WO2020181575A1 - 一种大方坯凸形辊连铸重压下偏析行为预测方法 - Google Patents

一种大方坯凸形辊连铸重压下偏析行为预测方法 Download PDF

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WO2020181575A1
WO2020181575A1 PCT/CN2019/079025 CN2019079025W WO2020181575A1 WO 2020181575 A1 WO2020181575 A1 WO 2020181575A1 CN 2019079025 W CN2019079025 W CN 2019079025W WO 2020181575 A1 WO2020181575 A1 WO 2020181575A1
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zone
reduction
bloom
slab
continuous casting
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祭程
关锐
朱苗勇
李应焕
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Northeastern University China
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22D—CASTING OF METALS; CASTING OF OTHER SUBSTANCES BY THE SAME PROCESSES OR DEVICES
    • B22D11/00—Continuous casting of metals, i.e. casting in indefinite lengths
    • B22D11/16—Controlling or regulating processes or operations
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/30—Computing systems specially adapted for manufacturing

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  • the invention belongs to the field of bloom continuous casting production in the iron and steel metallurgical industry, and in particular relates to a method for predicting segregation behavior under continuous casting of bloom convex rolls.
  • the internal macro-segregation defect of continuous casting blooms is a typical internal quality problem, and this defect cannot be effectively removed by means of rolling and post-treatment, which seriously affects the mechanical properties of the final rolled material.
  • the convex roll reduction technology at the solidification end of continuous casting blooms is one of the most effective technical means to replace the traditional light reduction process.
  • the heavy reduction technology at the solidification end of the bloom can effectively promote the reverse flow and secondary distribution of the enriched solute at the solidification front through a larger mechanical reduction deformation, thereby improving the macrosegregation of the cast slab Process effect of behavior.
  • the bloom solidification end convex roll reduction technology can avoid the solidified shells on both sides of the bloom, significantly reduce the contact resistance of the roll blank, and increase the billet without the overall upgrade of the hydraulic system.
  • the rolling reduction is more than 2.5 times, which greatly improves the penetration effect of the reduction force to the center of the cast slab, and can further promote the reverse transfer of the enriched solute in the solidification front, and better improve the macro-segregation behavior.
  • Chinese patent CN201710948669.7 discloses a continuous casting billet production method for low pressure reduction ratio rolling. At the end of solidification, it is rolled by the convex roller heavy reduction technology. By adjusting the casting process of the casting machine and the reduction amount and reduction distribution of the heavy reduction equipment, the effective control of the center quality of the cast slab is realized. However, the effect of improving segregation after the solidification end convex roll reduction process is not considered.
  • Chinese patent CN201611029498.X discloses a numerical simulation method for studying the center segregation behavior of continuous casting slabs. It divides the calculation area of the continuous casting slab flow field, and realizes the link between the multi-dimensional model data through interface data conversion, and realizes the calculation of the center segregation behavior of the continuous casting slab by using ANSYS and Fluent software.
  • this model cannot consider the influence of the deformation of the blank shell on the segregation behavior of the cast slab under the mechanical reduction of the solidification end.
  • the present invention discloses a method for predicting the segregation behavior of bloom convex rolls under continuous casting heavy reduction.
  • Quantitative calculation of the internal macro-segregation behavior of blooms under different casting and reduction process conditions during the implementation process, to clarify the reduction deformation during the convex roll reduction process The improvement mechanism of solidification segregation of blooms provides reliable theoretical support for achieving stable production of high-homogenous cast slabs.
