JPH11309507A - Method for estimating thermal flux in cooling of steel and cooling control method using the same - Google Patents
Method for estimating thermal flux in cooling of steel and cooling control method using the sameInfo
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- JPH11309507A JPH11309507A JP10118637A JP11863798A JPH11309507A JP H11309507 A JPH11309507 A JP H11309507A JP 10118637 A JP10118637 A JP 10118637A JP 11863798 A JP11863798 A JP 11863798A JP H11309507 A JPH11309507 A JP H11309507A
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- temperature
- cooling
- steel
- boiling
- heat flux
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- Control Of Heat Treatment Processes (AREA)
- Heat Treatment Of Strip Materials And Filament Materials (AREA)
Abstract
Description
【０００１】[0001]
【発明の属する技術分野】本発明は、高温鋼材を冷却水
で冷却するときの鋼材表面における熱流束を予測し、鋼
材の温度変化を推定する方法とそれを用いた冷却制御方
法に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for estimating a heat flux on a steel material surface when cooling a high-temperature steel material with cooling water and estimating a temperature change of the steel material, and a cooling control method using the same.
【０００２】[0002]
【従来の技術】高温鋼材を冷却水で冷却するプロセス
は、鉄鋼の製造工程ではいたるところに見られる。例え
ば、熱間圧延ラインのランアウトテーブルでは圧延を終
えた鋼帯に冷却水をかけ、所定の冷却履歴を与えること
によって目的とする性能（強度、靱性など）を得てい
る。また、制御冷却法では、圧延終了後二相域（フェラ
イト＋オーステナイト組織）まで冷却し、その後加速冷
却することで微細なフェライト組織として、強度と靱性
を得ている。2. Description of the Related Art The process of cooling a high-temperature steel material with cooling water is ubiquitous in the steel manufacturing process. For example, in a run-out table of a hot rolling line, cooling water is applied to a rolled steel strip, and a predetermined cooling history is given to obtain desired performance (strength, toughness, etc.). In the controlled cooling method, the steel is cooled to a two-phase region (ferrite + austenite structure) after the completion of rolling, and then accelerated to obtain a fine ferrite structure to obtain strength and toughness.
【０００３】いずれの冷却工程においても、冷却速度、
冷却終了温度および冷却終了時間などを高精度で制御す
ることが重要である。制御冷却法を高い精度で実現する
には、高温鋼材と冷却水との間の熱流束を正確に予測す
ることが必要であり、これまで種々の予測モデルが提案
されている。[0003] In each cooling step, the cooling rate,
It is important to control the cooling end temperature and the cooling end time with high accuracy. In order to realize the controlled cooling method with high accuracy, it is necessary to accurately predict the heat flux between the high-temperature steel material and the cooling water, and various prediction models have been proposed so far.
【０００４】例えば、鋼板の冷却開始時の表面温度、冷
媒温度、冷媒流量の関数として表した熱伝達（熱流束）
方程式を解くことにより、平均冷却速度と冷却停止温度
の両方を満足する時間とともに漸減する冷媒流量ならび
に冷却時間を求め、冷媒流量と冷却時間に基づき鋼板の
冷却停止温度を目標値に近づけることによって鋼板を目
標温度に冷却する方法が提案されている（特開昭60-174
834号公報参照）。また、冷却装置の前段に予備冷却装
置を設け、これであらかじめ鋼板を冷却し、このときの
鋼板の冷却開始温度、冷却終了温度および通板速度の実
測値とから鋼板の熱伝達係数を求め、この熱伝達係数を
用いて、冷却装置により鋼板の温度が所定値になるよう
冷却する方法が提案されている（特開昭63-115610号公
報参照）。For example, heat transfer (heat flux) expressed as a function of the surface temperature at the start of cooling of a steel sheet, the refrigerant temperature, and the refrigerant flow rate
By solving the equation, the refrigerant flow rate and cooling time that gradually decrease with time that satisfies both the average cooling rate and the cooling stop temperature are obtained, and the steel sheet cooling stop temperature approaches the target value based on the refrigerant flow rate and the cooling time. There has been proposed a method of cooling a target to a target temperature (JP-A-60-174).
No. 834). In addition, a preliminary cooling device is provided in the preceding stage of the cooling device, and the steel plate is cooled in advance with this, and the heat transfer coefficient of the steel plate is determined from the cooling start temperature of the steel plate at this time, the cooling end temperature and the measured value of the passing speed, A method has been proposed in which a cooling device is used to cool the steel sheet to a predetermined value using the heat transfer coefficient (see Japanese Patent Application Laid-Open No. 63-115610).
