JP2003001386A - Estimation method for temperature distribution, flow rate distribution and flow rate vector distribution inside continuous casting mold, and their visualization apparatus - Google Patents
Estimation method for temperature distribution, flow rate distribution and flow rate vector distribution inside continuous casting mold, and their visualization apparatusInfo
- Publication number
- JP2003001386A JP2003001386A JP2001178665A JP2001178665A JP2003001386A JP 2003001386 A JP2003001386 A JP 2003001386A JP 2001178665 A JP2001178665 A JP 2001178665A JP 2001178665 A JP2001178665 A JP 2001178665A JP 2003001386 A JP2003001386 A JP 2003001386A
- Authority
- JP
- Japan
- Prior art keywords
- temperature
- distribution
- continuous casting
- casting mold
- molten steel
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Links
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- Continuous Casting (AREA)
Abstract
Description
【０００１】[0001]
【発明の属する技術分野】本発明は、連続鋳造設備にお
ける温度分布、流速分布及び流速ベクトル分布の推定方
法及びその可視化装置に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for estimating a temperature distribution, a flow velocity distribution and a flow velocity vector distribution in a continuous casting facility and a visualization device therefor.
【０００２】[0002]
【従来の技術】従来より、連続鋳造における鋳片温度監
視装置が提案されている。図４に示すように、連続鋳造
設備における鋳型において、浸漬ノズル４から溶鋼２が
連続鋳造鋳型１に供給され、溶鋼２は連続鋳造鋳型１の
表面から抜熱されて凝固し、凝固シェル３を形成する。
この凝固シェル３はロール６により連続鋳造鋳型１の下
方から引き抜かれる。この凝固シェル３の厚さの分布、
介在物の分布、気泡の分布は鋳込まれた鋳片の品質に影
響する。このため従来、鋳片品質のモニターのため、鋳
型１の冷却銅板内部に熱電対５を設置し、鋳片温度を監
視する技術開発が行われている。この連続鋳造における
鋳片温度監視装置に関する技術は、例えば、特開平４−
３７４５８号公報（以下、「先行技術例１」という）に
信頼性の高いブレークアウト予知を行うため、時系列的
に鋳型温度をパターン化し、推移パターンが予め設定し
たパターンと一致したときにブレークアウトの発生を予
知する発明、特開平１−２６２０５０号公報（以下、
「先行技術例２」という）に溶鋼の偏流を検知を行なう
ため、鋳型長辺と短辺の左右対称位置の温度差あるいは
熱流量差および偏差をもとに溶鋼の偏流を検知する発明
が開示されている。図５は、先行技術例１による連続鋳
造における鋳片温度監視方法を示す図である。図１０は
先行技術例２による連続鋳造における鋳片温度監視方法
を示す図である。2. Description of the Related Art Conventionally, a slab temperature monitoring device in continuous casting has been proposed. As shown in FIG. 4, in the mold in the continuous casting facility, the molten steel 2 is supplied from the immersion nozzle 4 to the continuous casting mold 1, the molten steel 2 is removed from the surface of the continuous casting mold 1 and solidifies, and the solidified shell 3 is formed. Form.
The solidified shell 3 is pulled out from below the continuous casting mold 1 by the roll 6. The thickness distribution of this solidified shell 3,
The distribution of inclusions and the distribution of bubbles affect the quality of the cast slab. For this reason, conventionally, in order to monitor the quality of the slab, a thermocouple 5 is installed inside the cooled copper plate of the mold 1 to develop a technique for monitoring the slab temperature. A technique relating to a slab temperature monitoring device in this continuous casting is disclosed in, for example, Japanese Unexamined Patent Publication No.
In order to perform reliable breakout prediction in Japanese Patent No. 37458 (hereinafter referred to as "Prior Art Example 1"), the mold temperature is patterned in a time series, and the breakout occurs when the transition pattern matches a preset pattern. Invention for predicting the occurrence of the phenomenon, Japanese Patent Laid-Open No. 1-262050 (hereinafter,
In order to detect the drift of molten steel in "Prior Art Example 2", an invention is disclosed in which drift of molten steel is detected based on a temperature difference or a heat flow rate difference and deviation between left and right symmetrical positions of a long side and a short side of a mold. Has been done. FIG. 5: is a figure which shows the slab temperature monitoring method in continuous casting by the prior art example 1. As shown in FIG. FIG. 10: is a figure which shows the slab temperature monitoring method in continuous casting by the prior art example 2. As shown in FIG.