  • a method for predicting segregation behavior under continuous casting of bloom convex rolls includes the following steps:
  • Step 1 Accurately describe the morphology of the bloom shell during continuous casting of blooms
  • Zone 1 mold and secondary cooling zone There are three zones, namely Zone 1 mold and secondary cooling zone, Zone 2 light reduction zone, Zone 3 convex roll heavy reduction zone, Zone 4 horizontal zone, which divide the casting flow into 5 subzones at the same time along the y direction;
  • y 1 (x,z), y 2 (x,z), y 3 (x,z), y 4 (x,z) are the heights in the y direction of each zone of the casting stream, mm;
  • x 0 , x 1 , x 2 , x 3 , and x 4 are the x-axis coordinates corresponding to the surface topography function of each section of the casting flow, mm;
  • z 0 , z 1 , z 2 , z 3 , z 4 , and z 5 are the casting flow respectively each sub-function corresponding to the region of the surface topography of the z-axis coordinate, mm;
  • T is the initial thickness of the blooms, mm;
  • r a S r a H and solidification were soft reduction process and the male roll weight reduction Lower process reduction, mm;
  • Step 2 Accurately describe the surface velocity of the bloom shell during continuous casting of bloom
  • Zone 1 can be deduced ⁇ 4
  • the formula for the surface velocity of the slab on the inner arc side of the cast slab along the x and y directions is as follows:
  • I the internal velocity of the cast slab along the x direction in Zone 1 ⁇ 4, m/min
  • I the internal velocity of the slab along the y direction in Zone 1 ⁇ 4, m/min
  • y 2 in (x,z) and y 3 in (x,z) are any node in the slab in Zone 2 and Zone 3 respectively The value in the y direction, mm;
  • Step 3 Multiphase solidification model coupling calculation process
  • i is the phase parameter in each transmission equation, representing liquid phase l, columnar crystal phase c and equiaxed crystal phase e;
  • f i is the volume fraction of each phase, %;
  • ⁇ i is the density of each phase, kg /m 3 ;
  • c i is the solute concentration of each phase, wt%;
  • Is the velocity of each phase, m/min;
  • H i is the enthalpy of each phase, J/mol;
  • C s , M s , D s , and H s are the solute transfer equation, mass transfer equation, momentum transfer equation, and heat transfer equation, respectively
  • the volume average multiphase solidification model coupling calculation is realized; the coupling implicit algorithm with high accuracy and convergence is adopted, and the convergence residual error is controlled below 10 -5 to obtain the continuous casting solidification end convex roller During the implementation of heavy reduction, different casting and reduction process conditions can improve the macro-segregation defects in blooms. Compared with the prior art, the present invention has the following beneficial technical effects:
  • the present invention proposes to be suitable for the implementation of the process of continuous casting solidification end convex roll reduction process, based on the slab shell morphology after the solidification end convex roll reduction, different casting and reduction
  • the quantitative calculation method of macro-segregation behavior in blooms under process conditions is helpful for high-speed, high-efficiency, and high-precision quantitative evaluation of the effects of different production processes on the improvement of macro-segregation in blooms, thereby providing excellent support for casting and reduction processes and related processes.
  • Equipment development provides quantitative data support. Through the calculation of the model, it is found that compared with the traditional soft reduction process, the bloom solidification end convex roll heavy reduction process can reduce the bloom center segregation degree from 1.18 to 1.10.
  • the present invention also fills the research gap in the calculation method of the macro-segregation inside the bloom during the convex rolling reduction process, and enriches the theoretical system of the continuous casting bloom solidification end weight reduction process.
  • Figure 1 is a schematic diagram of the division of continuous casting bloom casting flow calculation area
  • Figure 2 is a schematic diagram of the horizontal sub-areas of continuous casting blooms
  • Figure 3 shows the trend of shell thickness of continuous casting blooms
  • Figure 4 shows the calculation results of macro-segregation of continuous casting blooms
  • Figure 5 is a low-magnification photo of the longitudinal section of the cast slab produced by the flat roll light reduction process
  • Figure 6 is a low-magnification photo of the longitudinal section of the cast slab produced by the convex roll reduction process
  • Figure 7 shows the comparison of the segregation behavior measured under the flat roll light reduction process and the convex roll heavy reduction process.
  • Example 1 Prediction of macro segregation behavior during bloom reduction process:
  • the macro-segregation prediction of the convex roll reduction process is simulated and predicted, which is mainly divided into the following steps:
  • Step 1 Accurate description of slab shell morphology during bloom continuous casting
  • Figure 1 is a three-dimensional geometric model of the bloom convex roll reduction process established for this example.
  • the thickness of the bloom is 280mm and the width is 380mm.
  • the bloom in the geometric model is divided into a hexahedral mesh, the mesh size is 5mm 2 , and the number of meshes is 3,400,000.
  • the convex roller under the heavy pressure at the solidification end of the bloom is installed on the 6# stretch straightening machine, which is located 27.95m away from the mold.