【０００５】鋼板冷却時の熱伝達係数を予測する式は、
たとえばスプレー冷却の場合、日本鉄鋼協会が推奨する
下記(a)式および(b)式がある（日本鉄鋼協会編「鋼材の
強制冷却」（1978年）参照）。[0005] The equation for estimating the heat transfer coefficient when cooling a steel sheet is as follows:
For example, in the case of spray cooling, there are the following equations (a) and (b) recommended by the Iron and Steel Institute of Japan (see "Forced Cooling of Steel" edited by the Iron and Steel Institute of Japan (1978)).
【０００６】 θS≧500 ℃ Log α＝2.030＋0.793LogＷ−0.00154θS・・・・・・・(a) 200 ℃≦θS≦500 ℃ Logα＝2.694＋0.595LogＷ−0.00179θS ・・・・・・・(b) ただし、θｓは鋼材の表面温度（℃）、αは熱伝達係数
［kcal/(m2・hr・℃）］、Ｗは水量密度［リットル／(m2・mi
n)］である。Θ S ≧ 500 ° C. Log α = 2.030 + 0.793LogW−0.00154θ S ... (A) 200 ° C. ≦ θ S ≦ 500 ° C. Logα = 2.694 + 0.595LogW−0.00179θ S・ ・ ・(B) where θs is the surface temperature (° C) of the steel material, α is the heat transfer coefficient [kcal / (m 2 · hr · ° C)], and W is the water density [liter / (m 2 · mi).
n)].
【０００７】[0007]
【発明が解決しようとする課題】圧延を終えた高温の鋼
板を水冷すると、鋼板の温度によって冷却特性が大幅に
変化するので予測精度が悪くなる。When a hot rolled steel sheet is water-cooled, the cooling accuracy changes greatly depending on the temperature of the steel sheet, and the prediction accuracy deteriorates.
【０００８】高温（圧延を終えたときの温度、たとえば
700 ℃以上の温度）の鋼材を冷却水で冷却すると、鋼材
と冷却水との間に蒸気膜が発生し、鋼材と冷却水とが直
接接触できない状態となる。この状態を膜沸騰と称し、
鋼材の熱は蒸気膜を介して冷却水に移動するため冷却能
（熱流束）は低い。High temperature (the temperature at the end of rolling, for example,
When a steel material (at a temperature of 700 ° C. or higher) is cooled with cooling water, a steam film is generated between the steel material and the cooling water, and the steel material and the cooling water cannot be in direct contact. This state is called film boiling,
Since the heat of the steel material moves to the cooling water via the steam film, the cooling capacity (heat flux) is low.
【０００９】一方、鋼材温度が冷却によって低くなると
蒸気膜の発生は少なくなり、鋼材と冷却水とが接触する
領域が増え、ついには全て固液接触状態となる。この状
態を遷移沸騰から核沸騰と称し、鋼材の熱は直接冷却水
に移動するので、冷却能（熱流束）は高い。従来法によ
る熱流束予測方法は、膜沸騰領域での鋼材温度を予測す
る精度は比較的良好であるが、遷移沸騰から核沸騰にか
けての温度領域においては精度が悪い。On the other hand, when the temperature of the steel material is lowered by cooling, the generation of a vapor film is reduced, the area where the steel material comes into contact with the cooling water is increased, and all the materials are brought into a solid-liquid contact state. This state is called transition boiling to nucleate boiling, and since the heat of the steel material is directly transferred to the cooling water, the cooling capacity (heat flux) is high. The heat flux prediction method according to the conventional method has relatively good accuracy in predicting the steel material temperature in the film boiling region, but is inaccurate in the temperature region from transition boiling to nucleate boiling.
【００１０】本発明の目的は、圧延直後の鋼板を水冷却
するときの遷移沸騰以降の熱流束を精度良く予測し、冷
却中の鋼板の温度変化を予測する方法およびそれを用い
た冷却制御方法を提供することにある。An object of the present invention is to accurately predict a heat flux after transition boiling when cooling a steel sheet immediately after rolling with water, to predict a temperature change of the steel sheet during cooling, and a cooling control method using the same. Is to provide.
【００１１】[0011]
【課題を解決するための手段】本発明者らは、圧延直後
の鋼板を水冷却するときの冷却特性について研究をおこ
なった結果、遷移沸騰開始温度ＴMを考慮することによ
って遷移沸騰以降の熱流束を精度良く予測できることを
確認し、本発明を完成した。Means for Solving the Problems The present inventors have studied the cooling characteristics of water-cooled steel sheets immediately after rolling. As a result, the heat flow after the transition boiling was determined by considering the transition boiling start temperature T M. After confirming that the bundle can be accurately predicted, the present invention was completed.
【００１２】本発明の要旨は、下記の熱流束予測方法
およびその熱流束予測方法を用いた鋼材の冷却制御方
法にある。The gist of the present invention resides in the following heat flux prediction method and a method for controlling cooling of steel using the heat flux prediction method.