【０００３】[0003]
【発明が解決しようとする課題】しかしながら、先行技
術例１に開示された連続鋳造における温度を時系列でモ
ニターする方法にあっては、この温度モニターは、熱電
対設置位置においてのみ可能であり、熱電対を設置して
いない点でのモニターは困難であった。また図６に示す
ように時系列データを横軸を時間、縦軸を温度とするグ
ラフにした場合、ブレークアウトのような激しい温度変
化を示す現象に対しては温度変化のパターンを判別し検
知して警報を出すことは可能であるが、定常時において
も湯面変動などのため，温度変動が激しいことが頻発し
ており、微妙な変化が起こっていたとしても判別するこ
とは困難であった。先行技術例２に開示された連続鋳造
における温度を時系列でモニターする方法にあっても、
この温度モニターは、熱電対設置位置においてのみ可能
であり、熱電対を設置していない点でのモニターは困難
であった。また、鋳片の縦割れやコーナー割れを起こす
ような激しい温度変化を示す現象に対しては温度変化の
パターンを判別し検知して警報を出すことは可能である
が、定常時における微妙な変化を判別することは困難で
あった。However, in the method of monitoring the temperature in continuous casting disclosed in Prior Art Example 1 in time series, this temperature monitoring is possible only at the thermocouple installation position, Monitoring was difficult because no thermocouple was installed. Further, as shown in FIG. 6, when the time-series data is plotted as a graph in which the horizontal axis represents time and the vertical axis represents temperature, a pattern of temperature change is detected and detected for a phenomenon such as a breakout showing a drastic temperature change. Although it is possible to issue an alarm by making a warning, temperature fluctuations frequently occur due to fluctuations in the molten metal level even in the steady state, and it is difficult to determine even slight changes. It was Even in the method for monitoring the temperature in continuous casting disclosed in Prior Art Example 2 in time series,
This temperature monitoring is possible only at the position where the thermocouple is installed, and it is difficult to monitor it because no thermocouple is installed. In addition, it is possible to detect the temperature change pattern and issue an alarm for a phenomenon that shows a severe temperature change such as vertical cracking or corner cracking of the slab. Was difficult to determine.
【０００４】溶鋼流速の推定に関しては、従来の流動セ
ンシング方法では熱電対５の設置位置（ｉ，ｊ）とその
点の温度Ｔ（ｉ，ｊ）の関数として次式（１）により流
速Ｕの絶対値（スカラー値）｜Ｕ｜が得られた。
｜Ｕ（ｉ，ｊ）｜＝ｇ（Ｔ（ｉ，ｊ））
＝ν/d/Pr(dq/0.048/λ/(T(i,j)−Tw))1.25・・・（１）
詳しくは、大中逸雄著「コンピュータ伝熱・凝固解析入
門」（丸善１９８５年）の３３６〜３３７頁記載から容
易に得られるように、熱電対温度Ｔ（ｉ，ｊ）（℃）、
流速の絶対値｜Ｕ（ｉ，ｊ）｜（メートル毎秒）、熱伝
達率ｈ（ワット毎平方メートル毎ケルビン）、冷却水温
度Ｔｗ（℃）、抜熱量ｑ（ワット毎平方メートル）、代
表長さｄ（メートル）、動粘性係数ν（平方メートル毎
秒）、熱伝導率λ（ワット毎メートル毎ケルビン）、ヌ
ッセルト数Ｎｕ［−］、レイノルズ数Ｒｅ［−］、プラ
ンドル数Ｐｒ［−］には次式（２）の関係があり、式変
形で式（１）が得られる。
Ｎｕ＝ｆ（Ｒｅ，Ｐｒ）
Ｎｕ＝ｈｄ／λ
Ｒｅ＝｜Ｕ（Ｘｉ，Ｙｉ）｜ｄ／ν ・・・（２）
ｈ＝ｑ／（Ｔｉ−Ｔｗ）
従来法でこれらの式を用いたとしても熱電対の設置位置
５以外では流速Ｕの絶対値が得られず、また熱電対の設
置位置５においても流速の方向を示す流速ベクトルは得
られなかった。さらに計測点を増加させることは費用が
かかるため精度を向上させることは困難であるという問
題があった。本発明は、上記課題に鑑み、連続鋳造設備
において、安価で、既設の熱電対により鋳型内全域の温
度分布や溶鋼流速ベクトル分布の推定ができ、ブレーク
アウトのような激しい温度変化を示す現象だけでなく定
常時の微妙な変化を判別できる方法及び装置を提供する
ことを目的とする。Regarding the estimation of the molten steel flow velocity, according to the conventional flow sensing method, the flow velocity U is calculated by the following equation (1) as a function of the installation position (i, j) of the thermocouple 5 and the temperature T (i, j) at that point. The absolute value (scalar value) | U | was obtained. | U (i, j) | = g (T (i, j)) = ν / d / Pr (dq / 0.048 / λ / (T (i, j) -Tw)) 1.25 (1) Details Is a thermocouple temperature T (i, j) (° C.), as easily obtained from “Introduction to Computer Heat Transfer and Solidification Analysis” by Maruzen 1985 by Itsuo Ohnaka.
Absolute value of flow velocity | U (i, j) | (meter / sec), heat transfer rate h (watt / square meter Kelvin), cooling water temperature Tw (° C), heat removal amount q (watt / square meter), representative length d (Meter), kinematic viscosity coefficient ν (square meter per second), thermal conductivity λ (watt per meter per kelvin), Nusselt number Nu [−], Reynolds number Re [−], and Prandle number Pr [−] are as follows. There is a relation of (2), and the formula (1) is obtained by modifying the formula. Nu = f (Re, Pr) Nu = hd / λ Re = | U (Xi, Yi) | d / ν (2) h = q / (Ti-Tw) These formulas were used in the conventional method. However, the absolute value of the flow velocity U was not obtained at positions other than the thermocouple installation position 5, and the flow velocity vector indicating the direction of the flow velocity was not obtained at the thermocouple installation position 5 as well. Furthermore, increasing the number of measurement points is expensive, and it is difficult to improve accuracy. In view of the above problems, the present invention is a continuous casting facility, is inexpensive, and can estimate the temperature distribution and molten steel flow velocity vector distribution in the entire mold by an existing thermocouple, and only a phenomenon that shows a severe temperature change such as breakout. It is an object of the present invention to provide a method and a device that can determine a subtle change in a steady state.
