JP2009241139A - Forecasting method for molten steel temperature within tundish, and management method - Google Patents
Forecasting method for molten steel temperature within tundish, and management method Download PDFInfo
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Abstract
Description
この発明は、取鍋から流入する溶鋼を鋳型に連続的に注入して鋼片を製造する連続鋳造プロセスに用いるタンディッシュ内の溶鋼温度の予測方法および(鋳型流出部の温度の)管理方法に関する。 The present invention relates to a method for predicting a molten steel temperature in a tundish used in a continuous casting process for continuously injecting molten steel flowing from a ladle into a mold to produce a steel slab, and a management method (for the temperature of the mold outlet). .
鋼の連続鋳造において、鋳型へ注入する溶鋼温度は、高過ぎると耐火物の溶損による湯漏れや凝固殻の薄い部分の割れが開口して内部の溶鋼が漏れるブレークアウト、低過ぎると注入ノズルの詰まりや開口不良などの操業トラブルが発生する。また、溶鋼温度の変動により凝固するまでの時間が目標時間からずれることは鋼片（鋳片）品質の低下を招くため、適切な溶鋼温度に管理することが重要となっている。このため、従来から、タンディッシュ内の溶鋼温度を測定し、この溶鋼温度が高い場合には鋳造速度を低下させ、低い場合には鋳造中止や加熱装置を用いて溶鋼温度を上昇させるなどの操業上の対応が行なわれている。 In continuous casting of steel, the temperature of the molten steel injected into the mold is too high, causing a leak of molten metal due to refractory erosion, or a breakout in which a thin portion of the solidified shell opens and leaks the molten steel inside. Operation troubles such as clogging or defective opening occur. Moreover, since the time until solidification due to fluctuations in the molten steel temperature deviates from the target time, the quality of the steel slab (slab) is deteriorated, so it is important to manage the molten steel temperature at an appropriate temperature. Therefore, conventionally, the temperature of the molten steel in the tundish is measured, and when the molten steel temperature is high, the casting speed is reduced, and when the molten steel temperature is low, the casting steel is stopped or the molten steel temperature is increased by using a heating device. The above response has been made.
一方、例えば、特許文献１では、連続鋳造工程の前工程の脱ガス精錬終了時の溶鋼温度を決定するにあたり、過去の実績操業データベースの中から、前記溶鋼温度を決定すべきチャージと類似のチャージを複数選定し、この複数選定した類似のチャージに基づいて、例えば、溶鋼の液相線温度、脱ガス精錬終了時の溶鋼温度、脱ガス処理終了から連続鋳造開始までの時間を要因項目として、タンディッシュ内における溶鋼温度の回帰式を作成して、この回帰式に基づいて、目標タンディッシュ内温度から、決定すべきチャージの脱ガス精錬終了時の溶鋼温度を決定することにより、タンディッシュ内の溶鋼の過熱度のバラツキを小さくする方法が開示されている。また、特許文献２では、出鋼後取鍋内に収容された溶鋼温度の推移を非定常伝熱計算により求め、この取鍋内溶鋼温度推移を用いてタンディッシュ内溶鋼温度推移を同様にして求め、タンディシュ内溶鋼温度推移において最低となる温度と溶鋼凝固温度との差（過熱度）が所定の値となるように前工程の最適な最終溶鋼温度を決定するようにしたタンデ゛ィッシュ内溶鋼温度の管理方法が開示されている。
しかし、取鍋からタンディッシュへの毎回における最初の湯溜時や、操業途中の取鍋交換時、鋳造速度の変化時などでは、図１０に模式的に示すように、取鍋から流入する溶鋼量と鋳型へ流出する溶鋼量が同一ではないため、タンディュシュ内の溶鋼の容量が変化する、すなわち湯面が変動する非定常操業となる。このような非定常操業の場合には、タンディッシュ内の溶鋼流動は複雑に変動し、それに伴って、溶鋼の温度分布も変化するため、タンディッシュ内の溶鋼容量が一定の定常時のみを想定したモデル式では精度のよい温度予測が困難となる。とくに、取鍋からタンディッシュへの毎回における初期の湯溜後の注入ノズルの開口時に開口不良が発生すると、このノズル部への酸素の吹き込みなど開口作業が別途発生すると、溶鋼の汚染や次のチャージのスケジュールへの影響が大きいため、開口不良は防止する必要がある。この開口不良は、タンディッシュ底部の鋳型への流出部の溶鋼が凝固して流れなくなるのが原因であるが、タンディッシュ底部の鋳型への流出部の温度を定常的に測定することは困難であるため、従来、タンディッシュ内溶鋼の通常の計測部の温度から鋳型流出部の温度を推測するしか術がなかった。このような鋳型流出部における溶鋼凝固現象を予測するために、熱流動シミュレーションなどの計算技術（手段）が存在するが、タンディッシュ内における溶鋼湯面変動を伴う非定常状態の流体についての計算には、数時間乃至数日にわたる規模の計算時間を要し、前記計算技術は、即座に判断が必要な実操業には使用することができない。 However, at the time of the first sump from the ladle to the tundish, when the ladle is changed during operation, or when the casting speed is changed, as shown schematically in FIG. Since the amount and the amount of molten steel flowing out to the mold are not the same, the capacity of the molten steel in the tundish changes , that is, the molten steel surface varies. In such an unsteady operation, the molten steel flow in the tundish fluctuates in a complicated manner, and the temperature distribution of the molten steel also changes accordingly.Therefore, it is assumed only when the molten steel capacity in the tundish is constant. With this model formula, accurate temperature prediction becomes difficult. In particular, if an opening failure occurs during the opening of the injection nozzle after the initial hot water pool from the ladle to the tundish, if an opening operation such as blowing oxygen into the nozzle occurs separately, contamination of the molten steel and the following Since the influence on the charging schedule is large, it is necessary to prevent the opening failure. This defective opening is caused by the molten steel at the outflow to the mold at the bottom of the tundish becoming solidified and not flowing, but it is difficult to constantly measure the temperature of the outflow to the mold at the bottom of the tundish. For this reason, conventionally, there has been no choice but to estimate the temperature of the mold outflow part from the temperature of the normal measurement part of the molten steel in the tundish. In order to predict the molten steel solidification phenomenon in the mold outflow part, there is a calculation technique (means) such as thermal flow simulation, but it is used for the calculation of unsteady state fluid with molten steel surface fluctuation in the tundish. Requires several hours to several days of calculation time, and the calculation technique cannot be used for actual operations that require immediate judgment.
この発明は、上記のような問題点に鑑みなされたもので、その課題は、タンディュシュ内の溶鋼の容量が変化する非定常操業の場合でも、注入ノズルの開口不良や湯漏れ、ブレークアウトなどの操業上のトラブルおよび鋳片（鋼片）品質の低下を防止するため、非定常操業時のタンディッシュ内の溶鋼温度分布をリアルタイムに予測できる温度予測方法および溶鋼温度の管理方法を提供することである。 The present invention has been made in view of the above-mentioned problems, and the problem is that even in the case of unsteady operation in which the capacity of molten steel in the tundish changes, such as poor injection nozzle opening, hot water leakage, breakout, etc. By providing a temperature prediction method and a molten steel temperature management method that can predict in real time the molten steel temperature distribution in the tundish during unsteady operations in order to prevent operational troubles and slab (steel) quality degradation. is there.
前記の課題を解決するために、この発明では以下の構成を採用したのである。 In order to solve the above problems, the present invention employs the following configuration.
請求項１に係るタンディッシュ内の溶鋼温度の予測方法は、取鍋からタンディッシュに流入する溶鋼流量Qinput（m3/s）が、タンディッシュから鋳型へ流出する溶鋼流量Qout(m3/s)よりも多く（Ｑin>Qout）、この鋳型へ流出する溶鋼流量Qout(m3/s)がタンディッシュへの湯溜時のゼロ（Qout(m3/s)＝０）の場合を含んだ、タンディッシュ内の溶鋼量Vtd（m3）が増加する非定常状態におけるタンディッシュ内の溶鋼温度の予測方法であって、前記タンディッシュ内の溶鋼を、取鍋流入部から鋳型流出部へ溶鋼の流れ方向に対して複数の要素に分割し、かつ、少なくとも鋳型への流出部の要素をタンディッシュの深さ方向に対して複数の要素に分割して、隣り合う要素間で、上流側の要素から下流側の要素へ流入する溶鋼流量を、分配係数を用いて決定して、前記各要素間の熱収支計算を行なうことにより、前記タンディッシュ内の溶鋼各要素の温度を算出することを特徴とする。
The method for predicting the molten steel temperature in the tundish according to
図１（ａ）および（ｂ）は、容量が６０tonのタンディッシュ１の湯溜時（Ｑｏｕｔ＝０）および定常時の溶鋼流動を模式的に示したものである。図２は、タンディッシ１内の鋳型流出部の深さ方向に異なる温度計測位置における実測温度の時間変化を示したものである。湯溜時（Ｑｏｕｔ＝０）の初期（タンディッシュ１内への溶鋼の充満率が３０％程度の時）では、流入部２から注入された溶鋼は、流出部３の底部３ａまで直送されるが、図１（ａ）に示したように、流出部３の近傍に溶鋼が溜まりだすと、注入流は溶鋼表面のみを流れて流出部の上部に達するが、流出部３の底部には新たな溶鋼が流れこんでいない。そのため流出部３ａ底部の溶鋼は周囲の耐火物に熱を奪われて温度は低下する。流出部の上部と下部の温度差は、図２に示すように、湯溜時間すなわちタンディッシュ内への溶鋼流入開始からの時間が長くなるにしたがって大きくなる。流出部３で鋳型への注入ノズルが開口すると、開口当初は、流出部３の底部３ａの、温度が低下した溶鋼が鋳型へ流出し、続いて流出部３の上部の温度の高い溶鋼が流出する。その後、タンディッシュの中央部の温度が低下した溶鋼が、取鍋からの注入流に押し出されて流出し、平均滞留時間（容量/流出量）以上が経過すると、図１（ｂ）に示したように、タンディッシュ内は均一な定常流れとなる。これらの溶鋼流動のシミュレーションおよび実測結果から、流出部３の底部３ａ（計測位置（１）（図２））よりも上部の計測位置（２）〜（４）（図２）での測温値は、流出部３の底部（計測位置（１）の測温値よりも高い温度を示しており、タンディッシュ内上部の溶鋼の測温値だけでは、注入ノズルの開口判断に必要な流出部３近傍の温度を予測することは困難である。したがって、上述のように、タンディッシュ内への溶鋼の流れを、
（１）溶鋼の流出部は（タンディッシュの）高さ（深さ）方向に複数の要素分割を行なう、（２）湯面（溶鋼表面）が上昇しているときには（流入量Ｑｉｎ＞流出量Ｑｏｕｔ）では、溶鋼量が増加している流出部の湯面近傍の要素に定常時よりも集中して上流側から溶鋼が流入するように、非定常状態の分配係数（αｈ）を用いる、
（３）湯面の上昇が停止する（流入量Ｑｉｎ＝流出量Ｑｏｕｔ）と、前記非定常状態の分配係数を、予め求めた定常状態の分配係数（αｔ）に切替える、
ことにより、湯溜過程などの非定常時非定常時の溶鋼の温度分布、とくに流出部における温度分布を精度よく予測することが可能となる。
FIGS. 1 (a) and 1 (b) schematically show the flow of molten steel in a tundish 1 having a capacity of 60 tons at the time of hot water accumulation (Qout = 0) and steady state. FIG. 2 shows the time change of the measured temperature at different temperature measurement positions in the depth direction of the mold outflow part in the tundish 1. At the initial stage of hot water accumulation (Qout = 0) (when the filling rate of the molten steel into the tundish 1 is about 30%), the molten steel injected from the
(1) The outflow part of the molten steel is divided into a plurality of elements in the height (depth) direction of (tundish). (2) When the molten metal surface (molten steel surface) is rising (inflow amount Qin> outflow amount) Qout) uses a non-steady state distribution coefficient (αh) so that the molten steel flows from the upstream side more concentrated in the elements near the molten metal surface of the outflow part where the molten steel amount is increasing than in the steady state.
