of casting speed, liquid steel pool depth, superheat, coatings on the wheel hot surface, strip detachment point, wheel wall thickness, and wheel material.     

双辊薄带连续铸轧熔池内金属流动及传热特性的研究

本文建立了双辊式薄带连续铸轧熔池内二维传热流动数学模型，使用有限元计算方法实现了控制方程及边界条件的数值求解，计算结果揭示了熔池内的流场、凝固温度场的特点和规律。     

Modelling steel flow in a three‐strand billet tundish using a turbulence inhibitor

A three‐strand tundish belonging to a billet caster was water modelled and plant trials were performed to compare the performance of a pouring box and a turbulence inhibitor in terms of melt flow parameters and steel cleanliness. A tailor made turbulence inhibitor for this tundish is useful to accomplish with flow control of fluid turbulence and even melt redirection to all strands. The turbulence inhibitor helps to decrease nitrogen pickup during ladle changes and to float out inclusions towards the covering slag. As a consequence, rod operations to take of alumina deposits from nozzle walls are considerably decreased using a turbulence inhibitor.     

单流厚板坯连铸中间包结构优化

针对鞍钢一炼钢的厚板坯连铸中间包,采用冷态物理模拟方法,对中间包的控流装置进行了优化,对实际中间包钢水流动建立了数学模型,得到中间包优化前后钢液流动的速度场。实验结果表明,原结构的中间包的控流装置和布置位置不合理。中间包采用湍流控制器和结构优化后,提高了钢水在中间包的停留时间,死区体积明显下降。实际应用的结果表明,中间包结构优化后,中间包钢液、第1和第3块铸坯试样中的平均夹杂物面积比明显下降。     

Thermal criteria for tundish nozzle or taphole blockage

A formulation is presented to describe the rate at which a solidified crust is formed (and possibly remelted) on the inside walls of a nozzle through which molten metal is being poured. The molten metal stream is considered to be turbulent and in the formulation allowance is made for transient heat conduction in the skull and in the refractory walls, together with the time dependent mass flow rate due to the presence of the skull. The resultant differential equations are solved numerically and computed results are presented for conditions that are thought representative of some tundish pouring practices. It was found that the growth and possible remelting of the solidified crust would take place very rapidly, in a matter of seconds. The effect of several parameters was examined, including the role played by the nozzle diameter, the superheat of the steel and the preheating of the nozzle walls. It was found that the nozzle diameter was the most critical variable; nozzles less than about 1/2 in. in diam were likely to freeze rather readily. The superheat of the steel was found important in affecting closure, but the preheat of the nozzle appeared to be less significant a variable, provided the nozzle was brought within about 500‡F of the freezing temperature of the steel.     

Conditions of Liquid Steel Treatment for Near Net‐Shape Casting Processes

Slab casting for hot rolled steel and strip casting using the twin roll casting (TRC) method are compared in terms of inclusions evolution. There are differences of the processes, mainly the use of casting flux in CC of slabs, or pool shapes and sizes in terms of TRC, particularly when roll diameters vary. The inclusion evolution of alumina in a low carbon steel grade was estimated. By modelling particle growth rate, coagulation and deposition, an ‘agglomeration index’ was created to describe the probability of clogging in the SEN. Similarly the growth of secondary alumina precipitation during cooling of the melt in the pool by Stokes collision and turbulent collision was estimated in terms of forming large particles which are able to float‐up. Influences of melt superheat or caster size were taken into account.     

A Model for Predicting the Melt Temperature in the Ladle and in the Tundish as a Function of Operating Parameters during Continuous Casting

A mathematical model for predicting the melt temperatures in the ladle and in the tundish during continuous casting has been developed. First of all, a chain of models was created for the following stages of the ladle cycle; the preheating of the empty ladle, filling of the ladle, period in the ladle furnace, waiting period prior to casting, the casting period, and, finally, the free cooling period of the empty ladle. Models, written in CFD code, were used in sequence so that each simulation continued from the results of the simulation of the previous stage. An intermediate model was constructed to estimate the outlet temperature of melt drained from the ladle. Then the work was continued by performing simulations in the tundish, using as input the temperature of the simulated melt feed from the ladle and, as an initial condition, the temperature field of the remaining melt in the tundish. The final model “TEMPARV3” was created and tested by means of measured tundish data received from a steel plant. By means of statistical analysis the coefficients of correlation between the test data and model data at the start, in the middle period, and at the end of casting were calculated to be 0.9, 0.92 and 0.87, respectively. So, the most effective predictive power of the model in the tundish by means of a sequential casting schedule is realized during the middle period of the casting process. The model is applied interactively by a user interface, which expresses the predicted melt temperatures numerically and with graphical curves. The predictive model can be used off‐line as a tool for scheduling the stage operations in advance. The program may be utilized on‐line to estimate the superheat needed and to control periods of the operation. In extreme cases, when the model alerts the operator about the danger of superheat loss having a critical effect on casting, the operator has a chance to take adjustment measures. In addition to production work, the model could be of benefit for studying changes in operating parameters, for training operators, and for use as a “low‐cost computational pilot plant” in process development in general.     