【０００５】[0005]
【課題を解決するための手段】本発明者は、連続鋳造設
備において、安価で、既設の熱電対により鋳型内全域の
温度分布や溶鋼流速ベクトル分布の推定ができ、ブレー
クアウトのような激しい温度変化を示す現象だけでなく
定常時の微妙な変化を判別できる方法について鋭意検討
を重ねた結果、連続鋳造鋳型内に設置した２以上の温度
計測器から得られた時系列データを用いて、各計測時間
で鋳型内の温度計測器が設置されていない領域まで含め
た温度分布を内挿あるいは外挿して推定し、画面に表示
し、溶鋼凝固面での液体の熱伝達と溶鋼凝固面での液体
流速の絶対値の関係式、抜熱量と温度計測器の関係式に
代入して、溶鋼凝固面全域の流速絶対値分布を推定し、
画面に表示し、流速絶対値分布データを、連続した２つ
の時間断面で比較し、運動学的条件を用いて流速ベクト
ルを推定し、画面に表示することにより、安価で、均一
冷却に悪影響を及ぼさないで鋳型内全域の時系列流動分
布推定ができることを見いだした。Means for Solving the Problems In the continuous casting equipment, the inventor of the present invention is capable of estimating the temperature distribution in the entire mold and the molten steel flow velocity vector distribution at a low cost in the continuous casting equipment by using an existing thermocouple, and thus, at a severe temperature such as breakout. As a result of intensive studies on a method that can distinguish not only a phenomenon indicating a change but also a subtle change in a steady state, as a result of using time series data obtained from two or more temperature measuring instruments installed in a continuous casting mold, Estimate the temperature distribution including the region where the temperature measuring device is not installed in the mold by the measurement time by interpolating or extrapolating it, display it on the screen, and transfer the liquid heat on the molten steel solidification surface and the molten steel solidification surface. Substituting into the relational expression of the absolute value of the liquid flow velocity and the relational expression of the heat removal amount and the temperature measuring device, the absolute value of the flow velocity over the molten steel solidification surface is estimated
Displaying on the screen, comparing absolute velocity distribution data on two consecutive time sections, estimating the velocity vector using kinematic conditions, and displaying it on the screen are inexpensive and adversely affect uniform cooling. It was found that it is possible to estimate the time-series flow distribution in the entire mold without affecting it.
【０００６】本発明は以上の知見に基づいてなされたも
のであって、その要旨とするところは、
（１）連続鋳造鋳型内に設置した２以上の温度計測器か
ら得られた時系列データを内挿又は外挿して用いて、鋳
型内の温度計測器が設置されていない領域における温度
分布を推定し、連続鋳造鋳型内の温度分布を時系列で画
面に表示することを特徴とする連続鋳造鋳型内の温度分
布の推定方法。
（２）前記（１）の推定方法から得られた連続鋳造鋳型
内の温度分布データと、溶鋼凝固面での溶鋼の熱伝達
率、溶鋼の熱伝導率、溶鋼の動粘性係数及び冷却水温
度、抜熱量に基づいて鋳型内溶鋼の流速絶対値分布を推
定し、連続鋳造鋳型内の溶鋼の流速絶対値分布を時系列
で画面に表示することを特徴とする溶鋼凝固面流速分布
の推定方法。
（３）前記（１）記載の推定方法から得られた連続鋳造
鋳型内の温度分布データの鋳造方向及び鋳造直角方向に
おける差分と、前記（２）の推定方法から得られた流速
絶対値分布データの連続した２つの時間における差分に
基づいて、運動学的条件を用いて流速ベクトルを推定
し、連続鋳造鋳型内の溶鋼の流速ベクトル分布を時系列
で画面に表示することを特徴とする連続鋳造鋳型内の溶
鋼凝固面流速ベクトル分布の推定方法。
（４）連続鋳造鋳型内に設置した２以上の温度計測手段
と、前記温度計測手段から得られた時系列データを内挿
又は外挿して、鋳型内の温度計測器が設置されていない
領域の温度を推定する温度推定手段と、前記温度推定手
段で推定した連続鋳造鋳型内の温度分布を時系列で画面
に表示する表示手段を有することを特徴とする連続鋳造
鋳型内の可視化装置。
（５）更に、前記温度推定手段で推定した連続鋳造鋳型
内の温度分布データと、溶鋼凝固面での溶鋼の熱伝達
率、溶鋼の熱伝導率、溶鋼の動粘性係数、抜熱量及び冷
却水温度に基づいて鋳型内溶鋼の流速絶対値分布を推定
する流速絶対値推定手段を有し、前記表示手段は連続鋳
造鋳型内の溶鋼の流速絶対値分布を時系列で画面に表示
する機能を有することを特徴とする前記（４）記載の連
続鋳造鋳型内の可視化装置。
（６）更に、前記前記温度推定手段で推定した連続鋳造
鋳型内の温度分布データの鋳造方向及び鋳造直角方向に
おける差分と，前記温度推定手段で推定した流速絶対値
分布データの連続した２つの時間における差分に基づい
て、運動学的条件を用いて流速ベクトルを推定する流速
推定手段を有し、前記表示手段は連続鋳造鋳型内の溶鋼
の流速ベクトル分布を時系列で画面に表示する機能を有
することを特徴とする前記（５）記載の連続鋳造鋳型内
の可視化装置。にある。The present invention has been made on the basis of the above findings, and the gist thereof is as follows. (1) Time series data obtained from two or more temperature measuring instruments installed in a continuous casting mold. Using the interpolated or extrapolated to estimate the temperature distribution in the region where the temperature measuring device is not installed in the mold, continuous casting characterized by displaying the temperature distribution in the continuous casting mold on the screen in time series A method for estimating the temperature distribution in the mold. (2) Temperature distribution data in the continuous casting mold obtained from the estimation method of (1), heat transfer coefficient of molten steel on the solidified surface of molten steel, thermal conductivity of molten steel, kinematic viscosity coefficient of molten steel, and cooling water temperature , Estimating the absolute flow velocity distribution of molten steel in the mold based on the amount of heat removed, and displaying the absolute flow velocity distribution of molten steel in the continuous casting mold on the screen in