  • the vertical area division parameters corresponding to the model in Fig. 1 are shown in Table 1
  • the horizontal subarea division parameters corresponding to the model in Fig. 2 are shown in Table 2.
  • Step 2 Accurate description of the surface velocity of the bloom shell during continuous casting of bloom
  • the accurate description of the surface velocity of the bloom shell during the bloom continuous casting process is realized by formulas (6) to (14).
  • the drawing speed is 0.72m/min.
  • Step 3 Coupling calculation of multiphase solidification model
  • the convergence residual is 10 -6 .
  • Step 4 Predict results of macro segregation under the weight of bloom convex roll
  • the macrosegregation simulation results of blooms calculated according to the model, as shown in Fig. 4 can obtain the segregation degree distribution trend along the y direction. It can be seen from the model prediction results that, compared with the traditional soft reduction process, the bloom solidification end convex roll heavy reduction process can reduce the bloom center segregation from 1.18 to 1.10.

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  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Continuous Casting (AREA)

Abstract

一种大方坯凸形辊连铸重压下偏析行为预测方法，先准确描述大方坯连铸过程坯壳形貌，然后准确描述大方坯连铸过程坯壳表面速度，最后进行多相凝固模型耦合计算。该预测方法是高速度、高效率、高精度的实现连铸凝固末端凸形辊重压下实施过程中不同浇铸、压下工艺条件下的大方坯内部宏观偏析行为定量计算，阐明了凸形辊重压下过程中压下变形对大方坯凝固偏析的改善机理，为实现高均质度铸坯的稳定生产提供了可靠的理论支撑。

Description

一种大方坯凸形辊连铸重压下偏析行为预测方法 技术领域
本发明属于钢铁冶金工业中的大方坯连铸生产领域，具体涉及一种大方坯凸形辊连铸重压下偏析行为预测方法。
背景技术
连铸大方坯内部宏观偏析缺陷作为典型的内部质量问题，且该缺陷不能通过轧制和后处理等手段有效去除，严重的影响最终轧材的机械性能。目前，连铸大方坯凝固末端凸形辊重压下技术是替代传统轻压下工艺的最为有效的技术手段之一。相比较传统的轻压下技术，大方坯凝固末端重压下技术能够通过较大的机械压下变形，有效的促进凝固前沿富集溶质的反向流动与二次分布，达到改善铸坯宏观偏析行为的工艺效果。同时，相比平辊重压下工艺，大方坯凝固末端凸辊重压下技术能够避开大方坯两侧已凝坯壳，显著降低辊坯接触抗力，在液压系统未整体升级条件下提升单辊压下量2.5倍以上，极大的提高压下力向铸坯中心的渗透效果，且能够进一步的促进凝固前沿富集溶质的反向传输，更好的改善宏观偏析行为。