(3) When the rise of the hot water surface stops (inflow amount Qin = outflow amount Qout), the distribution coefficient in the unsteady state is switched to the distribution coefficient (αt) obtained in advance.
This makes it possible to accurately predict the temperature distribution of the molten steel during unsteady times such as a hot water process, particularly the temperature distribution in the outflow part.
請求項２に係るタンディッシュ内の溶鋼温度の予測方法は、前記流出部のタンディッシュの深さ方向に対して複数分割した流出部の各要素Ｂｄ（ｉ）へ、その上流側の要素Ｂｕ（ｊ）から流入する溶鋼流量の前記流出部の各要素Ｂｄ（ｉ）についての総和をＱｄｉｎ（ｉ）としたとき、前記流出部の各要素Ｂｄ（ｉ）に対する非定常状態での分配係数αｈ（ｉ）を、前記Ｑｄｉｎ（ｉ）と、以下の（１）式により算出される上流側の（各）要素Ｂｕ（ｊ）から流出部における各要素Ｂｄ（ｉ）へ流入する総溶鋼流量Ｑｕｏｕｔｓとを用いて、以下の（２）式により算出し、前記非定常状態での分配係数αｈ（ｉ）と、予め求めておいた、タンディッシュ内の溶鋼量Vtd（m3）が一定である（流入量Ｑｉｎ＝流出量Ｑｏｕｔ）定常状態での分配係数αｔ（ｉ）から、以下の（３）式により流量調整係数β（ｉ）を算出し、この流量調整係数β（ｉ）と前記定常状態の分配係数αｔ（ｉ）とから、以下の（４）式により算出した非定常状態の分配係数αｈ（ｉ）を用いて前記流出部の各要素Ｂｄ（ｉ）に対して溶鋼流量を分配することを特徴とする。
Ｑｕｏｕｔｓ＝ＳＵＭ（Ｑｕｏｕｔ（ｋ）、ｋ＝１ ｔｏ Ｍ） --------（１）
αｈ（ｉ）＝Ｑｄｉｎ（ｉ）／Ｑｕｏｕｔｓ ------------------（２）
β（ｉ）＝αｈ（ｉ）／αｔ（ｉ） ------------------------（３）
αｈ（ｉ）＝β（ｉ）×αｔ（ｉ） ------------------------（４）
ここで、Ｑｕｏｕｔ（ｋ）は、上流側の各要素Ｂｕ（ｋ）から流出部における各要素Ｂｄ（ｉ）へ流入する溶鋼流量であり、ｉ、ｋは要素番号を、Ｍは要素Ｂｕ（ｋ）の分割数である。また、ＳＵＭは、合計（Σ）を表す。
According to the method for predicting the molten steel temperature in the tundish according to
Quouts = SUM (Quout (k), k = 1 to M) -------- (1)
αh (i) = Qdin (i) / Quouts ------------------ (2)
β (i) = αh (i) / αt (i) ------------------------ (3)
αh (i) = β (i) × αt (i) ----------------------- (4)
Here, Quout (k) is a molten steel flow rate flowing from each upstream element Bu (k) to each element Bd (i) in the outflow part, i and k are element numbers, and M is an element Bu (k ). SUM represents the total (Σ).
このようにすれば、非定常時の分配係数αｈ（ｉ）を、流量調整係数β（ｉ）を用いて上記（４）式で求めることができ、上流側の要素から流出部の各要素Ｂｄ（ｉ）へ流入する溶鋼流量を簡便かつ精度よく算出することができる。それによって、溶鋼の各要素間の熱収支計算の精度も向上し、非定常状態における流出部の各要素の温度を正しく予測することができる。なお、流量調整係数β（ｉ）は、熱流動解析手段により算出した非定常および定常状態の分配係数αｈ（ｉ）およびαｔ（ｉ）を用いて式（３）から予め算出することができ、例えば、各タンディッシュの形状ごとに、プロセス制御用計算機の記憶装置に格納しておくことができる。この流量調整係数β（ｉ）を介して、非定常分配係数αｈ（ｉ）を算出することにより、実機での実績データの多い定常状態における分割要素を使用できるなど、非定常分配係数の算出が簡便になり、かつ温度予測精度を向上させることが可能となる。 In this way, the distribution coefficient αh (i) at the time of non-steady state can be obtained by the above equation (4) using the flow rate adjustment coefficient β (i), and each element Bd in the outflow portion from the upstream element. The flow rate of the molten steel flowing into (i) can be calculated easily and accurately. Thereby, the accuracy of the heat balance calculation between each element of the molten steel is also improved, and the temperature of each element in the outflow portion in the unsteady state can be correctly predicted. The flow rate adjustment coefficient β (i) can be calculated in advance from the equation (3) using the unsteady and steady state distribution coefficients αh (i) and αt (i) calculated by the thermal fluid analysis means. For example, each tundish shape can be stored in a storage device of a process control computer. By calculating the unsteady distribution coefficient αh (i) through the flow rate adjustment coefficient β (i), the unsteady distribution coefficient can be calculated, for example, by using a division element in a steady state with a lot of actual data in an actual machine. It becomes simple and it becomes possible to improve temperature prediction accuracy.
請求項３に係るタンディッシュ内の溶鋼温度の予測方法は、前記調整係数β（ｉ）の範囲が、溶鋼表面が上昇しつつある流出部の要素Ｂｄ（ｉ）（ｉ＝Ｌ）については、以下の（４）式により、それ以外の要素Ｂｄ（ｉ）（ｉ≠Ｌ）については、以下の（５）式により、それぞれ表された範囲にあることを特徴とする。
１／αｔ（Ｌ）≧β（Ｌ）≧ＳＵＭ（αｔ（ｋ）、ｋ＝Ｌ ｔｏ Ｎ）／αｔ（Ｌ） ----（５）
１≧β（ｉ）≧０ --------------------------------------------（６）
ここで、ｉ、ｋは要素番号を、Ｎは、流出部における分割した要素Ｂｄ（ｉ）の数を、Ｌは、溶鋼表面が上昇しつつある要素Ｂｄ（ｉ）の番号を意味し、αｔ（Ｌ）およびαｔ（ｋ）は、要素Ｂｄ（Ｌ）およびＢｄ（ｋ）に対する定常状態での分配係数を示す。また、ＳＵＭは、合計（Σ）を表す。
In the method for predicting the molten steel temperature in the tundish according to
1 / αt (L) ≧ β (L) ≧ SUM (αt (k), k = L to N) / αt (L) ---- (5)
1 ≧ β (i) ≧ 0 ------------------------------------------ -(6)
Here, i and k are element numbers, N is the number of divided elements Bd (i) in the outflow part, L is the number of element Bd (i) where the molten steel surface is rising, αt (L) and αt (k) indicate the distribution coefficients in the steady state for the elements Bd (L) and Bd (k). SUM represents the total (Σ).
上記（４）式で、左辺の１／αｔ（Ｌ）は、定常状態において、タンディッシュに注入される溶鋼流量Ｑｉｎｐｕｔ（ｍ３／ｓ）が、すべて要素Ｂｄ（Ｌ）に流入する場合を示しており、流量修正係数β（ｉ）の上限値となる。また、右辺のＳＵＭ（αｔ（ｋ）、ｋ＝Ｌ ｔｏ Ｎ）／αｈ（Ｌ）は、非定常状態で溶鋼表面が上昇しつつある要素Ｂｄ（Ｌ）以上の要素における分配係数αｔ（ｉ）の和の、定常状態の分配係数αｈ（Ｌ）に対する比率を示しており、流量修正係数β（Ｌ）の下限値となる。したがって、溶鋼表面が上昇しつつある要素Ｂｄ（Ｌ）に対する流量修正係数β（Ｌ）は、式（５）で示される修正範囲にあり、例えば、溶鋼要素に溜まっている溶鋼量が少ない場合や、孔つきなど特殊な形状のタンディッシュでは底部に短絡流が発生するなどの操業上の不都合が発生することがあるため、β（Ｌ）の値を、この修正範囲内で再調整して、前記操業上の不都合を解消することも可能である。一方、溶鋼表面が上昇しつつある要素Ｂｄ（Ｌ）以外の要素Ｂｄ（ｉ）では、定常状態での溶鋼流量が維持されるか、またはこの溶鋼流量よりも流量が減少するため、β（ｉ）≦１となり、さらに非定常状態での空の状態が維持されている場合には、β（ｉ）はゼロの値となるため、範囲で表示すれば、上記（６）式のようになる。 In the above equation (4), 1 / αt (L) on the left side indicates a case where the molten steel flow rate Qinput (m 3 / s) injected into the tundish flows into the element Bd (L) in a steady state. The upper limit value of the flow rate correction coefficient β (i). Further, the SUM (αt (k), k = L to N) / αh (L) on the right side is the distribution coefficient αt (i) in an element greater than the element Bd (L) where the molten steel surface is rising in an unsteady state. Is the lower limit value of the flow rate correction coefficient β (L). Therefore, the flow rate correction coefficient β (L) for the element Bd (L) whose molten steel surface is rising is in the correction range represented by the equation (5). For example, when the amount of molten steel accumulated in the molten steel element is small, In a tundish with a special shape such as a hole, there may be an inconvenience in operation such as a short-circuit flow occurring at the bottom. Therefore, readjust the value of β (L) within this correction range, It is also possible to eliminate the operational inconvenience. On the other hand, in the element Bd (i) other than the element Bd (L) whose molten steel surface is rising, the molten steel flow rate in the steady state is maintained, or the flow rate is reduced from this molten steel flow rate, so β (i ) ≦ 1, and when the unsteady state is maintained in an empty state, β (i) has a value of zero. Therefore, when displayed in a range, the equation (6) is obtained. .