time series . (3) Differences in temperature distribution data in the continuous casting mold in the casting direction and casting orthogonal direction obtained by the estimation method described in (1) above, and absolute flow velocity distribution data obtained by the estimation method in (2) above. Based on the difference between two consecutive times, the flow velocity vector is estimated using kinematic conditions, and the flow velocity vector distribution of the molten steel in the continuous casting mold is displayed on the screen in time series. Estimation method of flow velocity vector distribution of molten steel solidification surface in mold. (4) Two or more temperature measuring means installed in the continuous casting mold and time series data obtained from the temperature measuring means are interpolated or extrapolated to obtain a temperature measuring device in a region where the temperature measuring device is not installed. A visualization device in a continuous casting mold, comprising: a temperature estimating means for estimating a temperature; and a display means for displaying the temperature distribution in the continuous casting mold estimated by the temperature estimating means on a screen in time series. (5) Further, the temperature distribution data in the continuous casting mold estimated by the temperature estimating means, the heat transfer coefficient of the molten steel on the molten steel solidification surface, the thermal conductivity of the molten steel, the kinematic viscosity coefficient of the molten steel, the heat removal amount and the cooling water. It has a flow velocity absolute value estimation means for estimating the flow velocity absolute value distribution of the molten steel in the mold based on the temperature, and the display means has a function of displaying the flow velocity absolute value distribution of the molten steel in the continuous casting mold on the screen in time series. The visualization device in the continuous casting mold according to (4) above. (6) Furthermore, the difference between the temperature distribution data in the continuous casting mold in the casting direction and the casting orthogonal direction estimated by the temperature estimating means, and two consecutive time periods of the flow velocity absolute value distribution data estimated by the temperature estimating means. Based on the difference in, has a flow velocity estimation means for estimating the flow velocity vector using kinematic conditions, the display means has a function of displaying the flow velocity vector distribution of the molten steel in the continuous casting mold on the screen in time series The visualization device in the continuous casting mold according to (5) above. It is in.
【０００７】[0007]
【発明の実施の形態】連続鋳造設備においてブレークア
ウトのような激しい温度変化を示す現象だけでなく定常
時の微妙な変化を判別できる連続鋳造鋳型の温度、鋳型
内溶鋼凝固面の流速分布および流速ベクトル分布の推定
方法、表示方法及びその可視化装置について図面を見な
がら説明する。本発明においては、連続鋳造鋳型内に設
置した２以上の温度計測器から得られた時系列データを
用いて、各計測時間で鋳型内の温度計測器が設置されて
いない領域における温度分布を内挿あるいは外挿して推
定し、推定した温度分布を時系列で画面に表示すること
で、定常時の微妙な変化を判別できる。特に、鋳型と相
似な図形に対応する座標における温度の階調を色の階調
で擬似的な分布表現とすることが好ましい。BEST MODE FOR CARRYING OUT THE INVENTION The temperature of a continuous casting mold, the flow velocity distribution and flow velocity of the solidified surface of molten steel in the mold, which can discriminate not only a phenomenon showing a drastic temperature change such as breakout in a continuous casting facility but also a subtle change in a steady state. A vector distribution estimation method, a display method, and a visualization device therefor will be described with reference to the drawings. In the present invention, by using time series data obtained from two or more temperature measuring instruments installed in the continuous casting mold, the temperature distribution in the region where the temperature measuring instrument is not installed in the mold is calculated at each measurement time. By estimating by extrapolation or extrapolation and displaying the estimated temperature distribution on the screen in time series, it is possible to determine a subtle change in the steady state. In particular, it is preferable that the gradation of the temperature at the coordinates corresponding to the figure similar to the template is expressed in the pseudo distribution by the gradation of the color.