【００１３】高温鋼板を水冷却するときの熱流束を予
測する方法であって、鋼板の遷移沸騰開始温度ＴMを冷
却条件から予め設定し、遷移沸騰開始から核沸騰終了領
域までの冷却面における熱流束ｑを下記(3)〜(5)式によ
り求める熱流束予測方法。This is a method for estimating a heat flux at the time of cooling a high-temperature steel sheet with water, wherein a transition boiling start temperature T M of the steel sheet is set in advance from cooling conditions, and a cooling surface from a transition boiling start to a nucleate boiling end region is set. A heat flux prediction method for obtaining the heat flux q by the following equations (3) to (5).
【００１４】[0014]
【数３】 (Equation 3)
【００１５】ただし、ｑは冷却面における熱流束(W/
m2)、λは鋼の熱伝導率［W/(m・K)］、ｃは鋼の比熱［Ｊ
／(kg・K)］、ρは鋼の密度(kg/m3)、Ｑは冷却の強さを
表すパラメータ(℃／秒)、Ｔは鋼板の表面温度(℃)、ａ
はＱ2／［4(ＴM−ＴS)］、ＴSは核沸騰が終了する温度
(℃)およびｔは(5)式から求まる時間（遷移沸騰が開始
してからの時間、秒）である。Here, q is the heat flux (W /
m 2 ), λ is the thermal conductivity of the steel [W / (m · K)], c is the specific heat of the steel [J
/ (Kg · K)], ρ is the density of the steel (kg / m 3 ), Q is a parameter indicating the cooling strength (° C./sec), T is the surface temperature of the steel sheet (° C.), a
The temperature Q 2 / [4 (T M -T S)], T S is the end of nucleate boiling
(° C.) and t are the times (time from the start of the transition boiling, seconds) obtained from the equation (5).
【００１６】高温鋼板を水冷却するとき、遷移沸騰領
域から核沸騰領域までの熱流束を予測する方法であっ
て、鋼板の遷移沸騰開始温度ＴMを冷却条件から予め設
定し、遷移沸騰開始から核沸騰終了までの冷却面におけ
る熱流束ｑを前記(3)〜(5)式により求め、該熱流束に従
い鋼板温度変化を予測し、鋼板温度が目標温度になるよ
う冷却水量、鋼板速度を調整する冷却制御方法。[0016] The hot steel plate when the water cooling, a method of predicting the heat flux to the nucleate boiling region from the transition boiling region, preset the transition boiling initiation temperature T M of the steel plate from the cooling conditions, the start transition boiling The heat flux q on the cooling surface until the end of nucleate boiling is determined by the above formulas (3) to (5), the temperature change of the steel sheet is predicted according to the heat flux, and the cooling water amount and the steel sheet speed are adjusted so that the steel sheet temperature reaches the target temperature. Cooling control method.
【００１７】遷移沸騰開始温度ＴMは、冷却水量、鋼板
の搬送速度、材質、スケールの厚さの関数として求めて
おく。The transition boiling start temperature T M is determined as a function of the amount of cooling water, the conveying speed of the steel sheet, the material, and the thickness of the scale.
【００１８】[0018]
【発明の実施の形態】本発明の第１は、高温鋼材を水冷
却する際、冷却の初期段階すなわち膜沸騰領域では、そ
の熱伝達（熱流束）を従来通り「鋼材表面温度」と「冷
却条件」で定義される予測式から計算する。そして、鋼
の材質、冷却条件等によってあらかじめ求められた遷移
沸騰開始温度に達した時、本発明で示す熱伝達（熱流
束）導出式に切り替えて以後の遷移沸騰・核沸騰時の熱
伝達（熱流束）を求め、鋼材の温度変化を計算する。DESCRIPTION OF THE PREFERRED EMBODIMENTS The first aspect of the present invention is that when water is cooled in a high-temperature steel material, the heat transfer (heat flux) in the initial stage of cooling, that is, in the film boiling region, is conventionally performed by "steel material surface temperature" and "cooling". It is calculated from the prediction formula defined in “Condition”. Then, when the temperature reaches the transition boiling start temperature determined in advance by the material of the steel, the cooling condition, and the like, the heat transfer (heat flux) derivation formula shown in the present invention is switched to the heat transfer at the time of transition boiling and nucleate boiling ( Heat flux) and calculate the temperature change of the steel material.