請求項４に係るタンディッシュ内の溶鋼温度の予測方法は、請求項１から３のいずれかに記載のタンディッシュ内の溶鋼温度の予測方法により求めた任意の（溶鋼）要素における温度Ｔｆと、この要素に対応する位置での実測により求めた溶鋼温度Ｔｍを用いて、前記予測方法により求めた鋳型流出部の最下層の要素Ｂｄ（１）（ｉ＝１）の温度Ｔｄ（１）を、以下の（６）式により補正することを特徴とする。
Ｔｄｃ（１）＝Ｔｄ（１）−（Ｔｆ−Ｔｍ） --------------------------（７）
ここで、Ｔｄｃ（１）は補正後の鋳型流出部最下層の要素Ｂｄ（１）の温度である。
The method for predicting the molten steel temperature in the tundish according to
Tdc (1) = Td (1)-(Tf-Tm) ------------------------- (7)
Here, Tdc (1) is the temperature of the element Bd (1) at the lowermost layer of the mold outflow portion after correction.
上述の溶鋼温度予測方法により求めた、温度実測位置に相当する溶鋼要素での温度と、実測温度が異なる場合には、溶鋼要素間の温度差（Ｔｆ−Ｔｍ）は正しいと見なして、上記（６）式を用いて補正することにより、流出部近傍すなわち鋳型流出部最下層の要素Ｂｄ（１）の温度を予測することができる。 When the temperature at the molten steel element corresponding to the temperature measurement position obtained by the molten steel temperature prediction method is different from the measured temperature, the temperature difference (Tf−Tm) between the molten steel elements is considered to be correct and the above ( By correcting using the equation (6), it is possible to predict the temperature of the element Bd (1) in the vicinity of the outflow portion, that is, the lowermost layer of the mold outflow portion.
請求項５に係るタンディッシュ内の溶鋼温度の管理方法は、溶鋼処理終了後の取鍋への溶鋼搬出温度Ｔｆを仮定するステップ１と、取鍋搬送中の溶鋼温度を予測し、タンディッシュへの注入温度を算出するステップ２と、このタンディッシュへの注入温度を用いて、請求項１から４のいずれかに記載のタンディッシュ内の溶鋼温度の予測方法により、鋳型流出部の最下層の要素Ｂｄ（１）の温度Ｔｄ（１）を求めるステップ３と、以下の式（８）または式（９）で表される、前記要素Ｂｄ（１）の温度Ｔｄ（ｉ）と、鋳型への流出流量（Ｑout）がゼロの湯溜中の基準温度Ｔｓ、または鋳造中の基準温度Ｔｍｉｎとの温度偏差ΔＴｅの絶対値が以下の式（１０）を満足するかどうかを判定するステップ４と、前記ΔＴｅの絶対値が式（１０）を満足しない場合に、ステップ１で仮定した溶鋼搬出温度Ｔｆを修正するステップ５とを備え、前記温度誤差ΔＴｅの絶対値が式（１０）を満足するまで、ステップ１〜ステップ５を繰り返すことにより、取鍋の搬出温度の下限値Ｔｆｍｉｎを求めて、溶鋼処理後の適正な取鍋搬出温度を決定するようにしたタンディッシュ内の溶鋼温度の管理方法である。
湯溜中（Qout=0）：ΔＴｅ＝Ｔｄ（１）−溶鋼凝固温度Ｔｓ ----------（８）
鋳造中（Qout≠0）：ΔＴｅ＝Ｔｄ（１）−温度管理下限値Ｔｍｉｎ ----（９）
■ΔＴｅ■＜許容計算誤差範囲Ｅｃ -----------------------------（１０）
The management method of the molten steel temperature in the tundish according to
In hot water reservoir (Qout = 0): ΔTe = Td (1) -solidification temperature Ts of molten steel ---------- (8)
During casting (Qout ≠ 0): ΔTe = Td (1) −Temperature control lower limit Tmin ---- (9)
■ ΔTe ■ <allowable calculation error range Ec ----------------------------- (10)
このように、タンディッシュ内の溶鋼温度の予測方法と、溶鋼処理終了時から搬送中の取鍋内の溶鋼温度計算方法を組み合わせることにより、鋳型流出部最下層の要素Ｂｄ（１）の温度Ｔｄ（１）が、上記基準温度ＴｓまたはＴｍｉｎからの許容計算誤差範囲ＥＣ内に収まるように、溶鋼処理終了後の取鍋の搬出温度Ｔｆの下限値Ｔｆｍｉｎを求めて、取鍋の適正な溶鋼搬出温度Ｔｆを決定するようにすれば、タンディッシュ内の溶鋼の容量が、すなわち湯面高さが変化する非定常操業でも、ノズル部の開口不良を起こさず、かつノズル開口後の鋳造中も、鋳型流出部における溶鋼温度を常に、操業トラブルを発生させない温度管理下限値以上に保つことができる。なお、取鍋の適正搬出温度は、通常、上記取鍋の搬出温度の下限値ＴｆｍｉｎよりもΔＴｆｓだけ高い目に設定する。この温度増加分ΔＴｆｓは、上記温度計算と同様にして、湯溜時または鋳造開始後の非定常状態における、前記要素Ｂｄ（１）の温度Ｔｄ（１）の温度管理上限値Ｔｍａｘに対応する取鍋の搬出温度Ｔｆの上限値Ｔｆｍａｘを求めて、（Ｔｆｍａｘ−Ｔｆｍｉｎ）の温度範囲内で適宜決定することができる。 Thus, by combining the method for predicting the molten steel temperature in the tundish and the method for calculating the molten steel temperature in the ladle being transferred from the end of the molten steel treatment, the temperature Td of the element Bd (1) at the bottom layer of the mold outflow portion The lower limit value Tfmin of the ladle unloading temperature Tf after completion of the molten steel processing is obtained so that (1) is within the allowable calculation error range EC from the reference temperature Ts or Tmin, and the appropriate molten steel unloading of the ladle is performed. If the temperature Tf is determined, the capacity of the molten steel in the tundish, that is, even in an unsteady operation in which the molten metal surface height changes, no nozzle opening failure occurs, and during casting after the nozzle opening, The molten steel temperature in the mold outflow part can always be kept above the temperature control lower limit value that does not cause operational troubles. In addition, the proper carry-out temperature of the ladle is normally set to an eye higher by ΔTfs than the lower limit value Tfmin of the carry-out temperature of the ladle. This temperature increase ΔTfs is taken corresponding to the temperature control upper limit value Tmax of the temperature Td (1) of the element Bd (1) in the unsteady state after the start of casting or after the start of casting, in the same manner as the above temperature calculation. An upper limit value Tfmax of the pan carry-out temperature Tf can be obtained and appropriately determined within the temperature range of (Tfmax−Tfmin).
この発明では、タンディッシュ内の溶鋼を、取鍋流入部から鋳型流出部へ溶鋼の流れ方向に対して複数の要素に分割し、かつ鋳型への流出部の要素をタンディッシュの深さ方向に対して複数の要素に分割して、隣り合う要素間で、上流側の要素から下流側の要素へ流入する溶鋼流量を、流動解析により求めた分配係数を用いて決定して各要素間の熱収支計算を行なうようにしたので、タンディュシュ内の溶鋼の容量が変化する非定常操業の場合でも、溶鋼の温度分布、とくに流出部の鋳型注入ノズル近傍の温度分布を精度よく予測することが可能となる。また、タンディッシュ内の溶鋼温度の実測値と温度測定位置に対応する要素の予測温度との差を求めて、この温度偏差分だけ鋳型注入ノズル近傍の予測温度を補正することにより、鋳型注入ノズル近傍の温度分布の予測精度を向上させることができる。それにより、鋳型注入ノズルの開口不良や鋳造中の湯漏れやブレークアウトやノズル詰まりなどの操業上のトラブルの発生を防止することができる。 In this invention, the molten steel in the tundish is divided into a plurality of elements with respect to the flow direction of the molten steel from the ladle inflow portion to the mold outflow portion, and the outflow portion elements to the mold are arranged in the tundish depth direction. On the other hand, it is divided into multiple elements, and the flow rate of molten steel flowing from the upstream element to the downstream element between adjacent elements is determined using the distribution coefficient obtained by flow analysis, and the heat between each element is determined. Since the balance calculation is performed, it is possible to accurately predict the temperature distribution of the molten steel, especially the temperature distribution in the vicinity of the mold injection nozzle in the outflow, even in the case of unsteady operation where the capacity of the molten steel in the tundesh changes. Become. Also, the mold injection nozzle is obtained by calculating the difference between the measured value of the molten steel temperature in the tundish and the predicted temperature of the element corresponding to the temperature measurement position, and correcting the predicted temperature near the mold injection nozzle by this temperature deviation. The prediction accuracy of the nearby temperature distribution can be improved. Accordingly, it is possible to prevent occurrence of operational troubles such as defective opening of the mold injection nozzle, leakage of hot water during casting, breakout and nozzle clogging.