鉴于大方坯凝固末端凸辊重压下技术在改善铸坯宏观偏析方面存在明显技术优势，该技术已得到许多研究者的重视，并开展了相关的科研工作。
中国专利CN201710948669.7公开了一种用于低圧缩比轧制的连铸坯生产方法。其在凝固末端采用凸辊重压下技术轧制，通过调整铸机的浇铸工艺与重压下设备的压下量及压下分配，实现对铸坯中心质量的有效控制。但是，未考虑实施凝固末端凸辊重压下工艺后的偏析改善效果。
中国专利CN201611029498.X公开了一种连铸坯中心偏析行为研究的数值模拟方法。其对连铸坯流场进行计算区域划分，并通过界面数据转换实现多维度模型数据之间的链接，利用ANSYS与Fluent软件实现了连铸坯中心偏析行为的计算。但是，该模型并不能考虑凝固末端机械压下作用下的坯壳变形对铸坯偏析行为的影响。
韩国浦项公司通过在2#大方坯连铸机凝固末端施加凸形辊(ISIJ International，Vol.52(2012)，No.7，pp.1266-1272)，使技术实施后的大方坯中心偏析评级从1.6降低为0.2，相比平辊压下显著的改善了大方坯内部的宏观偏析行为。但是该技术尚处于工业试验研究，并没有介绍凸形辊压下过程的大方坯偏析行为的定量预测。
目前，已有众多关于压下工艺及装备设计的相关技术专利，但凝固末端凸形辊压下过程铸坯宏观偏析行为的定量预测方法还鲜有报道。
发明内容
针对连铸大方坯凝固末端凸形辊压下过程宏观偏析行为定量预测方法上的研究不足，本发明公开了一种大方坯凸形辊连铸重压下偏析行为预测方法，目的是高速度、高效率、高精度的实现连铸凝固末端凸形辊重压下实施过程中不同浇铸、压下工艺条件下的大方坯内部宏观偏析行为定量计算，阐明凸形辊重压下过程中压下变形对大方坯凝固偏析的改善机理，为 实现高均质度铸坯的稳定生产提供可靠的理论支撑。
具体技术方案如下：
一种大方坯凸形辊连铸重压下偏析行为预测方法，包括如下步骤：
步骤1：准确描述大方坯连铸过程坯壳形貌
基于大方坯连铸过程中凝固末端轻压下与凸形辊重压下工艺，忽略铸坯坯壳的z向展宽，对铸坯的坯壳形貌进行准确描述将连铸铸流划分为4个分区，分别为Zone 1结晶器与二冷段、Zone 2轻压下段、Zone 3凸形辊重压下段、Zone 4水平段，将铸流沿y方向同时被划分为5个子区域；
各个分区内的y方向高度计算公式如下：
y 1(x,z)＝T,x＝x 0～x 1,z＝z 0～z 5  (1)
Figure PCTCN2019079025-appb-000001
Figure PCTCN2019079025-appb-000002
y 4(x,z)＝y 3(x 4,z),x＝x 3～x 4,z＝z 0～z 5  (4)
式中，y 1(x,z)、y 2(x,z)、y 3(x,z)、y 4(x,z)为铸流各个分区内的y方向高度，mm；x 0、x 1、x 2、x 3、x 4分别为铸流各段表面形貌函数对应的x轴坐标，mm；z 0、z 1、z 2、z 3、z 4、z 5分别为铸流内各子区域表面形貌函数对应的z轴坐标，mm；T为大方坯的初始厚度，mm；r a S和r a H分别为凝固末端轻压下工艺压下量和凸形辊重压下工艺压下量，mm；
对于Zone 4水平段，在凸形辊重压下工艺实施后，该区域内内沿y方向5个子区域内表面形貌的具体计算公式如下：
Figure PCTCN2019079025-appb-000003
式中，a 0、a 1、a 2、a 3、a 4分别为Zone 3凸形辊压下段内z 1～z 2侧弧线过渡区的高次多项式函数的辊型系数；b 0、b 1、b 2、b 3、b 4为Zone 3凸形辊压下段内z 4～z 5侧弧线过渡区的高次 多项式函数的辊型系数；n为Zone 3凸形辊压下段内中心凸形辊凸起段对应的压下厚度，mm；
步骤2：准确描述大方坯连铸过程坯壳表面速度
由于铸坯坯壳z向展宽被忽略，所以Zone 1～4内z轴方向的速度全部为0；根据式(1)～式(5)所示的坯壳表面形貌公式，可以推出Zone 1～4内沿x、y方向铸坯内弧侧的坯壳表面速度公式如下：
Figure PCTCN2019079025-appb-000004
Figure PCTCN2019079025-appb-000005
Figure PCTCN2019079025-appb-000006
Figure PCTCN2019079025-appb-000007
Figure PCTCN2019079025-appb-000008