【００１９】本発明の第２は、極めて強冷却か、あるい
は鋼材温度が比較的低く、水冷開始直後に濡れが発生
し、遷移沸騰・核沸騰が生じる場合は、はじめから本発
明で示す熱伝達（熱流束）導出式を用いて熱伝達（熱流
束）を求める。The second aspect of the present invention is that when the steel material is extremely cooled or the temperature of the steel material is relatively low and wetting occurs immediately after the start of water cooling to cause transition boiling and nucleate boiling, the heat transfer shown in the present invention from the beginning. (Heat flux) The heat transfer (heat flux) is calculated using the derivation formula.
【００２０】図２は、厚さの異なる高温鋼板を水スプレ
ーにより冷却したときの鋼板温度の時間経過（冷却曲
線）を示す図である。鋼板の温度は、厚さ(t)が９mmお
よび30mmの鋼板では水冷面から深さ３mmの位置に、厚さ
３mmの鋼板では水冷面の反対側の面に熱電対を取り付け
て測定を行った。いずれの鋼板厚さにおいても温度が35
0℃から450℃の範囲に変曲点（矢印の位置）があり、こ
れ以上の温度域では鋼板温度は緩やかに低下しており、
膜沸騰領域であることがわかる。一方、350℃から450℃
の範囲以下の温度域では鋼板温度は急激に低下してお
り、遷移沸騰・核沸騰領域であることがわかる。FIG. 2 is a diagram showing a time course (cooling curve) of the temperature of the steel sheet when high-temperature steel sheets having different thicknesses are cooled by water spray. The temperature of the steel plate was measured by attaching a thermocouple to the surface of the steel plate having a thickness (t) of 9 mm and 30 mm at a depth of 3 mm from the water-cooled surface, and attaching a thermocouple to the surface of the steel plate having a thickness of 3 mm opposite to the water-cooled surface. . Temperature of 35 for all steel thicknesses
There is an inflection point (position of the arrow) in the range of 0 ° C to 450 ° C, and in the temperature range higher than this, the steel sheet temperature decreases gradually,
It can be seen that this is a film boiling region. On the other hand, 350 ° C to 450 ° C
In the temperature range below the range, the temperature of the steel sheet sharply decreases, and it can be seen that the temperature is in the transition boiling / nucleate boiling range.
【００２１】図２から、各板厚の冷却曲線は、膜沸騰領
域では板厚によって異なるが、遷移沸騰・核沸騰領域で
は板厚による差は小さく、３本の曲線ともほぼ等しい形
状をしていることがわかる。これは、膜沸騰から遷移沸
騰・核沸騰に変化すると熱伝達（熱流束）が急激に上昇
するため、鋼板表面から冷却水への熱移動に鋼板内部か
らの熱移動が追いつかず、鋼板表面近傍の温度変化に及
ぼす板厚の影響が小さくなるためと考えられる。From FIG. 2, the cooling curve of each sheet thickness differs depending on the sheet thickness in the film boiling region, but the difference due to the sheet thickness is small in the transition boiling and nucleate boiling regions, and the three curves have substantially the same shape. You can see that there is. This is because heat transfer (heat flux) rises abruptly when film boiling changes to transition boiling / nucleate boiling, so that the heat transfer from the inside of the steel sheet cannot catch up with the heat transfer from the steel sheet surface to the cooling water, and the vicinity of the steel sheet surface It is considered that the influence of the sheet thickness on the temperature change of the steel sheet becomes small.
【００２２】そこで、本発明者らは、図２から遷移沸騰
・核沸騰領域における冷却面の温度変化は、板厚に関係
なくある１つの関数で近似できるのではないかと考え
た。そして、鋼板の冷却面温度がその関数に従って変化
すると仮定した時の熱流束を逆に導出する式を求めるこ
とにした。The inventors of the present invention thought from FIG. 2 that the temperature change of the cooling surface in the transition boiling / nucleate boiling region could be approximated by a certain function regardless of the plate thickness. Then, an equation for reversely deriving the heat flux when the cooling surface temperature of the steel sheet changes according to the function is determined.
【００２３】次に、本発明の遷移沸騰・核沸騰領域の熱
流束導出式について説明する。Next, the heat flux derivation formula in the transition boiling / nucleate boiling region of the present invention will be described.
【００２４】I．遷移沸騰・核沸騰時の冷却面の温度変
化について：遷移沸騰・核沸騰時の冷却面の温度変化を
次の二次式で近似した。I. Temperature change of the cooling surface during transition boiling and nucleate boiling: The temperature change of the cooling surface during transition boiling and nucleate boiling was approximated by the following quadratic equation.