さらに、上記のタンディッシュ内の溶鋼温度の予測方法と、取鍋での溶鋼処理終了時からタンディッシュへの搬送中の溶鋼の温度計算モデルと組み合わせることにより、取鍋からタンディッシュ内への溶鋼を供給中（湯溜中）には、凝固限界温度よりも高い温度となるように、また、ノズル開口後の鋳造中には、所要の温度管理範囲となるようにして、上記操業上のトラブルの発生を防止できる、取鍋からの適正な搬出温度を求めることもできる。 Furthermore, by combining the method for predicting the molten steel temperature in the tundish with the temperature calculation model of the molten steel being transferred to the tundish from the end of the molten steel treatment in the ladle, the molten steel from the ladle to the tundish is used. During the operation (during hot water), the above operating troubles should be set so that the temperature is higher than the solidification limit temperature, and during casting after opening the nozzle, the required temperature control range is maintained. Appropriate carry-out temperature from the ladle can be obtained.
以下に、この発明の実施形態を添付の図３から図９に基づいて説明する。 Hereinafter, an embodiment of the present invention will be described with reference to FIGS.
図３は、実施形態におけるタンディッシュ内の溶鋼要素の分割状態、および各要素間の溶鋼の流出入量の一例を模式的に示したものである（流出部深さ方向の流れの追加）。図３の要素分割例では、タンディッシュを流れ方向に対して４分割し、流出部およびそれに隣接する要素を、高さ方向にそれぞれ3分割および２分割している。図４（ａ）〜（ｃ）は、この要素分割状態における非定常状態の湯溜過程での各要素間の溶鋼流量の非定常分配係数αｈの切替えパターンの一例を示す。取鍋から、流量Ｑinput(m3/s)で、要素Ｂｅ（１）に流入した溶鋼は、流量Ｑout(1,1)で、隣接する下流側の要素Ｂｅ（２）へ流出する。この要素Ｂｅ（２）に流量Ｑin(2,1)（＝Ｑout(1,1)）で流入した溶鋼は、流量Ｑout(2,1)で、深さ方向に2分割した隣接する要素Ｂｕ（１）およびＢｕ（２）に流出する。この流出溶鋼は、まず、流量Ｑｕin(1)（＝Ｑout(2,1)）で下側の要素Ｂｕ（１）に流入し、流入した溶鋼が満載容量Ｖｕｆ（１）に到達すると、前記流出溶鋼は、流量Ｑｕin(２)（＝Ｑout(2,1)）で、上側の要素Ｂｕ（２）に流入する。これらの要素Ｂｕ（１）およびＢｕ（２）に流入した溶鋼は、図４（ａ）に示したように、湯溜初期（Ａ）では、まず、前記下側の要素Ｂｕ（１）から流量Ｑｕout（１）で流出した溶鋼が、隣接する下流側の要素、すなわち鋳型流出部における深さ方向に ３分割した要素Ｂｄ（１）、Ｂｄ（２）、Ｂｄ（３）のうち、まず、最下層の要素Ｂｄ（１）に流量Ｑｄin（１）（＝Ｑｕout（１））で流入し、下側の要素Ｂｕ（１）に流入した溶鋼容量Ｖｄ（１）が満載容量Ｖｕｆ（１）に到達するまでは（Ｖｄ（１）＜Ｖｕｆ（１））、流入し続ける。この要素Ｂｄ（１）に流入した溶鋼容量Ｖｄ（１）が満載容量Ｖｄｆ（１）に到達すると、図４（ｂ）に示すように、湯面がその直上の要素Ｂｄ（２）へ上昇し、（上流側の）前記下側の要素Ｂｕ（１）から流量Ｑｕout（１）で流出した溶鋼は、流量Ｑｄin（２）（＝Ｑｕout（１））で、真中の要素Ｂｄ（２）へ流入する。この湯溜中期（Ｂ）では、真中の要素Ｂｄ（２）の溶鋼容量Ｖｄ（２）が満載容量Ｖｄｆ（２）に到達する前に（Ｖｄ（２）＜Ｖｄｆ（２））、上流側の下側の要素Ｂｕ（１）が満載容量Ｖｕｆ（２）に到達すると、上側の要素Ｂｕ（２）から、流量Ｑｕout（２）で流出する溶鋼が、流量Ｑｄin（２）（＝Ｑｕout（２））で真中の要素Ｂｄ（２）に流入する。そして、要素Ｂｄ（２）の溶鋼容量Ｖｄ（２）が満載容量Ｖｄｆ（２）に到達すると、図４（ｃ）に示したように、湯溜末期（Ｃ）（Ｖｄ（３）＜Ｖｄｆ（３））では、上側の要素Ｂｕ（２）から流量Ｑｕout（２）で流出する溶鋼、および下側の要素Ｂｕ（１）から流量Ｑｕout（１）で流出する溶鋼の合計流量（Ｑｕout（１）＋Ｑｕout（２））が、流入流量Ｑｄin（３）（＝Ｑｕout（１）＋Ｑｕout（２））となって、最上層の要素Ｂｄ（３）に流入して湯面が上昇する。したがって、上記タンディッシュ内の溶鋼容量が変化する非定常状態の湯溜過程での、鋳型流出部における要素Ｂｄ（１）、Ｂｄ（２）およびＢｄ（３）に対する分配係数αｈ（ｉ）（ｉ：要素番号）は、非定常操業時の溶鋼熱流動解析結果、すなわち上流側の要素から当該要素に流入する溶鋼流速分布に基づいて、湯溜初期（Ａ）では、αｈ（１）＝１、αｈ（２）＝０、αｈ（３）＝０、湯溜中期（Ｂ）では、αｈ（１）＝０、αｈ（２）＝１、αｈ（３）＝０、湯溜末期（Ｃ）では、αｈ（１）＝０、αｈ（２）＝０、αｈ（３）＝１となる。そして、湯溜初期（Ａ）から湯溜中期（Ｂ）、湯溜中期（Ｂ）から湯溜末期（Ｃ）へと、湯面の上昇に伴って、分配係数αｈ（１）については、１→０→０、αｈ（２）については、０→１→０、α（３）については、０→０→１と切り替えて、各要素間の熱収支計算を行なうことができる。なお、図４（ｂ）で、破線の矢印で示した流出部の要素Ｂｄ（２）から要素Ｂｄ（１）への溶鋼流量Ｑｄｅｘ（２，１）＝Ｑｏｕｔ、および図４（ｃ）で、破線の矢印でそれぞれ示した、流出部の要素Ｂｄ（３）から要素Ｂｄ（２）への溶鋼流量Ｑｄｅｘ（３，２）＝Ｑｏｕｔ、および要素Ｂｄ（２）から要素Ｂｄ（１）への溶鋼流量Ｑｄｅｘ（２，１）＝Ｑｏｕｔは、溶鋼流量Ｑｏｕｔで鋳型への流出開始後も、タンディッシュへの溶鋼流入流量Ｑｉｎ＞溶鋼流出流量Ｑｏｕｔにより、湯面上昇を伴う非定常操業の場合（図１０参照）の流出部における深さ方向の溶鋼流量を示すものである。この鋳造開始後、湯面上昇を伴う非定常操業の場合は、同じタンディッシュ形状であれば、流出部の各要素に流入する溶鋼流速分布は、湯溜時（Ｑｏｕｔ＝０）の非定常操業の場合と殆ど変わらないため、同じ分配係数αｈを用いることができる。 FIG. 3 schematically shows an example of a state of division of molten steel elements in the tundish and an inflow and outflow amount of molten steel between the elements in the embodiment (addition of a flow in the outflow portion depth direction). In the example of element division in FIG. 3, the tundish is divided into four in the flow direction, and the outflow portion and the adjacent elements are divided into three and two in the height direction, respectively. FIGS. 4A to 4C show an example of a switching pattern of the unsteady distribution coefficient αh of the molten steel flow rate between the elements in the unsteady state of the hot water accumulation process in the element divided state. The molten steel that has flowed from the ladle into the element Be (1) at the flow rate Qinput (m3 / s) flows out to the adjacent downstream element Be (2) at the flow rate Qout (1,1). The molten steel that has flowed into this element Be (2) at a flow rate Qin (2,1) (= Qout (1,1)) is divided into two in the depth direction at the flow rate Qout (2,1). Outflow to 1) and Bu (2). The spilled molten steel first flows into the lower element Bu (1) at a flow rate Quin (1) (= Qout (2,1)). When the molten steel reaches the full capacity Vuf (1), The molten steel flows into the upper element Bu (2) at a flow rate Quin (2) (= Qout (2,1)). As shown in FIG. 4A, the molten steel flowing into these elements Bu (1) and Bu (2) is first flowed from the lower element Bu (1) in the initial stage (A). Among the elements Bd (1), Bd (2), and Bd (3) divided into three in the depth direction at the adjacent downstream element, that is, the mold outflow part, the molten steel flowing out at Quout (1) The molten steel capacity Vd (1) flowing into the lower element Bd (1) at the flow rate Qdin (1) (= Quout (1)) and flowing into the lower element Bu (1) reaches the full capacity Vuf (1). Until it is done (Vd (1) <Vuf (1)), it continues to flow. When the molten steel capacity Vd (1) flowing into the element Bd (1) reaches the full capacity Vdf (1), as shown in FIG. 4 (b), the molten metal surface rises to the element Bd (2) immediately above it. The molten steel flowing out from the lower element Bu (1) (upstream) at the flow rate Quout (1) flows into the middle element Bd (2) at the flow rate Qdin (2) (= Quout (1)). To do. In the middle of the hot water pool (B), before the molten steel capacity Vd (2) of the middle element Bd (2) reaches the full capacity Vdf (2) (Vd (2) <Vdf (2)), the upstream side When the lower element Bu (1) reaches the full capacity Vuf (2), the molten steel flowing out from the upper element Bu (2) at the flow rate Quout (2) flows into the flow rate Qdin (2) (= Quout (2). ) Flows into the middle element Bd (2). When the molten steel capacity Vd (2) of the element Bd (2) reaches the full capacity Vdf (2), as shown in FIG. 4C, the hot water end stage (C) (Vd (3) <Vdf ( 3)), the total flow rate of the molten steel flowing out at the flow rate Quout (2) from the upper element Bu (2) and the molten steel flowing out at the flow rate Quout (1) from the lower element Bu (1) (Quout (1) + Quout (2)) becomes the inflow flow rate Qdin (3) (= Quout (1) + Quout (2)), and flows into the uppermost element Bd (3) to raise the hot water surface. Therefore, the distribution coefficient αh (i) (i) for the elements Bd (1), Bd (2) and Bd (3) in the mold outflow portion in the unsteady state of the hot water accumulation process in which the molten steel capacity in the tundish changes. : Element number) is based on the molten steel thermal flow analysis result during unsteady operation, that is, the molten steel flow velocity distribution flowing into the element from the upstream element, αh (1) = 1 αh (2) = 0, αh (3) = 0, in the middle of hot water (B), αh (1) = 0, αh (2) = 1, αh (3) = 0, in the hot water end (C) , Αh (1) = 0, αh (2) = 0, and αh (3) = 1. The distribution coefficient αh (1) is 1 as the hot water level rises from the initial stage (A) to the middle stage (B), and from the middle stage (B) to the end stage (C). → 0 → 0, αh (2) can be switched from 0 → 1 → 0, and α (3) can be switched from 0 → 0 → 1 to calculate the heat balance between the elements. In FIG. 4 (b), the molten steel flow rate Qdex (2,1) = Qout from the element Bd (2) to the element Bd (1) of the outflow part indicated by the dashed arrow, and FIG. 4 (c) The molten steel flow rate Qdex (3,2) = Qout from the element Bd (3) to the element Bd (2) and the molten steel from the element Bd (2) to the element Bd (1), respectively, indicated by broken arrows The flow rate Qdex (2,1) = Qout is the case of the unsteady operation accompanied by the rise of the molten metal surface by the molten steel inflow flow rate Qin> the molten steel outflow flow rate Qout even after the molten steel flow rate Qout starts to flow into the mold (Fig. 10) shows the flow rate of molten steel in the depth direction at the outflow part. In the case of unsteady operation accompanied by rise of the molten metal surface after the start of casting, if the same tundish shape is used, the molten steel flow velocity distribution flowing into each element of the outflow portion is unsteady operation at the time of hot water accumulation (Qout = 0). The same distribution coefficient αh can be used since it is almost the same as in the case of.
