WO2020181575A1 - Prediction method for behavior of bloom continuous casting reduction segregation using convex roller - Google Patents

Prediction method for behavior of bloom continuous casting reduction segregation using convex roller 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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PCT/CN2019/079025
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祭程
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朱苗勇
李应焕
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东北大学
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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

A prediction method for the behavior of bloom continuous casting reduction segregation using a convex roller, involving: first, accurately describing the bloom shell morphology of a bloom continuous casting process; then, accurately describing the bloom shell surface speed of the bloom continuous casting process; and finally, carrying out a multiphase solidification model coupling calculation. The prediction method is high-speed, high-efficiency and high-precision, and achieves a quantitative calculation for bloom internal macro-segregation behavior under various casting and reduction process conditions in the process of implementing continuous casting solidification end convex roller heavy reduction; and clarifies a mechanism for improving bloom solidification and segregation using reduction deformation in a convex roller heavy reduction process; and provides reliable theoretical support for the stable production of high-homogeneity casting billets.

Description

一种大方坯凸形辊连铸重压下偏析行为预测方法A Method for Predicting Segregation Behavior under Continuous Casting of Bloom Convex Roll 技术领域Technical field
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。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.
背景技术Background technique
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。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. At present, 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. Compared with the traditional light reduction technology, 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. At the same time, compared with the flat roll reduction process, 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.
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。In view of the obvious technical advantages of the crown roll reduction technology at the solidification end of blooms in improving the macro-segregation of cast slabs, this technology has attracted the attention of many researchers and related scientific research work has been carried out.
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。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.
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。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. However, 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.
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。South Korea’s Pohang Company applied convex rolls (ISIJ International, Vol.52(2012), No.7, pp.1266-1272) to the solidification end of the 2# bloom continuous caster to segregate the center of the bloom after the technology was implemented. The rating was reduced from 1.6 to 0.2, which significantly improved the macro-segregation behavior inside the bloom compared to flat rolling. However, this technology is still in industrial experimental research, and it does not introduce quantitative prediction of bloom segregation behavior during convex roll reduction.
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。At present, there are many related technical patents on the reduction process and equipment design, but there are few reports on the quantitative prediction method of the macro-segregation behavior of the casting slab during the convex roll reduction process at the solidification end.
发明内容Summary of the invention
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。In view of the insufficient research on the quantitative prediction method of the macro-segregation behavior of the convex roll reduction process at the solidification end of continuous casting blooms, the present invention discloses a method for predicting the segregation behavior of bloom convex rolls under continuous casting heavy reduction. High-efficiency and high-precision realization of continuous casting solidification end convex roll weight 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.
具体技术方案如下：The specific technical solutions are as follows:
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：A method for predicting segregation behavior under continuous casting of bloom convex rolls includes the following steps:
步骤1：准确描述大方坯连铸过程坯壳形貌Step 1: Accurately describe the morphology of the bloom shell during continuous casting of blooms
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；Based on the soft reduction of the solidification end and the heavy reduction of the convex roll in the bloom continuous casting process, the z-direction expansion of the slab shell is ignored, and the slab shell morphology of the slab is accurately described. The continuous casting stream is divided into 4 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;
各个分区内的y方向高度计算公式如下：The calculation formula for the height in the y direction in each partition is as follows:
y 1(x,z)＝T,x＝x 0～x 1,z＝z 0～z 5  (1) y 1 (x,z)=T,x=x 0 ～x 1 , z=z 0 ～z 5 (1)
Figure PCTCN2019079025-appb-000001
Figure PCTCN2019079025-appb-000001
Figure PCTCN2019079025-appb-000002
Figure PCTCN2019079025-appb-000002
y 4(x,z)＝y 3(x 4,z),x＝x 3～x 4,z＝z 0～z 5  (4) 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； In the formula, 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;
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：For the Zone 4 horizontal section, after the process of under the pressure of the convex roller is implemented, the specific calculation formula of the inner surface topography of the 5 sub-regions along the y direction in the region is as follows:
Figure PCTCN2019079025-appb-000003
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； In the formula, a 0 , a 1 , a 2 , a 3 , and a 4 are the roll profile coefficients of the higher-order polynomial function of the arc transition zone on the side of z 1 to z 2 in the convex roll reduction section of Zone 3; b 0 , b 1 , b 2 , b 3 , and b 4 are the roll shape coefficients of the higher order polynomial function in the transition zone of the arc transition zone on the side of z 4 ～ z 5 in the convex roll reduction section of Zone 3; n is the roll reduction section of the convex roll reduction section of Zone 3 The corresponding reduction thickness of the convex section of the central convex roller, mm;
步骤2：准确描述大方坯连铸过程坯壳表面速度Step 2: Accurately describe the surface velocity of the bloom shell during continuous casting of bloom
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：Since the z-direction expansion of the slab shell is neglected, the speeds in the z-axis direction in Zone 1 to 4 are all 0; according to the surface morphology formula of the blank shell shown in equations (1) to (5), 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:
Figure PCTCN2019079025-appb-000004
Figure PCTCN2019079025-appb-000004
Figure PCTCN2019079025-appb-000005
Figure PCTCN2019079025-appb-000005
Figure PCTCN2019079025-appb-000006
Figure PCTCN2019079025-appb-000006
Figure PCTCN2019079025-appb-000007
Figure PCTCN2019079025-appb-000007
Figure PCTCN2019079025-appb-000008
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： Where
Figure PCTCN2019079025-appb-000009
Is the surface velocity of the slab shell on the inner arc side of the cast slab in the x direction in Zone 1～4, m/min;
Figure PCTCN2019079025-appb-000010
It is the surface velocity of the slab on the inner arc side of the cast slab in the y direction in Zone 1～4, m/min; in order to accurately characterize the velocity distribution inside the cast slab after the bloom convex roll is pressed, the velocity distribution in the zone 1～4 The formula for the internal velocity of the cast slab along the x and y directions is as follows:
Figure PCTCN2019079025-appb-000011
Figure PCTCN2019079025-appb-000011
Figure PCTCN2019079025-appb-000012
Figure PCTCN2019079025-appb-000012
Figure PCTCN2019079025-appb-000013
Figure PCTCN2019079025-appb-000013
Figure PCTCN2019079025-appb-000014
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； Where
Figure PCTCN2019079025-appb-000015
Is the internal velocity of the cast slab along the x direction in Zone 1～4, m/min;
Figure PCTCN2019079025-appb-000016
Is 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;
步骤3：多相凝固模型耦合计算过程Step 3: Multiphase solidification model coupling calculation process
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：On the basis of accurately describing the morphology and velocity distribution of the slab shell, a volume-average multiphase solidification coupling calculation model is established to calculate the solute transfer equation, mass transfer equation, and mass transfer equation of the liquid phase, columnar crystal phase, and equiaxed crystal phase during solidification. The momentum transfer equation and heat transfer equation are coupled to calculate; the specific expression form of the above equation is as follows:
Figure PCTCN2019079025-appb-000017
Figure PCTCN2019079025-appb-000017
Figure PCTCN2019079025-appb-000018
Figure PCTCN2019079025-appb-000018
Figure PCTCN2019079025-appb-000019
Figure PCTCN2019079025-appb-000019
Figure PCTCN2019079025-appb-000020
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； In the formula, 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, %; ρ i is the density of each phase, kg /m 3 ; c i is the solute concentration of each phase, wt%;
Figure PCTCN2019079025-appb-000021
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 Source term
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： Through the "phase coupling Simple" algorithm, 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:
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。Aiming at the continuous casting of large-section billets, 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. At the same time, through the actual detection of the element distribution law of the cast slab section, the accuracy of the simulation calculation results was verified, and the model was further quantitatively explained that the model is helpful for the high-speed, high-efficiency, and high-precision quantitative evaluation of macro-segregation defects at the solidification end of the bloom . In addition, 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.
附图说明Description of the drawings
图1为连铸大方坯铸流计算区域划分示意图；Figure 1 is a schematic diagram of the division of continuous casting bloom casting flow calculation area;
图2为连铸大方坯横向子区域划分示意图；Figure 2 is a schematic diagram of the horizontal sub-areas of continuous casting blooms;
图3为连铸大方坯坯壳厚度变化趋势；Figure 3 shows the trend of shell thickness of continuous casting blooms;
图4为连铸大方坯宏观偏析计算结果；Figure 4 shows the calculation results of macro-segregation of continuous casting blooms;
图5为平辊轻压下工艺生产的铸坯纵断面低倍照片；Figure 5 is a low-magnification photo of the longitudinal section of the cast slab produced by the flat roll light reduction process;
图6为凸形辊重压下工艺生产的铸坯纵断面低倍照片；Figure 6 is a low-magnification photo of the longitudinal section of the cast slab produced by the convex roll reduction process;
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。Figure 7 shows the comparison of the segregation behavior measured under the flat roll light reduction process and the convex roll heavy reduction process.
具体实施方式detailed description
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。The present invention will be described in detail below with reference to the drawings and specific embodiments, but the protection scope of the present invention is not limited by the embodiments.