式中，
Figure PCTCN2019079025-appb-000009
为Zone 1～4内沿x方向铸坯内弧侧的坯壳表面速度，m/min；
Figure PCTCN2019079025-appb-000010
为Zone 1～4内沿y方向铸坯内弧侧的坯壳表面速度，m/min；为了精准的表征大方坯凸辊重压下实施后铸坯内部的速度分布，其Zone 1～4 内沿x、y方向的铸坯内部速度公式如下：
Figure PCTCN2019079025-appb-000011
Figure PCTCN2019079025-appb-000012
Figure PCTCN2019079025-appb-000013
Figure PCTCN2019079025-appb-000014
式中，
Figure PCTCN2019079025-appb-000015
为Zone 1～4内沿x方向的铸坯内部速度，m/min；
Figure PCTCN2019079025-appb-000016
为Zone 1～4内沿y方向的铸坯内部速度，m/min；y 2 in(x,z)和y 3 in(x,z)分别为Zone 2和Zone 3区域铸坯内任一节点的y方向数值，mm；
步骤3：多相凝固模型耦合计算过程
在准确描述铸坯坯壳形貌及速度分布的基础上，建立体积平均多相凝固耦合计算模型，对凝固过程中液相、柱状晶相、等轴晶相的溶质传输方程、质量传输方程、动量传输方程、热量传输方程进行耦合计算；上述方程的具体表述形式如下：
Figure PCTCN2019079025-appb-000017
Figure PCTCN2019079025-appb-000018
Figure PCTCN2019079025-appb-000019
Figure PCTCN2019079025-appb-000020
式中，i为各传输方程中的相参数，分别代表液相l、柱状晶相c和等轴晶相e；f i为各相的体积分数，％；ρ i为各相的密度，kg/m 3；c i为各相的溶质浓度，wt％；
Figure PCTCN2019079025-appb-000021
为各相速度， m/min；H i为各相的焓，J/mol；C s、M s、D s、H s分别为溶质传输方程、质量传输方程、动量传输方程、热量传输方程的源项；
通过“相耦合Simple”算法，实现体积平均多相凝固模型的耦合计算；采用精度和收敛性高的耦合隐式算法，并控制收敛残差在10 -5以下，得到连铸凝固末端凸形辊重压下实施过程中不同浇铸、压下工艺条件对大方坯内部宏观偏析缺陷的改善作用规律。与现有技术相比，本发明具有如下有益技术效果：
本发明针对连铸大断面方坯，基于凝固末端凸形辊重压下后的坯壳形貌，提出了适用于连铸凝固末端凸形辊重压下工艺实施过程中，不同浇铸、压下工艺条件下的大方坯内部宏观偏析行为定量计算方法，有助于高速度、高效率、高精度的定量评估不同生产工艺对大方坯内部宏观偏析的改善效果，从而为浇铸、压下工艺及相关设备开发提供定量化的数据支撑。通过模型的计算，发现相比传统轻压下工艺，采用大方坯凝固末端凸形辊重压下工艺可以使大方坯中心偏析度由1.18降低到1.10。同时，通过实际检测铸坯断面的元素分布规律，验证了模拟计算结果的准确性，进一步定量说明了该模型有助于高速度、高效率、高精度的定量评估大方坯凝固末端的宏观偏析缺陷。此外，本发明也填补了凸形辊压下过程大方坯内部宏观偏析计算方法上的研究空白，丰富了连铸大方坯凝固末端重压下工艺理论体系。
附图说明
图1为连铸大方坯铸流计算区域划分示意图；
图2为连铸大方坯横向子区域划分示意图；
图3为连铸大方坯坯壳厚度变化趋势；
图4为连铸大方坯宏观偏析计算结果；
图5为平辊轻压下工艺生产的铸坯纵断面低倍照片；
图6为凸形辊重压下工艺生产的铸坯纵断面低倍照片；
图7为平辊轻压下与凸型辊重压下工艺下的偏析行为实测对比。
具体实施方式
下面结合附图和具体实施例对本发明进行详细说明，但本发明的保护范围不受实施例所限。
实施例1：大方坯压下过程宏观偏析行为预测：
结合现场的大方坯连铸机实际生产工艺，对凸形辊压下过程的宏观偏析进行模拟预测，主要分为以下步骤：
步骤1：大方坯连铸过程坯壳形貌的准确描述