図５は、この要素分割状態における定常状態、すなわち図９に示した、タンディッシュへの流入流量と鋳型流出流量が等しくなる状態での各要素間の溶鋼流量の定常分配係数αｔのパターンの一例を示したものである。図４（ｃ）に示したように、湯溜末期（Ｃ）で、湯面は流出部における最上層の要素Ｂｄ（３）に到達しており、定常状態では、この湯面は一定に保たれる。図１（ｂ）に模式的に流動状態を示したように、この定常状態の一例についての熱流動解析により、タンディッシュ内に流入した溶鋼は、上流側の上側の要素Ｂｕ（２）を経由して、流出部の最上層の要素Ｂｄ（３）に定常分配係数αｔ＝０．２で、最下層の要素Ｂｄ（１）に定常分配係数αｔ＝０．４でそれぞれ流入し、流出部の真中の要素Ｂｄ（２）に定常分配係数αｔ＝０．４で流入する結果が得られている。前記図４（ａ）〜（ｃ）の湯溜過程における流量調整係数β（ｉ）は、この定常分配係数αｔを用いて、湯溜初期（Ａ）では、β（１）＝１／０．４＝２．５（１．５≦β（１）≦２．５）、湯溜中期（Ｂ）では、β（２）＝１／０．４＝２．５（１．５≦β（１）≦２．５）、湯溜末期（Ｃ）では、β（３）＝５．０（１．０≦β（２）≦５．０）となる。これらの流量調整係数β（ｉ）は、いずれも、式（５）および式（６）に示した、上記括弧内に記載の範囲を満足する。このように、流量調整係数β（ｉ）は、定常および非定常のそれぞれの状態における溶鋼の熱流動解析結果、すなわち上流側の要素から当該要素に流入する溶鋼流速分布に基づいて算出した非定常および定常分配係数から、前記式（３）により算出することができる。なお、熱流動解析により得られた前記分配係数は、流出部の各要素の実機温度実績に基づいて修正しておくことが望ましい。 FIG. 5 shows an example of the steady distribution coefficient αt pattern of the molten steel flow rate between the elements in the steady state in this element division state, that is, in the state where the inflow flow rate to the tundish and the mold outflow flow rate are equal to each other as shown in FIG. Is shown. As shown in FIG. 4 (c), at the end of the hot water (C), the hot water surface reaches the uppermost element Bd (3) in the outflow portion, and this hot water surface is kept constant in the steady state. Be drunk. As schematically shown in FIG. 1 (b), the molten steel that has flowed into the tundish passes through the upper element Bu (2) on the upstream side by the thermal flow analysis of an example of this steady state. Then, it flows into the uppermost element Bd (3) of the outflow portion with a steady distribution coefficient αt = 0.2 and into the lowermost element Bd (1) with a steady distribution coefficient αt = 0.4, respectively. The result of flowing into the middle element Bd (2) with the steady distribution coefficient αt = 0.4 is obtained. The flow rate adjustment coefficient β (i) in the hot water accumulation process of FIGS. 4A to 4C uses this steady distribution coefficient αt, and β (1) = 1/0. 4 = 2.5 (1.5 ≦ β (1) ≦ 2.5), β (2) = 1 / 0.4 = 2.5 (1.5 ≦ β (1) ) ≦ 2.5), and at the end of hot water (C), β (3) = 5.0 (1.0 ≦ β (2) ≦ 5.0). Each of these flow rate adjustment coefficients β (i) satisfies the range described in parentheses shown in the equations (5) and (6). As described above, the flow rate adjustment coefficient β (i) is calculated based on the thermal flow analysis result of the molten steel in each of the steady state and the unsteady state, that is, based on the molten steel flow velocity distribution flowing into the element from the upstream element. From the steady distribution coefficient, it can be calculated by the above equation (3). In addition, it is desirable to correct the distribution coefficient obtained by the thermal flow analysis based on the actual machine temperature record of each element of the outflow part.
このような湯溜過程など、温度分布を有する溶鋼の非定常状態における温度変化をリアルタイムで簡易的に扱うためには、タンディッシュを溶鋼部、耐火物部など複数の要素に分けて、現在時間（kΔｔ）での要素間の熱収支を求めて次の時間（K+1）Δｔ の温度計算をおこなう、非定常の伝熱計算が用いられている。この非定常伝熱計算は、溶鋼の流れによる熱移動があるため、まず、要素間の溶鋼の流入出量を求め、これらの流量から要素に入る熱流束、および要素から出る熱流束を求めた後、各要素における溶鋼温度の時間変化を求めることによって行なうことができ、陽解法を用いることにより、計算を簡便に行なうことができる。まず、次の時刻（k+1）Δｔにおける要素の溶鋼量は、（１）式のようになる。
（次の時刻（k+1）Δｔでの要素Ｂの溶鋼量Ｍ（k+1））＝（現在の時刻(kΔｔ)での要素Ｂの溶鋼量Ｍ(k)）＋（（他の要素Ｃから流入する溶鋼流量Qinの和）−（他の要素Ｃへ流出する溶鋼流量Ｑoutの和））×（時間刻みΔｔ） ----------------------（１１）
タンディッシュ形状によって溶鋼の流れは異なるため、適切な要素の分割数や上記（１）式における当該要素Ｂおよび他の要素Ｃ間の溶鋼の流入出量は、予め流動解析や実機計測などにより決定することができる（図２のＱｉｎ、Ｑｏｕｔと関連付ける）。例えば、当該要素Ｂが、図２（ａ）に示した、流出部における最下層の要素Ｂｄ（１）であり、他の要素Ｃにその上流側の要素Ｂｕ（１）およびＢｕ（２）がそれぞれ該当するとき、他の要素Ｃから流入する溶鋼流量Qinの和は、Ｑｄｉｎ（１）＝Ｑｕｏｕｔ（１）（Ｑｕｏｕｔ（２）＝０）となる。また、当該要素Ｂが、図２（ｃ）に示した、流出部の最上層のＢｄ（３）であり、他の要素Ｃに、その上流側の要素Ｂｕ（１）およびＢｕ（２）がそれぞれ該当するとき、他の要素Ｃから流入する溶鋼流量Qinの和は、Ｑｄｉｎ（３）＝Ｑｕｏｕｔ（１）＋Ｑｕｏｕｔ（２）となる。また、これらの場合、湯溜中であるため、他の要素Ｃへ流出する溶鋼流量Ｑoutの和は、いずれもゼロとなる。上記要素間の溶鋼の流入出量から、要素Ｂに入る熱流束、または要素から出る熱流束は、（２）式および（３）式のようになる。
（他の要素Ｃから流入する熱流束Φ１）＝（他の要素Ｃの温度Ｔｃ）×（比熱Ｋｃ）×（密度ρｃ）×（他の要素Ｃから流入する溶鋼流量Ｍ１） ----------------（１２）
（他の要素Ｃへ流出する熱流束Φ２）＝（要素Ｂの温度Ｔｂ）×（比熱Ｋｂ）×（密度ρｂ）×（他の要素Ｃへ流出する溶鋼流量Ｍ２） -------------------------（１３）
上記（２）式および（３）式を用いると、次の時刻（k+1）Δｔで要素Ｂの持つ総熱量Ｈｂは、（４）式のようになる。
（次の時刻（k+1）Δｔで要素Ｂの持つ総熱量Ｈｂ（k+1））＝（現在の時刻(kΔｔ)で要素Ｂの持つ総熱量Ｈｂ(k)）＋（（接触する耐火物、スラグ要素へ逃げる熱流束Φｓの和）＋（他の要素から流入する熱流束Φ１の和）＋（他の要素へ流出する熱流束Φ２の和）＋（大気へ逃げる熱流束Φａの和）＋（加熱装置により印加される熱量Ｒｈの和））×（時間刻Δｔ） ------------------------------------------------------（１４）
したがって、次の時刻（k+1）Δｔでの要素Ｂの温度Ｔｂ（k+1）は、(５)式で算出することができる。
（次の時刻（k+1）Δｔでの要素Ｂの温度Ｔｂ（k+1））＝（要素Ｂの持つ総熱量Ｈｂ（k+1））／（比熱Ｋｂ）／（密度ρｂ）／（要素の溶鋼量Ｍ（k+1））-------（１５）
In order to handle the temperature change in the unsteady state of molten steel with a temperature distribution, such as a hot water process, in real time, the tundish is divided into multiple elements such as the molten steel part and the refractory part. Unsteady heat transfer calculation is used in which the heat balance between elements at (kΔt) is obtained and the temperature is calculated at the next time (K + 1) Δt. In this unsteady heat transfer calculation, there is heat transfer due to the flow of molten steel. First, the inflow and outflow amount of molten steel between elements was obtained, and the heat flux entering the element and the heat flux exiting the element were obtained from these flow rates. Thereafter, it can be performed by obtaining the time change of the molten steel temperature in each element, and the calculation can be easily performed by using the explicit method. First, the amount of molten steel of the element at the next time (k + 1) Δt is expressed by equation (1).