【００２５】 Ｔ−ＴM＝ａ・ｔ2＋Ｑ・ｔ ・・・・・(1) ａ＝Ｑ2／［4(ＴM−ＴS）］ ・・・・・(2) ただし、Ｔは鋼板表面温度(℃)、ＴMは遷移沸騰開始温
度(℃)、ＴSは核沸騰の終了温度（通常は水の飽和温
度、℃）、Ｑは冷却の強さを表すパラメータ（負の値、
℃/秒）、ｔは後述の(5)式から求まる時間であり、遷移
沸騰が開始してからの時間（秒）である。[0025] T-T M = a · t 2 + Q · t ····· (1) a = Q 2 / [4 (T M -T S)] ····· (2) where, T is Steel sheet surface temperature (° C), T M is transition boiling onset temperature (° C), T S is nucleate boiling end temperature (usually water saturation temperature, ° C), and Q is a parameter (negative value) representing cooling intensity. ,
° C / sec) and t are the times determined from the expression (5) described later, and are the times (seconds) from the start of the transition boiling.
【００２６】II．熱流束を求める式について：遷移沸騰
開始時には鋼板内部に温度分布がなく、Ｔ＝ＴMと一定
であると仮定する。また、冷却面における遷移沸騰・核
沸騰時の温度変化は非常に急激であり、短い時間につい
ては温度変化として冷却面近傍のみを考慮すればよいの
で、鋼板は厚さ方向に半無限体と仮定すると、この場合
の冷却面における熱流束の変化は、下記の(3) 式のよう
に表すことができる。II. Formula for calculating heat flux: It is assumed that there is no temperature distribution inside the steel sheet at the start of transition boiling and that T = TM is constant. In addition, the temperature change during transition boiling and nucleate boiling on the cooling surface is very rapid, and for short periods, only the vicinity of the cooling surface needs to be considered as the temperature change, so the steel sheet is assumed to be a semi-infinite body in the thickness direction. Then, the change of the heat flux on the cooling surface in this case can be expressed as the following equation (3).
【００２７】[0027]
【数４】 (Equation 4)
【００２８】ただし、ｑは冷却面における熱流束（Ｗ／
ｍ2）、λは鋼の熱伝導率［Ｗ／(ｍ・Ｋ)］、ｃは鋼の比
熱［Ｊ／(kg・Ｋ)］、ρは鋼の密度（kg／ｍ3）である。Here, q is the heat flux (W /
m 2 ), λ is the thermal conductivity of the steel [W / (m · K)], c is the specific heat of the steel [J / (kg · K)], and ρ is the density of the steel (kg / m 3 ).
【００２９】前記(1)式をｔについて解いて得られる(5)
式によって、冷却面の各温度Ｔにおける時間ｔを求
め、これを（3)式に代入することによって各冷却面温度
における熱流束を求めることができる。(5) obtained by solving the above equation (1) for t
The time t at each temperature T of the cooling surface is obtained by the equation, and the heat flux at each cooling surface temperature can be obtained by substituting the time into the equation (3).
【００３０】[0030]
【数５】 (Equation 5)
【００３１】以上、(2)〜(5)式を用いて遷移沸騰から核
沸騰までの熱流束を求めることが本発明方法の骨子とな
る。As described above, determining the heat flux from transition boiling to nucleate boiling using the equations (2) to (5) is the gist of the method of the present invention.
【００３２】しかし、実際には遷移沸騰開始時、鋼材内
部には温度分布が生じており、(3)式の導出でのＴ＝ＴM
（一定）の仮定が成立せず、遷移沸騰の初期段階で誤差
を生じてしまう。したがって、以下に説明する補正が必
要となる。補正方法として次に示す２例を挙げることが
できる。[0032] However, when actually starting transition boiling, inside the steel has a temperature distribution occurs, (3) T = T M in the derivation of formula
The (constant) assumption is not satisfied, and an error occurs in the initial stage of transition boiling. Therefore, the correction described below is required. The following two examples can be given as a correction method.
【００３３】図５は、補正の方法を説明するための模式
図である。FIG. 5 is a schematic diagram for explaining a correction method.
【００３４】いずれの方法も基本的には図５に示すよう
に(3)式から求められるＴMでの熱流束ｑが、遷移沸騰開
始直前の熱流束ｑMと等しくなるように見掛けの遷移沸
騰開始温度ＴM'をＴMよりも高温側に設定し、このＴM'
を以後の熱流束計算でＴMとして使用するというもので
ある。In any of the methods, basically, as shown in FIG. 5, an apparent transition such that the heat flux q at T M obtained from the equation (3) becomes equal to the heat flux q M immediately before the start of transition boiling. The boiling start temperature T M ′ is set higher than T M , and this T M ′
Is used as T M in the subsequent heat flux calculation.
【００３５】第１の方法は、ＴM'を数値解析によって
計算機を使用して求める方法である。The first method is to find T M ′ by using a computer by numerical analysis.