【０００８】温度分布を内挿あるいは外挿し表示する方
法を図９を用いて説明する。図９に示すように、鋳型に
対応する表示面を格子状の領域に分割し、それぞれの領
域に温度計測器が設置されている点と温度計測器が設置
されていない点を設定し、温度計測器が設置されている
点の温度を用いて温度計測器が設置されていない点の温
度を内挿あるいは外挿する。内挿あるいは外挿方法は線
形性などを仮定して行なうことができる。温度計測点は
例えば（２，２）、（２，４）、（４，２）、（４，
４）と番号つけできる。これらの点の温度をＴ（２，
２） Ｔ（２，４） Ｔ（４，２）Ｔ（４，４）とする
と、例えばＴ（３，３）の値はそれらの値を（４）式を
用いて内挿することにより推定できる。A method of displaying the temperature distribution by interpolation or extrapolation will be described with reference to FIG. As shown in FIG. 9, the display surface corresponding to the mold is divided into grid-shaped regions, and the points where the temperature measuring device is installed and the points where the temperature measuring device is not installed are set in each region to determine the temperature. Using the temperature at the point where the measuring instrument is installed, the temperature at the point where the temperature measuring instrument is not installed is interpolated or extrapolated. The interpolation or extrapolation method can be performed assuming linearity. The temperature measurement points are, for example, (2,2), (2,4), (4,2), (4
You can number it as 4). Let the temperature at these points be T (2,
2) T (2,4) T (4,2) T (4,4), for example, the value of T (3,3) is estimated by interpolating those values using equation (4). it can.
【数１】
また、Ｔ（２，１）の値であれば、（５）式を用いて外
挿することにより推定できる。[Equation 1] Further, the value of T (2,1) can be estimated by extrapolation using the equation (5).
【数２】
異常検知のため温度分布を時系列で観察するが、人間が
理解しやすくために、計測あるいは推定した温度の価を
色の階調で擬似的に表現して当該領域の色として表示す
ることが好ましい。[Equation 2] The temperature distribution is observed in time series to detect anomalies, but in order to make it easier for humans to understand, it is possible to display the measured or estimated temperature value as a color gradation in a pseudo manner. preferable.
【０００９】図７は本発明の鋳型温度分布の推定表示例
である。図７では鋳型の長辺２面と短片２面を横方向に
展開し、図６の時系列データを用いて温度が高い部分を
赤、温度が低い部分を青で表示させており、従来の図６
の時系列データと比較して人間が理解することが可能で
あると言える。溶鋼凝固面流速分布の推定方法は式
（１）、（２）を用いて行ない、時系列で画面に表示す
る。表示方法は温度分布と同様に流速絶対値分布を鋳型
と相似な図形上の対応する座標における色の階調で擬似
的な分布表現とすることが好ましい。FIG. 7 shows an example of an estimated display of the mold temperature distribution of the present invention. In FIG. 7, two long sides and two short sides of the mold are developed in the lateral direction, and the high temperature portion is displayed in red and the low temperature portion is displayed in blue using the time series data of FIG. Figure 6
It can be said that it can be understood by humans in comparison with the time series data of. The molten steel solidification surface flow velocity distribution is estimated using the equations (1) and (2) and displayed in time series on the screen. As for the display method, it is preferable that the flow velocity absolute value distribution is represented in a pseudo distribution by gradations of colors at corresponding coordinates on a figure similar to the template, like the temperature distribution.
【００１０】溶鋼凝固面流速ベクトル分布は運動学的条
件を用いて推定する。時系列の各点において物理量の移
流方程式である（３）式を運動学的条件として満たす移
流速度（Ｕ，Ｖ）を求めることができる。The molten steel solidification surface velocity vector distribution is estimated using kinematic conditions. At each point in the time series, the advection velocity (U, V) that satisfies equation (3), which is the advection equation of the physical quantity, as a kinematic condition can be obtained.
【数３】
物理量φとしては温度Tと（１）、（２）式から得られ
た流速の絶対値を用いる。また物理量φの時間微分∂φ
/∂ｔは物理量φとして用いた温度Tあるいは（１）、
（２）式から得られた流速の絶対値の時系列データの２
点の値を用いて差分近似し、物理量φの空間微分∂φ/
∂ｘ、∂φ/∂ｙは図９の格子点を用いて差分近似す
る。式（３）は移流速度（Ｕ，Ｖ）を変数とする連立方
程式であり、容易に解くことが可能である。この移流速
度（Ｕ，Ｖ）を推定流速ベクトルとみなし時系列で画面
に表示する。温度分布と同様に流速絶対値分布を鋳型と
相似な図形上の対応する座標における色の階調で擬似的
に分布表現することが好ましい。[Equation 3] As the physical quantity φ, the temperature T and the absolute value of the flow velocity obtained from the equations (1) and (2) are used. Also, the time derivative of the physical quantity φ ∂φ
/ ∂t is the temperature T used as the physical quantity φ or (1),
2 of time series data of absolute value of flow velocity obtained from equation (2)
Difference approximation is performed using the value of the point, and the spatial derivative of the physical quantity φ ∂φ /
∂x and ∂φ / ∂y are subjected to difference approximation using the grid points in FIG. Equation (3) is a simultaneous equation with the advection velocity (U, V) as a variable, and can be easily solved. This advection velocity (U, V) is regarded as an estimated flow velocity vector and displayed on the screen in time series. Like the temperature distribution, it is preferable that the absolute value of the flow velocity is represented in a pseudo distribution by the gradation of color at corresponding coordinates on a figure similar to the template.