(The amount of molten steel M (k + 1) of element B at the next time (k + 1) Δt) = (the amount of molten steel M (k) of element B at the current time (kΔt)) + ((other elements Sum of molten steel flow rate Qin flowing in from C)-(sum of molten steel flow rate Qout flowing out to other elements C)) x (time increment Δt) ------------------ ---- (11)
Since the flow of molten steel differs depending on the tundish shape, the appropriate number of element divisions and the inflow / outflow amount of molten steel between the element B and the other element C in the above equation (1) are determined in advance by flow analysis or actual machine measurement. (Relate to Qin and Qout in FIG. 2). For example, the element B is the lowermost element Bd (1) in the outflow portion shown in FIG. 2A, and the upstream elements Bu (1) and Bu (2) are connected to the other element C. When each corresponds, the sum of the molten steel flow rates Qin flowing from the other elements C is Qdin (1) = Quout (1) (Quout (2) = 0). Further, the element B is Bd (3) in the uppermost layer of the outflow portion shown in FIG. 2C, and the elements Bu (1) and Bu (2) on the upstream side thereof are included in the other element C. When each corresponds, the sum of the molten steel flow rates Qin flowing from the other elements C is Qdin (3) = Quout (1) + Quout (2). In these cases, since the hot water is being accumulated, the sum of the molten steel flow rates Qout flowing out to the other elements C is all zero. From the inflow and outflow amount of the molten steel between the elements, the heat flux entering the element B or the heat flux exiting the element is expressed by the equations (2) and (3).
(Heat flux Φ1 flowing from the other element C) = (Temperature Tc of the other element C) × (Specific heat Kc) × (Density ρc) × (Mold steel flow rate M1 flowing from the other element C) ----- ----------- (12)
(Heat flux Φ2 flowing out to other element C) = (temperature Tb of element B) × (specific heat Kb) × (density ρb) × (flow rate of molten steel M2 flowing out to other element C) ------- ------------------ (13)
When the above equations (2) and (3) are used, the total heat amount Hb of the element B at the next time (k + 1) Δt is expressed by the following equation (4).
(Total heat amount Hb (k + 1) of element B at next time (k + 1) Δt) = (Total heat amount Hb (k) of element B at current time (kΔt)) + ((Fire resistance in contact Sum of heat flux Φs escaping to the object and slag element) + (sum of heat flux Φ1 flowing in from other elements) + (sum of heat flux Φ2 flowing out to other elements) + (sum of heat flux Φa escaping to the atmosphere) ) + (Sum of amount of heat Rh applied by heating device)) × (time increment Δt) ----------------------------- ------------------------- (14)
Therefore, the temperature Tb (k + 1) of the element B at the next time (k + 1) Δt can be calculated by the equation (5).
(Temperature Tb (k + 1) of element B at next time (k + 1) Δt) = (total heat quantity Hb (k + 1) of element B) / (specific heat Kb) / (density ρb) / ( Molten steel amount M (k + 1)) ------- (15)
図６（ａ）〜（ｃ）は、図３に示した要素分割状態における非定常状態の湯溜過程での各要素間の溶鋼流量の分配係数αｈの切替えパターンの他の一例を示したものである。図６（ａ）の湯溜初期（Ａ）の流出部における最下層の要素Ｂｄ（１）への溶鋼の流入状況は、図４（ａ）に示した場合と同様である。図６（ｂ）の湯溜中期（Ｂ）では、要素Ｂｄ（１）に流入した溶鋼容量Ｖｄ（１）が満載容量Ｖｄｆ（１）に到達して、湯面がその直上の要素Ｂｄ（２）へ上昇すると、上流側の下側の要素Ｂｕ（１）から流量Ｑｕout（１）で流出した溶鋼は、満載容量となった流出部における最下層の要素Ｂｄ（１）へ流量Ｑｄin（１）＝0.2×Ｑｕout（１）（αｈ＝0.2）で、真中の要素Ｂｄ（２）へ流量Ｑｄin（２）＝0.8×Ｑｕout（１）（αｈ＝0.8）で、それぞれ流入する。そして、分配係数αｈ＝0.2で最下層の要素Ｂｄ（１）へ流入した溶鋼は、湯面が上昇している直上の要素Ｂｄ（２）へ、流量Ｑｄex（１，２）＝-Ｑｄin（１）（負号は、上方向を意味する）で流出する。そして、要素Ｂｄ（２）の溶鋼容量Ｖｄ（２）が満載容量Ｖｄｆ（２）に到達すると、湯溜末期（Ｃ）（Ｖｄ（３）＜Ｖｄｆ（３））では、図６（ｃ）に示すように、上流側の要素Ｂｕ（２）から流量Ｑｕout（２）で流出する溶鋼、および下側の要素Ｂｕ（１）から流量Ｑｕout（１）で流出する溶鋼の合計流量（Ｑｕout（１）＋Ｑｕout（２））の中、流出部の真中の要素Ｂｄ（２）には、流量Ｑｄin（２）＝0.2×（Ｑｕout（１）＋Ｑｕout（２））（分配係数αｈ＝0.2）が、最上層の要素Ｂｄ（３）には、流量Ｑｄin（３）＝0.8×（Ｑｕout（１）＋Ｑｕout（２））（分配係数αｈ＝0.8）が、それぞれ流入する。そして、分配係数αｈ＝0.2で最下層の要素Ｂｄ（１）へ流入した溶鋼は、湯面が上昇している直上の要素Ｂｄ（２）へ、流量Ｑｄex（２，３）＝-Ｑｄin（２）（負号は、上方向を意味する）で流出する。したがって、上記タンディッシュ内の溶鋼容量が変化する非定常状態の湯溜過程での、鋳型流出部における要素Ｂｄ（１）、Ｂｄ（２）およびＢｄ（３）に対する分配係数αｈ（ｉ）（ｉ：要素番号）は、湯溜初期（Ａ）では、αｈ（１）＝１、αｈ（２）＝０、αｈ（３）＝０と、図４（ａ）の場合と同様であるが、湯溜中期（Ｂ）では、αｈ（１）＝０．２、αｈ（２）＝０．８、αｈ（３）＝０となり、湯溜末期（Ｃ）では、αｈ（１）＝０、αｈ（２）＝０．２、αｈ（３）＝０．８となって図４（ｂ）および（ｃ）の場合と異なり、湯溜初期（Ａ）から湯溜中期（Ｂ）、湯溜中期（Ｂ）から湯溜末期（Ｃ）へと、湯面の上昇に伴って、分配係数αｈ（１）については、１→０．２→０、αｈ（２）については、０→０．８→０．２、α（３）については、０→０→０．８と切り替えて、各要素間の熱収支計算を行なうことができる。前記流量調整係数β（ｉ）は、湯溜初期（Ａ）では、β（１）＝２．５となり、図４（ａ）の場合と同じであるが、湯溜中期（Ｂ）では、β（１）＝０．５（０≦β（１）＜１）、β（２）＝２．０（１．５≦β（２）≦２．５）となり、湯溜末期（Ｃ）では、β（２）＝０．５（０≦β（２）＜１）、β（３）＝４．０（１．０≦β（２）≦５．０）となり、これらの流量調整係数β（ｉ）の値は、式（５）および式（６）に示した、上記括弧内に記載のβ（ｉ）の範囲を満足する。このように図４（ａ）〜（ｃ）および図６（ａ）〜（ｃ）で、流量調整係数β（ｉ）の値が異なり、したがって、流量調整係数β（ｉ）の値は、常に一定ではなく、主に、タンディッシュの形状により異なる。また、流量調整係数β（ｉ）は、同じタンディッシュ形状であっても、鋳造開始後（Ｑｏｕｔ≠０）も湯面の上昇を伴う非定常操業の場合と、湯溜時（Ｑｏｕｔ＝０）の非定常操業の場合とは、必ずしも同一ではなくなるため、このような非定常の操業状態に応じて、変化させることもできる。 6 (a) to 6 (c) show another example of the switching pattern of the distribution coefficient αh of the molten steel flow rate between the elements in the unsteady state of the hot water accumulation process in the element split state shown in FIG. It is. The state of inflow of molten steel into the lowermost element Bd (1) at the outflow part in the initial stage (A) of the hot water reservoir in FIG. 6 (a) is the same as that shown in FIG. 4 (a). In the hot water middle stage (B) of FIG. 6B, the molten steel capacity Vd (1) flowing into the element Bd (1) reaches the full capacity Vdf (1), and the molten metal surface has an element Bd (2 ), The molten steel that has flowed out of the upstream element Bu (1) at the flow rate Quout (1) flows into the bottom layer element Bd (1) in the outflow portion where the full capacity is reached. = 0.2 × Quout (1) (αh = 0.2), and flows into the middle element Bd (2) at a flow rate Qdin (2) = 0.8 × Quout (1) (αh = 0.8). Then, the molten steel that has flowed into the lowermost element Bd (1) with a distribution coefficient αh = 0.2 flows to the element Bd (2) immediately above the molten metal surface where the flow rate Qdex (1,2) = − Qdin (1 ) (Negative sign means upward direction). Then, when the molten steel capacity Vd (2) of the element Bd (2) reaches the full capacity Vdf (2), in the hot water end stage (C) (Vd (3) <Vdf (3)), FIG. As shown, the total flow rate of the molten steel flowing out from the upstream element Bu (2) at the flow rate Quout (2) and the molten steel flowing out from the lower element Bu (1) at the flow rate Quout (1) (Quout (1) + Quout (2)), the flow rate Qdin (2) = 0.2 × (Quout (1) + Quout (2)) (distribution coefficient αh = 0.2) is the top layer in the element Bd (2) in the middle of the outflow part. The flow rate Qdin (3) = 0.8 × (Quout (1) + Quout (2)) (distribution coefficient αh = 0.8) flows into the element Bd (3). Then, the molten steel that has flowed into the lowermost element Bd (1) with a distribution coefficient αh = 0.2 flows to the element Bd (2) immediately above where the molten metal surface is rising, and the flow rate Qdex (2,3) = − Qdin (2 ) (Negative sign means upward direction). Therefore, the distribution coefficient αh (i) (i) for the elements Bd (1), Bd (2) and Bd (3) in the mold outflow portion in the unsteady state of the hot water accumulation process in which the molten steel capacity in the tundish changes. : Element number) is the same as in the case of FIG. 4 (a), αh (1) = 1, αh (2) = 0, αh (3) = 0 in the initial stage of hot water (A). In the middle period (B), αh (1) = 0.2, αh (2) = 0.8, and αh (3) = 0, and in the end stage of hot water (C), αh (1) = 0, αh ( 2) = 0.2 and αh (3) = 0.8, which is different from the cases of FIGS. 4B and 4C, from the initial stage of hot water (A) to the middle of hot water (B), the middle of hot water ( From B) to the end of hot water (C), as the hot water level rises, 1 → 0.2 → 0 for the distribution coefficient αh (1) and 0 → 0.8 → for αh (2). 0.2, α (3 For, it is possible to switch the 0 → 0 → 0.8, performs heat balance calculation between the elements. The flow rate adjustment coefficient β (i) is β (1) = 2.5 in the initial stage of hot water (A), which is the same as in FIG. 4A, but in the middle stage of hot water (B), β (1) = 0.5 (0 ≦ β (1) <1), β (2) = 2.0 (1.5 ≦ β (2) ≦ 2.5), and at the end of hot water (C), β (2) = 0.5 (0 ≦ β (2) <1), β (3) = 4.0 (1.0 ≦ β (2) ≦ 5.0), and these flow rate adjustment coefficients β ( The value of i) satisfies the range of β (i) shown in the parentheses shown in the equations (5) and (6). As described above, the value of the flow rate adjustment coefficient β (i) is different between FIGS. 4A to 4C and FIGS. 6A to 6C. Therefore, the value of the flow rate adjustment coefficient β (i) is always It is not constant and mainly depends on the shape of the tundish. In addition, the flow rate adjustment coefficient β (i) has the same tundish shape, even after the start of casting (Qout ≠ 0), in the case of unsteady operation with the rise of the molten metal level, and at the time of hot water accumulation (Qout = 0). Since this is not necessarily the same as in the case of the unsteady operation, it can be changed according to such an unsteady operation state.