实施例1：大方坯压下过程宏观偏析行为预测：Example 1: Prediction of macro segregation behavior during bloom reduction process:
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：Combined with the actual production process of the bloom caster on site, the macro-segregation prediction of the convex roll reduction process is simulated and predicted, which is mainly divided into the following steps:
步骤1：大方坯连铸过程坯壳形貌的准确描述Step 1: Accurate description of slab shell morphology during bloom continuous casting
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。 Figure 1 is a three-dimensional geometric model of the bloom convex roll reduction process established for this example. In 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. Combined with the actual production on site, the vertical area division parameters corresponding to the model in Fig. 1 are shown in Table 1, and the horizontal subarea division parameters corresponding to the model in Fig. 2 are shown in Table 2.
表1计算模型纵向区域划分Table 1 The longitudinal division of the calculation model
Figure PCTCN2019079025-appb-000022
Figure PCTCN2019079025-appb-000022
表2计算模型横向子区域划分Table 2 Horizontal sub-region division of calculation model
Figure PCTCN2019079025-appb-000023
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。 Solidification soft reduction process of reduction r a S 2 ~ 13mm, the convex roll reduction process r a H weight of 9 ~ 15mm. In the lateral profile of the convex roller, the roller profile coefficient of the high-order polynomial function in the transition area on both sides is shown in Table 3, and n is 30mm.
表3高次多项式函数的辊型系数Table 3 Roll shape coefficients of high-order polynomial functions
Figure PCTCN2019079025-appb-000024
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Step 2: Accurate description of the surface velocity of the bloom shell during continuous casting of bloom
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。On the basis of the accurate surface morphology of the bloom shell obtained by the convex roll reduction process in step 1, 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.
步骤3：多相凝固模型的耦合计算Step 3: Coupling calculation of multiphase solidification model
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。 Using the "phase coupling Simple" algorithm and the coupling implicit algorithm with high accuracy and convergence, the convergence residual is 10 -6 .
步骤4：大方坯凸形辊重压下宏观偏析预测结果Step 4: Predict results of macro segregation under the weight of bloom convex roll
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。Using this model to calculate the segregation behavior under the weight of the convex roll at the solidification end of continuous casting blooms, it is possible to obtain the corresponding trend of the thickness change of the blank shell under the pulling speed of 0.72m/min in Figure 3. From the calculation result of the blank shell thickness, it can be concluded that the solidification end point is located at 28.32m from the meniscus of the mold, behind the convex roll position (27.95m) of the 6# stretch straightening machine, indicating that the convex roll at this position is under heavy pressure It can effectively promote the reverse flow of the solute melt in the center of the bloom to improve the segregation.
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。In addition, 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.
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。Putting the convex roll with progressive curvature at the solidification end of the bloom into use, according to the comparison of the low magnification results of the cast slab in the field test, the center position of the longitudinal section of the cast slab produced by the flat roll soft reduction process in Figure 5 has obvious central macro-segregation behavior. However, the macro-segregation behavior at the center of the longitudinal section of the cast slab produced by the convex roll reduction process in Fig. 6 is lighter. It can be seen that the effect of improving the center segregation of the cast slab is obvious after the implementation of the convex roll reduction.
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。In order to quantitatively characterize the degree of improvement in macro segregation after the implementation of the convex roll reduction process in actual production, horizontal drill cuttings experiments were carried out on the cast blanks in Figs. 5 and 6, and the drill cuttings were measured by a carbon and sulfur analyzer. Component detection, the results are shown in Figure 7. It can be seen that the center segregation degree of the cast slab can be reduced from 1.17 to 1.11 after the heavy reduction process of the convex roll at the solidification end of the bloom is implemented, compared with the traditional flat roll light reduction process. The simulation prediction results in Fig. 4 are compared with the actual production results in Fig. 7 to verify the accuracy of the simulation calculation results, and further quantify that the convex roll reduction process at the solidification end of the bloom can effectively improve the inside of the cast slab. The macro-segregation defects.
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。The above-mentioned embodiments are only preferred specific implementations of the present invention, and the protection scope of the present invention is not limited thereto. Any person skilled in the art can clearly obtain the technical solution within the technical scope disclosed by the present invention. Simple changes or equivalent replacements and application to the solidification end reduction process of the convex roll of the continuous casting slab are all within the protection scope of the present invention.