【００３６】具体的には(3)式においてｑ＝ｑM、(5)式
は、 ｔ＝｛−Ｑ−［Ｑ2＋4ａ（ＴM−ＴM'）］0.5｝／(2ａ)・・・・・・(6) (2)式は、 ａ＝Ｑ2／［4（ＴM'−ＴS）］・・・・・・・・・・・・・・・・・・（７） が成立するものとして、未知数ＴＭ’を既知の数値計算
手法によって求めるものである。[0036] Specifically, (3) q = q M in equation (5) is, t = {- Q- [Q 2 + 4a (T M -T M ')] 0.5} / (2a) ·· ... (6) (2) is, a = Q 2 / [4 (T M '-T S)] ·················· (7) Is established, the unknown number T M ′ is obtained by a known numerical calculation method.
【００３７】第２の方法は、ＴM'を近似的に以下の式
で求める方法である。In the second method, T M ′ is approximately obtained by the following equation.
【００３８】[0038]
【数６】 (Equation 6)
【００３９】(8)式は、次のようにして得られた。Equation (8) was obtained as follows.
【００４０】(3)式においてｑ＝ｑMとおくとともに、ｔ
が小さければ、(3)式は第２項が支配的であるので、 ｑM＝2ｂ・Ｑ（ｔ／π）0.5 となり、よって ｔ＝π［ｑM／（2ｂ・Ｑ）］2 となる。In equation (3), q = q M and t
Is small, the second term is dominant in equation (3), so that q M = 2b · Q (t / π) 0.5 , and therefore t = π [q M / (2b · Q)] 2 .
【００４１】これを(6)式に代入し、展開することで(8)
式を得る。ただし、このときのａは(2)式より求める。By substituting this into equation (6) and expanding it, (8)
Get the expression. However, a at this time is obtained from equation (2).
【００４２】以上が、本発明の遷移沸騰・核沸騰の熱流
束を導出する方法であり、特に遷移沸騰・核沸騰時の冷
却曲線を二次式で近似した場合について説明したが、他
の近似式を用いた場合についても考え方は同様である。The above is the method of deriving the heat flux of transition boiling and nucleate boiling according to the present invention. In particular, the case where the cooling curve during transition boiling and nucleate boiling is approximated by a quadratic equation has been described. The same applies to the case where an expression is used.
【００４３】本発明方法の最大の特徴は、熱流束導出式
（(2)〜(5)式）中に遷移沸騰開始温度ＴMを含んでいる
点であり、これにより、後述するが、ＴMによる遷移沸
騰・核沸騰域の熱流束の変動を予測できるようになって
いる。The most important feature of the method of the present invention is that the heat flux derivation equations (Equations (2) to (5)) include the transition boiling onset temperature T M. It is possible to predict fluctuations in heat flux in the transition boiling and nucleate boiling regions due to M.
【００４４】また、本発明方法で言及している遷移沸騰
開始温度ＴMは、「膜沸騰下限界温度」と同義であり、
現象的にはこの温度で「濡れの発生」が観察されるので
「濡れの発生温度」と考えてもよい。The transition boiling start temperature T M referred to in the method of the present invention is synonymous with “the lower limit of film boiling temperature”.
Phenomenologically, "generation of wetting" is observed at this temperature, so it may be considered as "temperature at which wetting occurs".
【００４５】[0045]
【実施例】図３は、加熱された鋼板を水で冷却するとき
の試験装置を示す図である。図において、鋼板1は、厚
さ３mm、一辺の長さが150 mmのオーステナイト系ステン
レス鋼（SUS 310S）の平板である。熱電対2を鋼板1の下
面中央部に溶接によって固定し、これを温度記録計4に
入力し、鋼板1の温度を測定記録した。FIG. 3 is a diagram showing a test apparatus for cooling a heated steel plate with water. In the drawing, a steel plate 1 is a flat plate of austenitic stainless steel (SUS 310S) having a thickness of 3 mm and a side length of 150 mm. The thermocouple 2 was fixed to the center of the lower surface of the steel sheet 1 by welding, and this was input to the temperature recorder 4, and the temperature of the steel sheet 1 was measured and recorded.
【００４６】試験は、熱電対2を取付けた鋼板1を加熱炉
で800 ℃以上に加熱し、図３の試験装置にセットし、鋼
板温度が800 ℃になったときフルコーン型スプレーノズ
ル3を用い、鋼板の上面に冷却水を吹き付け冷却し、鋼
板温度を測定した。In the test, the steel plate 1 to which the thermocouple 2 was attached was heated to 800 ° C. or more in a heating furnace, set in the test apparatus shown in FIG. 3, and when the steel plate temperature reached 800 ° C., the full cone type spray nozzle 3 was used. Then, cooling water was sprayed on the upper surface of the steel sheet to cool the steel sheet, and the temperature of the steel sheet was measured.