上述の溶鋼温度の予測方法を用いて、容量６０tonのタンディッシュ内の溶鋼温度変化を計算した結果を以下に示す。図７は、このタンディッシュの溶鋼の分割状態を示したもので、（ａ）は実施例の分割状態で、溶鋼流れ方向に対して４分割、鋳型流出部およびそれに隣接する要素は高さ方向にさらに２分割したものである。（ｂ）は、比較例の分割状態で、溶鋼の流れ方向のみに6等分した要素分割である。実施例および比較例ともに、分割された各要素の容量は１０tonとし、側壁耐火物へ伝わって逃げる熱量は実機の測定結果より決定し、（ａ）、（ｂ）の両分割要素とも同じ値を用いた。溶鋼の湯面レベルが一定である定常状態時の分配係数αｔ（ｉ）は、溶鋼の測温結果と熱流動解析により求めて、流出部下側の要素Ｂｄ（１）についてはαｔ（１）＝0.4、同上側の要素Ｂｄ（２）については、αｔ（２）＝0.6とした。非定常時の分配係数αｈ（ｉ）に切替えるための流量調整係数β（ｉ）は、溶鋼表面（湯面）が、下側の要素Ｂｄ（１）内にあるときは、β（１）＝2.5、β（２）＝0.0とし、溶鋼表面が上昇して上側の要素Ｂｄ（２）内にあるときに、β（１）＝0.0、β（２）＝1.67とした。また取鍋からタンディッシュへの溶鋼注入流の温度分布は実機計測値と温度シミュレーション結果から求めた値を使用した。 The calculation result of the molten steel temperature change in the tundish with a capacity of 60 tons using the above-described molten steel temperature prediction method is shown below. FIG. 7 shows a divided state of the molten steel of this tundish. (A) is a divided state of the example, and is divided into four in the molten steel flow direction, and the mold outflow portion and the adjacent elements are in the height direction. Is further divided into two. (B) is the division | segmentation state of a comparative example, and is the element division | segmentation divided into 6 equally only in the flow direction of molten steel. In both the example and the comparative example, the capacity of each divided element is 10 tons, and the amount of heat transmitted to the side wall refractory and escaping is determined from the measurement result of the actual machine, and both the divided elements (a) and (b) have the same value. Using. The distribution coefficient αt (i) in the steady state where the molten steel surface level is constant is obtained from the temperature measurement result of the molten steel and the thermal flow analysis. For the element Bd (1) below the outflow part, αt (1) = For the element Bd (2) on the upper side of 0.4, αt (2) = 0.6. The flow rate adjustment coefficient β (i) for switching to the non-stationary distribution coefficient αh (i) is β (1) = when the molten steel surface (molten metal surface) is in the lower element Bd (1). 2.5, β (2) = 1.0, and β (1) = 0.0, β (2) = 1.67 when the surface of the molten steel rose and was in the upper element Bd (2). For the temperature distribution of the molten steel injection flow from the ladle to the tundish, the values obtained from the actual machine measurements and temperature simulation results were used.
図８（ａ）に、本願発明の溶鋼温度予測方法による温度計算結果（実施例）および測温結果との比較を、同（ｂ）に、従来の直列要素分割モデル（比較例）による温度計算結果（比較例）と測温結果との比較を、それぞれ示す。図８（ａ）から、本願発明の溶鋼温度予測方法によれば、非定常状態である湯溜中、定常状態である鋳造中の、湯面から約５０ｃｍの深さの測温位置における温度計算結果、すなわち鋳造開始時を基準点とした溶鋼温度の推移は、測温値とよく一致しており、溶鋼温度の時間変化の傾向が正しく表されている。これに対して、図８（ｂ）に示した、従来の要素分割による温度計算結果では、非定常状態である湯溜中の溶鋼温度変化は測温値と合致せず、異なる傾向を示している。また、図８（ａ）に示したノズル開口の可否の判断に必要な鋳造直前の鋳型流出部の温度についても、本願発明では流出部の要素を上下に２分割しているため、実際の溶鋼温度をよく反映した計算結果が得られている。一方、従来の要素分割による温度計算では、図８（ｂ）に示したように、鋳造直前の鋳型流出部の温度は、本願発明の場合よりも高い結果となっており、この高い温度に基づいてノズル開口の判断をした場合、開口不良を引き起こす危険性がある。 FIG. 8 (a) shows a comparison between the temperature calculation result (Example) and the temperature measurement result by the molten steel temperature prediction method of the present invention, and FIG. 8 (b) shows the temperature calculation by the conventional serial element division model (Comparative Example). A comparison between the result (comparative example) and the temperature measurement result is shown. From FIG. 8 (a), according to the molten steel temperature prediction method of the present invention, the temperature calculation at a temperature measuring position at a depth of about 50 cm from the molten metal surface in the unsteady state of the hot water pool and in the steady state of casting. The result, that is, the transition of the molten steel temperature with the casting start point as the reference point is in good agreement with the temperature measurement value, and the tendency of the molten steel temperature to change with time is correctly represented. On the other hand, in the temperature calculation result by the conventional element division shown in FIG. 8 (b), the molten steel temperature change in the hot water reservoir which is in an unsteady state does not match the temperature measurement value, and shows a different tendency. Yes. In addition, regarding the temperature of the mold outflow part immediately before casting, which is necessary for determining whether or not the nozzle opening is shown in FIG. 8 (a), since the element of the outflow part is vertically divided into two in the present invention, the actual molten steel Calculation results that reflect the temperature well. On the other hand, in the temperature calculation based on the conventional element division, as shown in FIG. 8B, the temperature of the mold outflow portion immediately before casting is higher than that in the case of the present invention, and based on this high temperature. If the nozzle opening is judged, there is a risk of causing a defective opening.