板坯连铸机中间包流场研究

运用三维流场软件包对太钢连铸机中间包内的流场分布进行研究。从钢水流动说明太钢中间包的设计方案对于实际生产比较合理，有利于钢水温度和浓度均匀，并对钢中夹杂物的形成和上浮非常有利。     

A simple fluid mechanical model for planar flow casting melt-spinning

A math model for melt-spinning based on a two-dimensional steady-state condition has been developed. Because of the complexity of the processes involved, the solution of the full governing nonlinear partial differential equations and boundary conditions is not sought. Instead, the problem is analyzed using a control volume approach. In this approach, overall conservation laws for mass, momentum, and energy are satisfied for each of the zones into which the flow field can be conveniently subdivided. The zones are the reservoir, the nozzle, the liquid pool, and the solidified thin metal sheet. The conservation laws can be solved to yield the thickness of the sheet with the reservoir pressure, the ambient pressure, the nozzle/drum gap, the drum speed, and the geometry as input parameters. Because the model contains all the essential parameters, it can be used to optimize operation of the process or its dependence on any of the geometric or physical parameters.     

Transient fluid flow and superheat transport in continuous casting of steel slabs

The turbulent flow of molten steel and the superheat transport in the mold region of a continuous caster of thin steel slabs are investigated with transient large-eddy simulations and plant experiments. The predicted fluid velocities matched measurements taken from dye-injection experiments on full-scale water models of the process. The corresponding predicted temperatures matched measurements by thermocouples lowered into the molten steel during continuous casting. The classic double-roll flow pattern is confirmed for this 132×984 mm slab caster at a 1.52 m/min casting speed, with about 85 pct of the single-phase flow leaving the two side ports of the three-port nozzle. The temperature in the top portion of the molten pool dropped to about 30 pct of the superheat-temperature difference entering the mold of 58 °C. About 12 pct of the superheat is extracted at the narrow face, where the peak heat flux averages almost 750 kW/m² and the instantaneous peaks exceed 1500 kW/m². Two-thirds of the superheat is removed in the mold. The jets exiting the nozzle ports exhibit chaotic variations, producing temperature fluctuations in the upper liquid pool of ±4 °C and peak heat-flux variations of±350 kW/m². Employing a static-k subgrid-scale (SGS) model into the three-dimensional (3-D) finite-volume code had little effect on the solution.     

板坯连铸机中间包的物理模拟

通过对超低头板坯中间包的物理模拟，采用聚乙烯粒子模拟大颗粒夹杂物在中间包的上浮行为研究，确认采用单墙单坝的控流方式有利于夹杂的上浮，并找到了上挡墙和坝在中间包的最佳位置。同时认为以塞棒控流中间包的临界液面高度应大于150mm。     

Transient steel quality under non-isothermal conditions in a multi-strand billet caster tundish: part I. Analysis of fluid flow,thermal behaviour and inclusion behaviour

A numerical model based on computational fluid dynamics was used to simulate the effect of non-isothermal conditions on melt flows in a multi-strand billet caster tundish. To start with, water was used as the operating fluid in a one-third scale tundish to calculate the fluid flow and temperature fields under isothermal and non-isothermal conditions. The model was then extended to the full-scale tundish with molten steel as the operating liquid in order to simulate the conditions in a real plant. It was observed that using step inputs of 10° and 23° for water and steel cases, respectively, changed the fluid flow patterns significantly, more so at locations far from the inlet, due to stronger buoyancy-driven natural convective flows. The temperature distribution and inclusion trajectories within the tundish were also affected due to the presence of non-isothermal conditions.     

Physical and Numerical Simulation of Fluid Flow and Solidification at the Twin‐Roll Strip Casting Process

The fluid flow in a twin‐roll strip caster is investigated by physical and numerical simulation on a 1:1‐scale water model. A laser‐optical measurement technique (Laser Doppler Anemometry ‐ LDA) is used to validate the numerical results for the water flow. The numerical simulations are then transferred to the melt flow in the strip caster. The investigations are focused on different SEN concepts (submerged entry nozzle), a single‐nozzle system with two outlet ports and a double‐nozzle system with one outlet port each. The Influence of these concepts on the velocity, turbulence, and temperature distribution inside the liquid pool between the casting rolls and on the solidification and growth of the strip shells are investigated by numerical simulations (Computational Fluid Dynamics ‐ CFD). The non‐isothermal melt flow is calculated considering the solidification enthalpy as well as the behaviour of the solidifying melt. In addition to the numerical simulations of the melt flow inside the pool the temperature distribution in the cast strip is simulated. The SEN concept directly correlates with the temperature distribution Inside the strip. Furthermore, the surface temperature of the strip below the outlet of the roll gap is measured using a line‐scanner and is compared with the CFD simulation. In order to simulate the shape of the free surface in the liquid pool, CFD simulations of the water flow in the physical model are carried out using a Volume of Fluid model (VoF). This two‐phase model is able to reproduce free surface waves.