图1为针对本例建立的大方坯凸形辊重压下过程三维几何模型。本例中，大方坯的厚度为280mm，宽度为380mm，几何模型中的大方坯采用6面体网格划分，网格尺寸为5mm 2，网格数量为3,400,000。大方坯凝固末端重压下凸形辊安装在6#拉矫机，位于距结晶器27.95m的位置上。结合现场生产实际，附图1中模型对应的纵向区域划分参数如表1所示，附图2 中模型对应的横向子区域划分参数如表2所示。
表1计算模型纵向区域划分
Figure PCTCN2019079025-appb-000022
表2计算模型横向子区域划分
Figure PCTCN2019079025-appb-000023
凝固末端轻压下工艺压下量r a S为2～13mm，凸形辊重压下工艺压下量r a H为9～15mm。在凸形辊横向辊身轮廓中，两侧过渡区内高次多项式函数的辊型系数如表3所示，n为30mm。
表3高次多项式函数的辊型系数
Figure PCTCN2019079025-appb-000024
步骤2：大方坯连铸过程坯壳表面速度的准确描述
在步骤1得到的大方坯凸形辊重压下过程的准确坯壳表面形貌的基础上，通过公式(6)～(14)实现对大方坯连铸过程坯壳表面速度的准确描述。其中拉坯速度为0.72m/min。
步骤3：多相凝固模型的耦合计算
采用“相耦合Simple”算法及精度和收敛性高的耦合隐式算法，收敛残差为10 -6。
步骤4：大方坯凸形辊重压下宏观偏析预测结果
采用该模型进行连铸大方坯凝固末端凸形辊重压下偏析行为的计算，可以得出图3中0.72m/min拉速下对应的坯壳厚度变化趋势。从坯壳厚度计算结果可以得出，凝固终点位于距结晶器弯月面28.32m处，处于6#拉矫机凸形辊位置(27.95m)之后，表明该位置处的凸形辊重压下可以有效的促进大方坯内部中心富集溶质熔体发生反向流动，进而改善偏析。
此外，根据模型计算的大方坯宏观偏析模拟结果，如图4所示，能够得到沿y方向的偏析度分布趋势。模型预测结果可以看出，相比传统轻压下工艺，采用大方坯凝固末端凸形辊重压下工艺可以使大方坯中心偏析度由1.18降低到1.10。
将大方坯凝固末端渐变曲率凸型辊投入使用，根据现场试验的铸坯低倍结果对比，图5中平辊轻压下工艺生产的铸坯纵断面中心位置存在着明显的中心宏观偏析行为，而图6凸形辊重压下工艺生产的铸坯纵断面中心位置的宏观偏析行为则较轻。由此可见，实施凸型辊重压下后，铸坯中心偏析改善效果明显。
为了定量表征实际生产中凸形辊重压下工艺实施后的宏观偏析改善程度，对图5和图6中的铸坯进行了横向的钻屑实验，并利用碳硫分析仪对钻屑进行了成分检测，结果如图7所示。可以看出，大方坯凝固末端凸形辊重压下工艺实施后，相比传统的平辊轻压下工艺，铸坯的中心偏析度可以由1.17降低到1.11。将图4中的模拟预测结果与图7的实际生产结果进行对比，验证了模拟计算结果的准确性，且进一步定量说明了大方坯凝固末端凸形辊重压下工艺可以有效的改善铸坯内部的宏观偏析缺陷。
以上所述的实施例仅为本发明较佳的具体实施方式，本发明的保护范围不限于此，任何熟悉本领域的技术人员在本发明披露的技术范围内，可显而易见地得到该技术方案的简单变化或等效替换，并应用于连铸板坯凸形辊凝固末端压下工艺中，均属于本发明的保护范围之内。

Claims (1)

  1. 一种大方坯凸形辊连铸重压下偏析行为预测方法，其特征在于，包括如下步骤：
    步骤1：准确描述大方坯连铸过程坯壳形貌
    基于大方坯连铸过程中凝固末端轻压下与凸形辊重压下工艺，忽略铸坯坯壳的z向展宽，对铸坯的坯壳形貌进行准确描述将连铸铸流划分为4个分区，分别为Zone 1结晶器与二冷段、Zone 2轻压下段、Zone 3凸形辊重压下段、Zone 4水平段，将铸流沿y方向同时被划分为5个子区域；
    各个分区内的y方向高度计算公式如下：
    y 1(x,z)＝T,x＝x 0～x 1,z＝z 0～z 5            (1)
    Figure PCTCN2019079025-appb-100001
    Figure PCTCN2019079025-appb-100002
    y 4(x,z)＝y 3(x 4,z),x＝x 3～x 4,z＝z 0～z 5           (4)
    式中，y 1(x,z)、y 2(x,z)、y 3(x,z)、y 4(x,z)为铸流各个分区内的y方向高度，mm；x 0、x 1、x 2、x 3、x 4分别为铸流各段表面形貌函数对应的x轴坐标，mm；z 0、z 1、z 2、z 3、z 4、z 5分别为铸流内各子区域表面形貌函数对应的z轴坐标，mm；T为大方坯的初始厚度，mm；r a S和r a H分别为凝固末端轻压下工艺压下量和凸形辊重压下工艺压下量，mm；