【００４７】図４は、試験によって得られた冷却曲線
（鋼板温度の経時変化）を示す図である。２つの曲線D1
およびD2は、同一冷却条件で冷却したにも関わらず、遷
移沸騰開始時期が異なり、冷却の終了時間に差が生じて
いる。この２つの曲線における遷移沸騰開始時期の相違
は、残存スケールの有無の違いであり、D1は冷却前にデ
スケーリングした場合、D2はデスケーリングしなかった
場合である。FIG. 4 is a diagram showing a cooling curve (temporal change in steel sheet temperature) obtained by the test. Two curves D1
Although D2 and D2 were cooled under the same cooling conditions, the transition boiling start timings were different, and there was a difference in the cooling end time. The difference between the transition boiling start times in these two curves is the difference in the presence or absence of the residual scale, where D1 is the case where descaling is performed before cooling and D2 is the case where no descaling is performed.
【００４８】図１は、高温鋼材を水冷却したときの熱流
束曲線を示す図である。曲線A1およびA2で示す熱流束
は、図４の実測値D1およびD2から既知の逆計算手法によ
って計算機を用いて求めたものであり、真の熱流束曲線
（実験値）といえる。また曲線Ｂで示す熱流束は、前述
の日本鉄鋼協会が推奨する(a) 式および(b) 式によって
計算した。FIG. 1 is a diagram showing a heat flux curve when a high-temperature steel material is water-cooled. The heat fluxes indicated by the curves A1 and A2 are obtained from the actual measured values D1 and D2 in FIG. 4 using a computer by a known inverse calculation method, and can be said to be true heat flux curves (experimental values). The heat flux shown by the curve B was calculated by the equations (a) and (b) recommended by the Iron and Steel Institute of Japan described above.
【００４９】２つの曲線A1およびA2は、鋼板表面温度が
約330 ℃あるいは約440 ℃において急激に熱流束が増加
しており、これらの温度を境に高温側で膜沸騰、低温側
で遷移沸騰・核沸騰であることがわかる。この境となる
温度が遷移沸騰開始温度である。また、２つの曲線A1、
A2は、同じ冷却条件で遷移沸騰開始温度が異なる場合の
熱流束曲線を示したものであるが、遷移沸騰・核沸騰域
の熱流束は遷移沸騰開始温度の違いで大きく変動し、鋼
材表面温度だけで一義的に定義できるものではないこと
がわかる。The two curves A1 and A2 show that the heat flux sharply increases when the steel sheet surface temperature is about 330 ° C. or about 440 ° C., and at these temperatures, the film boiling occurs on the high temperature side and the transition boiling occurs on the low temperature side. -It turns out that it is nucleate boiling. The temperature at this boundary is the transition boiling start temperature. Also, two curves A1,
A2 shows the heat flux curve when the transition boiling onset temperature is different under the same cooling conditions.The heat flux in the transition boiling and nucleate boiling regions fluctuates greatly due to the difference in transition boiling onset temperature, and the steel surface temperature It can be seen that it cannot be uniquely defined by itself.
【００５０】一方、図１より従来の推定式で求めた曲線
Ｂは、この遷移沸騰開始温度が不明瞭な曲線となってお
り、必ずしも忠実に水冷却特性を表しているものではな
いことがわかる。従来、実製造ラインで用いられている
鋼材温度予測モデルも多くは遷移沸騰開始温度を考慮し
ていないか、あるいは考慮していても、その温度で熱伝
達（熱流束）の導出式が切り替わるだけで、熱伝達（熱
流束）は「遷移沸騰開始温度」に無関係に「鋼材表面温
度」や「冷却条件」の関数として一義的に導出され、熱
伝達（熱流束）の値自体が、ＴMによって変動するモデ
ルは提案されていなかった。On the other hand, it can be seen from FIG. 1 that the curve B obtained by the conventional estimation formula is a curve in which the transition boiling start temperature is unclear, and does not always accurately represent the water cooling characteristic. . Conventionally, many steel temperature prediction models used in actual production lines do not consider the transition boiling onset temperature, or even if they do, the derivation formula of heat transfer (heat flux) switches at that temperature. The heat transfer (heat flux) is uniquely derived as a function of the “steel surface temperature” and “cooling condition” regardless of the “transition boiling start temperature”, and the value of the heat transfer (heat flux) itself is T M A model that fluctuates according to was not proposed.
【００５１】本発明方法は、ＴMで熱伝達（熱流束）の
導出式が切り替わり、かつ、遷移沸騰・核沸騰域の熱流
束の値が、ＴMの値によって変化する点が従来法と異な
る。The method of the present invention is different from the conventional method in that the derivation formula of heat transfer (heat flux) is switched at T M , and the value of the heat flux in the transition boiling / nucleate boiling region changes depending on the value of T M. different.