【００１１】式（３）の物理量φとしてＴと｜Ｕ（ｉ，
ｊ）｜を用いる方法以外に、物理量φとして同一物理量
を、連続した２つの時間断面について（３）式を連立さ
せ、流速ベクトルを推定することもできる。また、式
（３）とｕ２＋ｖ２＝｜Ｕ（ｉ，ｊ）｜２を連立させて
解くこともできる。未知数U,Vに対し方程式数が多いの
で最小２乗法を用いて誤差が最小となるようにすること
が望ましい。図１〜図３に本発明の可視化装置による推
定方法の流れ図の例を示す。As the physical quantity φ of the equation (3), T and | U (i,
In addition to the method using j) |, it is also possible to estimate the flow velocity vector by using the same physical quantity as the physical quantity φ and simultaneously using equations (3) for two continuous time sections. Further, the equation (3) and u 2 + v 2 = | U (i, j) | 2 can be simultaneous and solved. Since there are many equations for the unknowns U and V, it is desirable to use the least squares method to minimize the error. 1 to 3 show examples of flow charts of the estimation method by the visualization device of the present invention.
【００１２】[0012]
【実施例】以下、本発明の実施例について具体的に説明
する。図４において、連続鋳造設備における内のり幅
（長辺）１ｍ、厚さ（短辺）３０ｃｍ、メニスカス〜鋳
型下端までの距離（深さ）６０ｃｍの鋳型１において、
直径２０ｃｍ２孔の浸漬ノズル４から溶鋼２が連続鋳造
鋳型１に供給され、連続鋳造が行われている。溶鋼２は
連続鋳造鋳型１の表面から抜熱され、凝固し凝固シェル
３を形成する。この凝固シェル３はロール６により引き
抜き速度毎分１ｍで連続鋳造鋳型１の下方から引き抜か
れる。この凝固シェル３の厚さの分布、介在物の分布、
気泡の分布は鋳込まれた鋳片の品質に影響する。このた
め従来から、鋳片品質のモニターのため、鋳型１の長辺
冷却銅板内部に熱電対５を鋳込み面から５ｃｍの深さに
左端からそれぞれ３０ｃｍ，５０ｃｍ，８０ｃｍ，上端
から３０ｃｍ，５０ｃｍの位置に片面６個ずつ設置し、
短辺中央に上端から３０ｃｍ，５０ｃｍの位置に設置し
温度を時系列でモニターした。温度表示画面を図９のよ
うに横格子間隔Δｘ＝１０ｃｍ、縦格子間隔Δｙ＝１０
ｃｍ、の格子状にとると、図１に示した流れ図に従い、
（４），（５）式により鋳型内温度分布を推定できる。EXAMPLES Examples of the present invention will be specifically described below. In FIG. 4, in the continuous casting facility, in the mold 1 having an inner width (long side) of 1 m, a thickness (short side) of 30 cm, and a distance (depth) of the meniscus to the lower end of the mold of 60 cm,
Molten steel 2 is supplied from a dipping nozzle 4 having a diameter of 20 cm2 to a continuous casting mold 1 to perform continuous casting. Molten steel 2 is removed from the surface of continuous casting mold 1 and solidifies to form solidified shell 3. The solidified shell 3 is pulled out from below the continuous casting mold 1 by a roll 6 at a pulling rate of 1 m / min. The thickness distribution of the solidified shell 3, the distribution of inclusions,
The distribution of bubbles affects the quality of the cast slab. Therefore, conventionally, in order to monitor the quality of the slab, the thermocouple 5 is placed inside the long-side cooling copper plate of the mold 1 at a depth of 5 cm from the casting surface at positions 30 cm, 50 cm, 80 cm from the left end, and 30 cm, 50 cm from the upper end, respectively. Place 6 on each side,
It was installed at the positions of 30 cm and 50 cm from the upper end in the center of the short side, and the temperature was monitored in time series. As shown in FIG. 9, the temperature display screen has a horizontal lattice spacing Δx = 10 cm and a vertical lattice spacing Δy = 10.
When taking a grid of cm, according to the flow chart shown in FIG.
The temperature distribution in the mold can be estimated by the equations (4) and (5).
【００１３】図７に鋳型温度分布の推定表示例を示し
た。図７では鋳型の長辺２面と短片２面を横方向に展開
し、図６の時系列データを用いて計算させ、温度２５０
℃を赤、温度５０℃を青で表示させており（図７上部に
赤の温度分布が生じている）、従来の図６の時系列デー
タと比較して人間が理解することが可能であると言え
る。FIG. 7 shows an example of estimated display of the mold temperature distribution. In FIG. 7, the two long sides and the two short sides of the mold are developed in the lateral direction, and calculation is performed using the time series data of FIG.
C. is displayed in red and temperature 50.degree. C. is displayed in blue (red temperature distribution occurs at the upper part of FIG. 7), which can be understood by humans in comparison with the conventional time series data of FIG. Can be said.