    对于Zone 4水平段，在凸形辊重压下工艺实施后，该区域内内沿y方向5个子区域内表面形貌的具体计算公式如下：
    Figure PCTCN2019079025-appb-100003
    式中，a 0、a 1、a 2、a 3、a 4分别为Zone 3凸形辊压下段内z 1～z 2侧弧线过渡区的高次多项式函数的辊型系数；b 0、b 1、b 2、b 3、b 4为Zone 3凸形辊压下段内z 4～z 5侧弧线过渡区的高次多项式函数的辊型系数；n为Zone 3凸形辊压下段内中心凸形辊凸起段对应的压下厚度，mm；
    步骤2：准确描述大方坯连铸过程坯壳表面速度
    由于铸坯坯壳z向展宽被忽略，所以Zone 1～4内z轴方向的速度全部为0；根据式(1)～式(5)所示的坯壳表面形貌公式，可以推出Zone 1～4内沿x、y方向铸坯内弧侧的坯壳表面速度公式如下：
    Figure PCTCN2019079025-appb-100004
    Figure PCTCN2019079025-appb-100005
    Figure PCTCN2019079025-appb-100006
    Figure PCTCN2019079025-appb-100007
    Figure PCTCN2019079025-appb-100008
    式中，
    Figure PCTCN2019079025-appb-100009
    为Zone 1～4内沿x方向铸坯内弧侧的坯壳表面速度，m/min；
    Figure PCTCN2019079025-appb-100010
    为Zone 1～4内沿y方向铸坯内弧侧的坯壳表面速度，m/min；为了精准的表征大方坯凸辊重压下实施后铸坯内部的速度分布，其Zone 1～4内沿x、y方向的铸坯内部速度公式如下：
    Figure PCTCN2019079025-appb-100011
    Figure PCTCN2019079025-appb-100012
    Figure PCTCN2019079025-appb-100013
    Figure PCTCN2019079025-appb-100014
    式中，
    Figure PCTCN2019079025-appb-100015
    为Zone 1～4内沿x方向的铸坯内部速度，m/min；
    Figure PCTCN2019079025-appb-100016
    为Zone 1～4内沿y方向的铸坯内部速度，m/min；y 2 in(x,z)和y 3 in(x,z)分别为Zone 2和Zone 3区域铸坯内任一节点的y方向数值，mm；
    步骤3：多相凝固模型耦合计算过程
    在准确描述铸坯坯壳形貌及速度分布的基础上，建立体积平均多相凝固耦合计算模型，对凝固过程中液相、柱状晶相、等轴晶相的溶质传输方程、质量传输方程、动量传输方程、热量传输方程进行耦合计算；上述方程的具体表述形式如下：
    Figure PCTCN2019079025-appb-100017
    Figure PCTCN2019079025-appb-100018
    Figure PCTCN2019079025-appb-100019
    Figure PCTCN2019079025-appb-100020
    式中，i为各传输方程中的相参数，分别代表液相l、柱状晶相c和等轴晶相e；f i为各相的体积分数，％；ρ i为各相的密度，kg/m 3；c i为各相的溶质浓度，wt％；
    Figure PCTCN2019079025-appb-100021
    为各相速度，m/min； H i为各相的焓，J/mol；C s、M s、D s、H s分别为溶质传输方程、质量传输方程、动量传输方程、热量传输方程的源项；
    通过“相耦合Simple”算法，实现体积平均多相凝固模型的耦合计算；采用精度和收敛性高的耦合隐式算法，并控制收敛残差在10 -5以下，得到连铸凝固末端凸形辊重压下实施过程中不同浇铸、压下工艺条件对大方坯内部宏观偏析缺陷的改善作用规律。
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