前記鋳型流出部の要素Ｔｄ（ｉ）の温度、とくに流出部最下層の要素Ｂｄ（１）の温度Ｔｄ（１）が、鋳型注入ノズルの開口不良や鋳造中の湯漏れやブレークアウトやノズル詰まりなどの操業上のトラブルの発生を防止することができる温度範囲に常に入るように、溶鋼処理終了時の取鍋の搬出温度が適正かどうかを判別する流れを、図９に示す。まず、溶鋼処理終了時の取鍋の搬出温度Ｔｆ（下限値）を仮定する（Ｓ１０）。次に、段落［００２４］に示した温度解析方法を、タンディッシュへの取鍋搬送中の溶鋼の温度変化の算出に適用して、タンディッシュへの注入温度すなわち流入温度Ｔｃを算出し（Ｓ２０）、この流入温度Ｔｃを用いて、本願の温度予測方法により、鋳型流出部の対象要素Ｔｄ（ｉ）、すなわち最下層の要素Ｂｄ（１）の温度Ｔｄ（１）を算出する（Ｓ３０）。そして、この温度Ｔｄ（１）と、前記式（８）または式（９）で表される、鋳型への流出流量（Ｑout）がゼロの湯溜中の基準温度とする溶鋼凝固温度Ｔｓ、または鋳造中の基準温度とする温度管理下限値Ｔｍｉｎとの温度誤差ΔＴｅの絶対値が前記式（１０）を満足するかどうか、すなわち計算許容範囲Ｅｃにあるかどうかを判定する（Ｓ４０）。この計算許容範囲Ｅｃは、例えば、１０−４と僅少な値である。前記式（１０）を満足する場合、Ｓ１０で仮定した搬出温度Ｔｆを取鍋搬出温度の下限値Ｔｆｍｉｎと判定する。式（１０）を満たさない場合、温度誤差ΔＴｅの正負に応じて仮定した搬出温度ＴｆをΔＴｆだけ増減する補正をして（Ｓ４０）、Ｓ１０〜Ｓ４０のステップを繰り返す。なお、式（９）における温度下限管理値Ｔｍｉｎは、操業温度実績に基づいて、適宜設定することができる。なお、式（８）および式（９）の基準温度（溶鋼凝固温度Ｔｓおよび温度下限管理値Ｔｍｉｎ）に加えて、他の基準温度、例えば、タンディッシュスラグの凝固による排滓トラブル防止に対しては、スラグの凝固温度Ｔｇを基準温度とし、流出部におけるスラグ部に対応する要素Ｂｄ（ｉ）を設けて、その温度Ｔｄ（ｉ）を、本願の溶鋼温度予測方法により求めて、前記温度誤差ΔＴｅを以下の式（１１）により求めることができる。そして
ΔＴｅ＝Ｔｄ（ｉ）−スラグ凝固温度Ｔｇ ----------（１６）
上記式（１６）により求めた温度誤差ΔＴｅについても、前記式（１０）を満足するかどうかを、上述のようにして判別し、排滓トラブルを発生させない溶鋼処理終了時の取鍋搬出温度の下限値Ｔｆｍｉｎを決定することができる。なお、上記判別は、必ずしも、流出部の最下層の要素Ｂｄ（１）に限るものではなく、流出部における他の要素について行なうこともできる。
The temperature of the element Td (i) in the mold outflow part, particularly the temperature Td (1) of the element Bd (1) in the lowermost part of the outflow part is a mold injection nozzle opening defect, hot water leakage during casting, breakout or nozzle clogging. FIG. 9 shows a flow for determining whether or not the ladle carry-out temperature at the end of the molten steel processing is appropriate so as to always fall within a temperature range in which the occurrence of operational troubles such as the above can be prevented. First, the ladle unloading temperature Tf (lower limit) at the end of the molten steel treatment is assumed (S10). Next, the temperature analysis method shown in the paragraph [0024] is applied to the calculation of the temperature change of the molten steel during the ladle conveyance to the tundish to calculate the injection temperature into the tundish, that is, the inflow temperature Tc (S20). ) Using the inflow temperature Tc, the temperature Td (1) of the target element Td (i) of the mold outflow part, that is, the lowermost element Bd (1) is calculated by the temperature prediction method of the present application (S30). Then, this temperature Td (1) and the molten steel solidification temperature Ts, which is expressed by the above formula (8) or formula (9), which is the reference temperature in the hot water reservoir where the outflow flow rate (Qout) to the mold is zero, or It is determined whether or not the absolute value of the temperature error ΔTe with respect to the temperature control lower limit value Tmin used as the reference temperature during casting satisfies the above formula (10), that is, whether it is within the calculation allowable range Ec (S40). The calculation allowable range Ec is a small value such as 10 −4 . When the above expression (10) is satisfied, the carry-out temperature Tf assumed in S10 is determined as the lower limit value Tfmin of the ladle carry-out temperature. When Expression (10) is not satisfied, correction is performed to increase / decrease the carry-out temperature Tf assumed according to the sign of the temperature error ΔTe by ΔTf (S40), and steps S10 to S40 are repeated. In addition, the temperature lower limit management value Tmin in Expression (9) can be set as appropriate based on the operating temperature record. In addition to the reference temperatures (molten steel solidification temperature Ts and temperature lower limit control value Tmin) of Equation (8) and Equation (9), other reference temperatures, for example, prevention of waste trouble due to solidification of tundish slag Is a slag solidification temperature Tg as a reference temperature, an element Bd (i) corresponding to the slag part in the outflow part is provided, and the temperature Td (i) is obtained by the molten steel temperature prediction method of the present application, and the temperature error ΔTe can be obtained by the following equation (11). And ΔTe = Td (i) -slag solidification temperature Tg ---------- (16)
Regarding the temperature error ΔTe obtained by the above equation (16), whether or not the equation (10) is satisfied is determined as described above, and the ladle unloading temperature at the end of the molten steel treatment that does not cause a waste trouble is determined. The lower limit value Tfmin can be determined. Note that the determination is not necessarily limited to the element Bd (1) in the lowermost layer of the outflow portion, and can be performed for other elements in the outflow portion.
１：タンディッシュ ２：流入部 ３：流出部
３ａ：流出部底部
1: Tundish 2: Inflow section 3: Outflow section 3a: Outflow section bottom
Claims (5)
Ｑｕｏｕｔｓ＝ＳＵＭ（Ｑｕｏｕｔ（ｋ）、ｊ＝１ ｔｏ Ｍ） --------（１）
αｈ（ｉ）＝Ｑｄｉｎ（ｉ）／Ｑｕｏｕｔｓ ------------------（２）
β（ｉ）＝αｈ（ｉ）／αｔ（ｉ） ------------------------（３）
αｈ（ｉ）＝β（ｉ）×αｔ（ｉ） ------------------------（４）
ここで、Ｑｕｏｕｔ（ｋ）は、上流側の各要素Ｂｕ（ｋ）から流出部における各要素Ｂｄ（ｉ）へ流入する溶鋼流量であり、ｉ、ｊは要素番号を、Ｍは要素Ｂｕ（ｊ）の分割数である。 Each element Bd of the outflow part of the flow rate of molten steel flowing from the element Bu (j) on the upstream side to each element Bd (i) of the outflow part divided into a plurality of parts in the depth direction of the tundish of the outflow part When the sum of i) is Qdin (i), the distribution coefficient αh (i) in the unsteady state with respect to each element Bd (i) of the outflow portion is defined as Qdin (i) and the following (1) Using the total molten steel flow rate Quouts flowing into each element Bd (i) in the outflow portion from each upstream element Bu (j) calculated by the expression, the unsteady state is calculated by the following expression (2) From the distribution coefficient αt (i) in the steady state and the distribution coefficient αh (i) obtained in advance and the amount of molten steel Vtd (m3) in the tundish is constant (inflow amount Qin = outflow amount Qout). The flow rate adjustment coefficient β (i) is calculated by the following equation (3) From the flow rate adjustment coefficient β (i) and the steady state distribution coefficient αt (i), the unsteady state distribution coefficient αh (i) calculated by the following equation (4) is used. The method for predicting the molten steel temperature in the tundish according to claim 1, wherein the molten steel flow rate is distributed to each element Bd (i).
Quouts = SUM (Quout (k), j = 1 to M) -------- (1)
αh (i) = Qdin (i) / Quouts ------------------ (2)
β (i) = αh (i) / αt (i) ------------------------ (3)
αh (i) = β (i) × αt (i) ----------------------- (4)
Here, Quout (k) is a molten steel flow rate flowing from each upstream element Bu (k) to each element Bd (i) in the outflow part, i and j are element numbers, and M is an element Bu (j ).
１／αｔ（Ｌ）≧β（Ｌ）≧ＳＵＭ（αｔ（ｋ）、ｋ＝Ｌ ｔｏ Ｎ）／αｔ（Ｌ） ----（５）
１≧β（ｉ）≧０ -------------------------------------------（６）
ここで、ｉ、ｋは要素番号を、Ｎは、流出部における分割した要素Ｂｄ（ｉ）の数を、Ｌは、溶鋼表面が上昇しつつある要素Ｂｄ（ｉ）の番号を意味し、αｔ（Ｌ）およびαｔ（ｋ）は、要素Ｂｄ（Ｌ）およびＢｄ（ｋ）に対する定常状態での分配係数を示す。 Regarding the element Bd (i) (i = L) of the outflow part where the range of the adjustment coefficient β (i) is rising on the surface of the molten steel, the other element Bd (i) according to the following equation (4) The method for predicting the molten steel temperature in the tundish according to claim 1 or 2, wherein (i ≠ L) is in a range represented by the following equation (5).
1 / αt (L) ≧ β (L) ≧ SUM (αt (k), k = L to N) / αt (L) ---- (5)
1 ≧ β (i) ≧ 0 ------------------------------------------ -(6)
Here, i and k are element numbers, N is the number of divided elements Bd (i) in the outflow part, L is the number of element Bd (i) where the molten steel surface is rising, αt (L) and αt (k) indicate the distribution coefficients in the steady state for the elements Bd (L) and Bd (k).
Ｔｄｃ（１）＝Ｔｄ（１）−（Ｔａ−Ｔｍ） --------------------------（７）
ここで、Ｔｄｃ（１）は補正後の鋳型流出部最下層の要素Ｂｄ（１）の温度である。 Using the temperature Ta in an arbitrary molten steel element obtained by the method for predicting the molten steel temperature in the tundish according to any one of claims 1 to 3, and the molten steel temperature Tm obtained by actual measurement at a position corresponding to the element. The temperature Td (1) of the element Bd (1) (i = 1) in the lowermost layer of the mold outflow portion determined by the molten steel temperature prediction method is corrected by the following equation (6). Method for predicting the molten steel temperature inside.
Tdc (1) = Td (1)-(Ta-Tm) ------------------------- (7)
Here, Tdc (1) is the temperature of the element Bd (1) at the lowermost layer of the mold outflow portion after correction.
湯溜中（Qout=0）：ΔＴｅ＝Ｔｄ（１）−溶鋼凝固温度Ｔｓ ----------（８）
鋳造中（Qout≠0）：ΔＴｅ＝Ｔｄ（１）−温度管理下限値Ｔｍｉｎ -------（９）
■ΔＴｅ■＜計算誤差許容範囲Ｅｃ --------------------------------（１０） Step 1 that assumes the ladle unloading temperature Tf after the end of the molten steel process, step 2 that predicts the molten steel temperature during ladle transport, and calculates the injection temperature into the tundish, and the injection temperature into the tundish Step 3 for determining the temperature Td (1) of the lowermost element Bd (1) of the mold outflow portion by the method for predicting the molten steel temperature in the tundish according to any one of claims 1 to 4, and The temperature Td (i) of the element Bd (1) represented by the formula (8) or the formula (9) and the reference temperature Ts in the hot water reservoir in which the flow rate (Qout) to the mold is zero, or casting Step 4 for determining whether or not the absolute value of the temperature deviation ΔTe with respect to the reference temperature Tmin satisfies the following equation (10), and if the absolute value of ΔTe does not satisfy the equation (10), step 1 The molten steel delivery temperature Tf assumed in step 1 is corrected. Step 5 is repeated until the absolute value of the temperature error ΔTe satisfies the formula (10), by repeating Step 1 to Step 5 to obtain the lower limit value Tfmin of the ladle unloading temperature Tf, and the molten steel treatment A method for managing the temperature of molten steel in the tundish so as to determine the proper ladle discharge temperature later.
In hot water reservoir (Qout = 0): ΔTe = Td (1) -solidification temperature Ts of molten steel ---------- (8)
During casting (Qout ≠ 0): ΔTe = Td (1) −Temperature control lower limit Tmin ------- (9)
■ ΔTe ■ <Calculation error tolerance Ec -------------------------------- (10)
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