【００１４】次に、図３に従い（１）〜（３）式を用い
て、鋳型内の流速ベクトルを推定した。図８において溶
鋼凝固面流速ベクトル分布の推定表示例を示した。図８
においても鋳型の長辺２面と短片２面を横方向に展開
し、図６の時系列データを用いて計算させ流速絶対値で
０．１ｍ／ｓを赤（図８上部の２段目、３段目に赤側の
温度のベクトル分布が生じている）、０．０ｍ／ｓを青
で表示させており、従来の図６の時系列データと比較し
て人間が理解することが可能であると言える。Next, the flow velocity vector in the mold was estimated using the equations (1) to (3) according to FIG. FIG. 8 shows an example of the estimated display of the molten steel solidification surface velocity vector distribution. Figure 8
Also, the two long sides of the mold and the two short sides of the mold are developed in the lateral direction, and calculation is performed using the time series data of FIG. 6, and the absolute value of the flow velocity is 0.1 m / s in red (the second step at the top of FIG. 8, The vector distribution of the temperature on the red side is generated in the third row), and 0.0 m / s is displayed in blue, which can be understood by humans in comparison with the conventional time series data of FIG. It can be said that there is.
【００１５】[0015]
【発明の効果】本発明により、連続鋳造鋳型内に設置し
た温度計測器から得られた時系列データを用いて、各計
測時間で鋳型内の温度計測器が設置されていない領域ま
で含めた温度分布を内挿あるいは外挿して推定し、推定
した温度分布を鋳型と相似な図形上の対応する座標にお
ける色の階調で擬似的に分布表現して時系列で画面に表
示しているため、また、推定した流速ベクトル分布を鋳
型と相似な図形上の対応する座標におけるベクトルで擬
似的に分布表現して時系列で画面に表示しているため、
ブレークアウトのような激しい温度変化を示す現象だけ
でなく定常時の微妙な変化を判別することができる。According to the present invention, by using time series data obtained from the temperature measuring device installed in the continuous casting mold, the temperature including the region in the mold where the temperature measuring device is not installed is measured at each measurement time. The distribution is estimated by interpolation or extrapolation, and the estimated temperature distribution is displayed on the screen in chronological order as a pseudo distribution representation with the color gradation at the corresponding coordinates on the figure similar to the template. In addition, since the estimated flow velocity vector distribution is displayed in a time series on the screen in a pseudo distribution representation with a vector at corresponding coordinates on a figure similar to the template,
It is possible to discriminate not only a phenomenon such as breakout that shows a drastic temperature change but also a subtle change in a steady state.
【図１】本発明の鋳型温度分布の推定方法、表示方法の
流れ図である。FIG. 1 is a flow chart of an estimation method and a display method of a mold temperature distribution of the present invention.
【図２】本発明の溶鋼凝固面流速分布の推定方法、表示
方法の流れ図である。FIG. 2 is a flow chart of an estimation method and a display method of a molten steel solidification surface flow velocity distribution according to the present invention.
【図３】本発明の溶鋼凝固面流速ベクトル分布の推定方
法、表示方法の流れ図である。FIG. 3 is a flow chart of a method for estimating and displaying a molten steel solidification surface flow velocity vector distribution according to the present invention.
【図４】一般的な連続鋳造と連続鋳造における鋳片温度
監視の図である。FIG. 4 is a diagram of general continuous casting and slab temperature monitoring in continuous casting.
【図５】従来の連続鋳造における鋳片温度監視方法の図
である。FIG. 5 is a diagram of a conventional slab temperature monitoring method in continuous casting.
【図６】時系列データを従来のグラフで表示した例であ
る。FIG. 6 is an example of displaying time series data in a conventional graph.
【図７】本発明の鋳型温度分布の推定表示例である。FIG. 7 is an estimated display example of the mold temperature distribution of the present invention.
【図８】本発明の溶鋼凝固面流速ベクトル分布の推定表
示例である。FIG. 8 is an estimated display example of a molten steel solidification surface flow velocity vector distribution of the present invention.
【図９】本発明の温度分布の推定方法の説明図である。FIG. 9 is an explanatory diagram of a temperature distribution estimation method of the present invention.
【図10】従来の連続鋳造における溶鋼偏流監視方法の図
である。FIG. 10 is a view of a conventional molten steel drift monitoring method in continuous casting.
１ 連続鋳造鋳型 ２ 溶鋼 ３ 凝固シェル ４ 浸漬ノズル ５ 熱電対 ６ 引き抜きロール ７ 温度表示器 ８ 熱電対設置点 ９ 熱電対が設置されていない点 １０ 温度表示領域 1 Continuous casting mold 2 Molten steel 3 solidification shell 4 immersion nozzle 5 thermocouple 6 Drawing roll 7 Temperature indicator 8 thermocouple installation points 9 Points where no thermocouple is installed 10 Temperature display area
Claims (6)
測器から得られた時系列データを内挿又は外挿して、鋳
型内の温度計測器が設置されていない領域の温度を推定
し、連続鋳造鋳型内の温度分布を時系列で画面に表示す
ることを特徴とする連続鋳造鋳型内の温度分布の推定方
法。1. A method for estimating the temperature of a region in a mold where a temperature measuring instrument is not installed by interpolating or extrapolating time series data obtained from two or more temperature measuring instruments installed in a continuous casting mold. , A method for estimating the temperature distribution in a continuous casting mold, characterized by displaying the temperature distribution in the continuous casting mold on a screen in time series.