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：A method for predicting segregation behavior under continuous casting of bloom convex rolls is characterized in that it comprises the following steps:
    步骤1：准确描述大方坯连铸过程坯壳形貌Step 1: Accurately describe the morphology of the bloom shell during continuous casting of blooms
    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；Based on the soft reduction of the solidification end and the heavy reduction of the convex roll in the bloom continuous casting process, the z-direction expansion of the slab shell is ignored, and the slab shell morphology of the slab is accurately described. The continuous casting stream is divided into 4 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;
    各个分区内的y方向高度计算公式如下：The calculation formula for the height in the y direction in each partition is as follows:
    y 1(x,z)＝T,x＝x 0～x 1,z＝z 0～z 5            (1) y 1 (x,z)=T,x=x 0 ～x 1 , z=z 0 ～z 5 (1)
    Figure PCTCN2019079025-appb-100001
    Figure PCTCN2019079025-appb-100001
    Figure PCTCN2019079025-appb-100002
    Figure PCTCN2019079025-appb-100002
    y 4(x,z)＝y 3(x 4,z),x＝x 3～x 4,z＝z 0～z 5           (4) 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； In the formula, 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;
    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：For the Zone 4 horizontal section, after the process of under the pressure of the convex roller is implemented, the specific calculation formula of the inner surface topography of the 5 sub-regions along the y direction in the region is as follows:
    Figure PCTCN2019079025-appb-100003
    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； In the formula, a 0 , a 1 , a 2 , a 3 , and a 4 are the roll profile coefficients of the higher-order polynomial function of the arc transition zone on the side of z 1 to z 2 in the convex roll reduction section of Zone 3; b 0 , b 1 , b 2 , b 3 , and b 4 are the roll shape coefficients of the higher order polynomial function in the transition zone of the arc transition zone on the side of z 4 ～ z 5 in the convex roll reduction section of Zone 3; n is the roll reduction section of the convex roll reduction section of Zone 3 The corresponding reduction thickness of the convex section of the central convex roller, mm;
    步骤2：准确描述大方坯连铸过程坯壳表面速度Step 2: Accurately describe the surface velocity of the bloom shell during continuous casting of bloom
    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：Since the z-direction widening of the slab shell is ignored, the speeds in the z-axis direction in Zone 1 to 4 are all 0; according to the surface morphology formulas of the blank shell shown in equations (1) to (5), 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:
    Figure PCTCN2019079025-appb-100004
    Figure PCTCN2019079025-appb-100004
    Figure PCTCN2019079025-appb-100005
    Figure PCTCN2019079025-appb-100005
    Figure PCTCN2019079025-appb-100006
    Figure PCTCN2019079025-appb-100006
    Figure PCTCN2019079025-appb-100007
    Figure PCTCN2019079025-appb-100007
    Figure PCTCN2019079025-appb-100008
    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：     Where
    Figure PCTCN2019079025-appb-100009
    Is the surface velocity of the slab shell on the inner arc side of the cast slab in the x direction in Zone 1～4, m/min;
    Figure PCTCN2019079025-appb-100010
    It is the surface velocity of the slab on the inner arc side of the cast slab in the y direction in Zone 1～4, m/min; in order to accurately characterize the velocity distribution inside the cast slab after the bloom convex roll is pressed, the velocity distribution in the zone 1～4 The formula for the internal velocity of the cast slab along the x and y directions is as follows:
    Figure PCTCN2019079025-appb-100011
    Figure PCTCN2019079025-appb-100011
    Figure PCTCN2019079025-appb-100012
    Figure PCTCN2019079025-appb-100012
    Figure PCTCN2019079025-appb-100013
    Figure PCTCN2019079025-appb-100013
    Figure PCTCN2019079025-appb-100014
    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；     Where
    Figure PCTCN2019079025-appb-100015
    Is the internal velocity of the cast slab along the x direction in Zone 1～4, m/min;
    Figure PCTCN2019079025-appb-100016
    Is 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;
    步骤3：多相凝固模型耦合计算过程Step 3: Multiphase solidification model coupling calculation process
    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：On the basis of accurately describing the morphology and velocity distribution of the slab shell, a volume-average multiphase solidification coupling calculation model is established to calculate the solute transfer equation, mass transfer equation, and mass transfer equation of the liquid phase, columnar crystal phase, and equiaxed crystal phase during solidification. The momentum transfer equation and heat transfer equation are coupled to calculate; the specific expression form of the above equation is as follows:
    Figure PCTCN2019079025-appb-100017
    Figure PCTCN2019079025-appb-100017
    Figure PCTCN2019079025-appb-100018
    Figure PCTCN2019079025-appb-100018
    Figure PCTCN2019079025-appb-100019
    Figure PCTCN2019079025-appb-100019
    Figure PCTCN2019079025-appb-100020
    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；     In the formula, 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, %; ρ i is the density of each phase, kg /m 3 ; c i is the solute concentration of each phase, wt%;
    Figure PCTCN2019079025-appb-100021
    Is the velocity of each phase, m/min; H i is the enthalpy of each phase, J/mol; C s , M s , D s , H s are the solute transfer equation, mass transfer equation, momentum transfer equation, and heat transfer equation, respectively Source term
    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。 Through the "phase coupling Simple" algorithm, 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.
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