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Towards a 'moving-point' formulation for the modelling of oscillation-mark formation in the continuous casting of steel

机译：迈向“动点”公式化​​，以建模钢的连续铸造中的振荡痕迹

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摘要

In the continuous casting of steel, solidification begins at a triple point where solid steel, molten steel and molten flux meet; the motion of this point determines how surface defects known as oscillation marks (OSMs) are formed. Here, under a number of simplifying assumptions, we derive an asymptotic model in 15 dimensionless parameters that describes the relevant momentum and heat transfer for the process, and involves both surface tension at the meniscus between molten flux and molten steel and solidification; further development couples an earlier lubrication-theory model for the region below the triple point to a reduced model for the region above that is based around a regular perturbation treatment of the Navier Stokes equations in terms of the capillary number. The resulting problem is then broken up into a hierarchy of four sub-problems; the first one for the velocity field in the molten flux-is considered in depth. A numerical algorithm is developed for an isothermal situation in which the triple point moves only perpendicular to the casting direction; this involves the solution of a novel "moving point" problem to determine motion of the triple point. Comparison of model and experimental results indicates that this reduced model could produce OSMs having the observed depth if the triple point were not too far below the top of the meniscus; otherwise, the computed marks would be too deep. The analysis also tentatively relates the location of the triple point to the fold- and overflow-type OSMs that generally form in practice. (C) 2018 Elsevier Inc. All rights reserved.
机译：在钢的连续铸造中，凝固从固态钢，熔融钢和熔融熔剂相遇的三点开始。该点的运动决定了如何形成称为振荡标记（OSM）的表面缺陷。这里，在许多简化的假设下，我们在15个无量纲参数中得出了一个渐近模型，该模型描述了该过程的相关动量和热传递，并涉及了熔剂和钢水之间的弯月面表面张力以及凝固过程。进一步的发展将早于三点以下区域的润滑理论模型与针对上层区域的简化模型相结合，后者基于毛细血管数对Navier Stokes方程的常规扰动处理。然后将产生的问题分解为四个子问题的层次结构；在深度上考虑了第一个熔融熔体速度场。针对等温情况开发了一种数值算法，其中三点仅垂直于浇铸方向移动。这涉及解决新颖的“运动点”问题以确定三点运动。模型与实验结果的比较表明，如果三点距弯液面顶部的距离不远，则该简化模型可以产生具有观察深度的OSM。否则，计算的标记将太深。该分析还尝试将三点的位置与通常在实践中形成的折叠型和溢流型OSM相关联。 （C）2018 Elsevier Inc.保留所有权利。

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  • 来源
    《Applied Mathematical Modelling》 |2018年第11期|243-265|共23页
  • 作者

    Vynnycky M.; Zambrano M.;

  • 作者单位

    Royal Inst Technol, Dept Mat Sci & Engn, Div Proc, Brinellvagen 23, S-10044 Stockholm, Sweden;

    Univ Sao Paulo Sao Carlos, Inst Math & Comp Sci, Dept Appl Math & Stat, POB 668, BR-13560970 Sao Carlos, SP, Brazil;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Continuous casting; Oscillation marks; Asymptotic analysis;

    机译：连铸;振荡痕迹;渐近分析;

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