鋳造鋳型内の温度分布データと、溶鋼凝固面での溶鋼の
熱伝達率、溶鋼の熱伝導率、溶鋼の動粘性係数及び冷却
水温度、抜熱量に基づいて鋳型内溶鋼の流速絶対値分布
を推定し、連続鋳造鋳型内の溶鋼の流速絶対値分布を時
系列で画面に表示することを特徴とする連続鋳造鋳型内
の流速分布の推定方法。2. The temperature distribution data in the continuous casting mold obtained by the estimation method according to claim 1, the heat transfer coefficient of the molten steel on the molten steel solidifying surface, the thermal conductivity of the molten steel, the kinematic viscosity coefficient of the molten steel, and the cooling. Flow velocity in continuous casting mold characterized by estimating absolute velocity distribution of molten steel in mold based on water temperature and heat removal amount and displaying absolute value distribution of molten steel velocity in continuous casting mold on the screen in time series Distribution estimation method.
鋳造鋳型内の温度分布データの鋳造方向及び鋳造直角方
向における差分と，請求項２記載の推定方法から得られ
た流速絶対値分布データの連続した２つの時間における
差分に基づいて、運動学的条件を用いて流速ベクトルを
推定し、連続鋳造鋳型内の溶鋼の流速ベクトル分布を時
系列で画面に表示することを特徴とする連続鋳造鋳型内
の流速ベクトル分布の推定方法。3. The difference between the temperature distribution data in the continuous casting mold in the casting direction and the direction perpendicular to the casting obtained by the estimation method according to claim 1, and the absolute flow velocity value distribution obtained by the estimation method according to claim 2. Based on the difference between two consecutive times of data, the flow velocity vector is estimated using kinematic conditions, and the flow velocity vector distribution of molten steel in the continuous casting mold is displayed on the screen in time series. A method for estimating the flow velocity vector distribution in a casting mold.
測手段と、 前記温度計測手段から得られた時系列データを内挿又は
外挿して、鋳型内の温度計測器が設置されていない領域
の温度を推定する温度推定手段と、 前記温度推定手段で推定した連続鋳造鋳型内の温度分布
を時系列で画面に表示する表示手段を有することを特徴
とする連続鋳造鋳型内の可視化装置。4. Two or more temperature measuring means installed in a continuous casting mold, and time series data obtained from the temperature measuring means are interpolated or extrapolated so that a temperature measuring device in the mold is not installed. A visualization device in a continuous casting mold, comprising: temperature estimation means for estimating the temperature of the region; and display means for displaying the temperature distribution in the continuous casting mold estimated by the temperature estimation means on the screen in a time series.
造鋳型内の温度分布データと、溶鋼凝固面での溶鋼の熱
伝達率、溶鋼の熱伝導率、溶鋼の動粘性係数及び冷却水
温度抜熱量に基づいて鋳型内溶鋼の流速絶対値分布を推
定する流速絶対値推定手段を有し、 前記表示手段は連続鋳造鋳型内の溶鋼の流速絶対値分布
を時系列で画面に表示する機能を有することを特徴とす
る請求項４記載の連続鋳造鋳型内の可視化装置。5. The temperature distribution data in the continuous casting mold estimated by the temperature estimating means, the heat transfer coefficient of the molten steel on the molten steel solidification surface, the thermal conductivity of the molten steel, the kinematic viscosity coefficient of the molten steel, and the cooling water temperature. It has a flow velocity absolute value estimating means for estimating the flow velocity absolute value distribution of the molten steel in the mold based on the amount of heat removed, and the display means has a function of displaying the flow velocity absolute value distribution of the molten steel in the continuous casting mold on the screen in time series. The apparatus for visualizing in a continuous casting mold according to claim 4, which has.
造鋳型内の温度分布データの鋳造方向及び鋳造直角方向
における差分と，前記温度推定手段で推定した流速絶対
値分布データの連続した２つの時間における差分に基づ
いて、運動学的条件を用いて流速ベクトルを推定する流
速推定手段を有し、 前記表示手段は連続鋳造鋳型内の溶鋼の流速ベクトル分
布を時系列で画面に表示する機能を有することを特徴と
する請求項５記載の連続鋳造鋳型内の可視化装置。6. A continuous two of the difference between the temperature distribution data in the continuous casting mold estimated by the temperature estimating means in the casting direction and the casting orthogonal direction and the absolute value of the flow velocity distribution data estimated by the temperature estimating means. Based on the difference in time, it has a flow velocity estimation means for estimating the flow velocity vector using kinematic conditions, and the display means has a function of displaying the flow velocity vector distribution of the molten steel in the continuous casting mold on the screen in time series. The visualization device in the continuous casting mold according to claim 5, characterized in that it has.
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| JP2006231375A (en) * | 2005-02-25 | 2006-09-07 | Jfe Steel Kk | Method for continuously casting steel |
| CN100402190C (en) * | 2005-11-03 | 2008-07-16 | 上海梅山钢铁股份有限公司 | Method and equipment for monitoring and analyzing temperature of target on surface of continuous casting billet |
| CN102169025A (en) * | 2010-12-30 | 2011-08-31 | 中冶连铸技术工程股份有限公司 | Method for drawing high-speed temperature cloud picture |
| CN103317105A (en) * | 2012-03-18 | 2013-09-25 | 昆山华盟电子精密模具有限公司 | Mold |
| CN103433448A (en) * | 2013-08-14 | 2013-12-11 | 东北大学 | Method for determining heat flux density of continuous casting crystallizer based on flux film and air gap dynamic distribution |
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