【００５２】従来法による熱伝達（熱流束）予測方法
は、膜沸騰領域での鋼材温度を予測する精度は比較的良
好であるが、遷移沸騰・核沸騰領域においては精度が悪
くなる。この原因は、従来法は遷移沸騰・核沸騰時の熱
伝達（熱流束）が遷移沸騰開始時の鋼板温度ＴMによっ
て変動することを考慮していないものであるためであ
る。In the heat transfer (heat flux) prediction method according to the conventional method, the accuracy of predicting the steel material temperature in the film boiling region is relatively good, but the accuracy is poor in the transition boiling / nucleate boiling region. The reason for this is that the conventional method does not consider that the heat transfer (heat flux) at the time of transition boiling / nucleate boiling varies depending on the steel sheet temperature T M at the start of transition boiling.
【００５３】従って、冷却水での冷却時の遷移沸騰・核
沸騰領域の熱伝達（熱流束）を高精度に予測するために
は、遷移沸騰開始温度の変動を考慮することが不可欠で
あり、特に比較的低温域の冷却制御を高精度に実現する
ための基礎技術となる。Therefore, in order to predict the heat transfer (heat flux) in the transition boiling / nucleate boiling region at the time of cooling with the cooling water with high accuracy, it is indispensable to consider the fluctuation of the transition boiling start temperature. In particular, it is a basic technology for realizing cooling control in a relatively low temperature range with high accuracy.
【００５４】本発明方法による熱流束曲線の予測値は、
それぞれ曲線Ｃのように求めることができる。曲線Ｃは
共にＱ＝−100 、ｂ＝8000、ＴS＝100 、そしてＴM＝44
0 、330 をそれぞれ用いて熱流束を計算し、前述のの
方法で補正を行ったものである。The predicted value of the heat flux curve according to the method of the present invention is
Each of them can be obtained as shown by a curve C. Curves C both have Q = −100, b = 8000, T S = 100, and T M = 44
The heat flux is calculated by using 0 and 330, respectively, and corrected by the above-described method.
【００５５】図１に、熱流束曲線における本発明方法に
よる予測値（曲線Ｃ）と、従来の予測方法による予測値
（曲線Ｂ）の比較を示した。同図から、従来の予測方法
では、曲線Ｂに示すように遷移沸騰開始温度の変動を考
慮しておらず、水冷特性を忠実に反映したものとは言い
難い。しかし、本発明の予測方法では、曲線Ｃに示すよ
うに試験値（曲線A1,A2 ）とほぼ合致しているのがわか
る。即ち、本発明の予測方法は、遷移沸騰開始温度の変
動による遷移沸騰・核沸騰時の熱伝達（熱流束）の変化
を予測することができる。FIG. 1 shows a comparison between the predicted value (curve C) of the heat flux curve according to the method of the present invention and the predicted value (curve B) of the conventional prediction method. From the figure, it is difficult to say that the conventional prediction method faithfully reflects the water-cooling characteristics without considering the change in the transition boiling start temperature as shown by the curve B. However, according to the prediction method of the present invention, as shown by the curve C, it can be seen that the values almost match the test values (curves A1 and A2). That is, the prediction method of the present invention can predict a change in heat transfer (heat flux) during transition boiling / nucleate boiling due to a change in transition boiling start temperature.
【００５６】図４に図１の本発明方法による熱流束曲線
（曲線Ｃ）を境界条件として用いて、数値差分計算によ
り求めた冷却曲線の予測値（曲線Ｅ）を示した。予測値
（曲線Ｅ）と試験値（曲線Ｄ）は良好に一致している。FIG. 4 shows a predicted value (curve E) of a cooling curve obtained by numerical difference calculation using the heat flux curve (curve C) according to the method of the present invention of FIG. 1 as a boundary condition. The predicted values (curve E) and the test values (curve D) are in good agreement.
【００５７】本発明の予測方法を熱間圧延ラインに適用
した。The prediction method of the present invention was applied to a hot rolling line.
【００５８】厚さ３mm、幅２ｍ、長さ600 ｍの鋼板
（Ｃ：0.07重量％、Si：0.78重量％、Mn：1.49重量％、
Ｐ：0.01重量％、Ｓ：0.0004重量％、その他不純物およ
びFe）を、制御冷却した後に巻取る際の巻取り温度を予
測した。A steel plate having a thickness of 3 mm, a width of 2 m and a length of 600 m (C: 0.07% by weight, Si: 0.78% by weight, Mn: 1.49% by weight,
P: 0.01% by weight, S: 0.0004% by weight, other impurities and Fe) were subjected to a controlled cooling, and the winding temperature at the time of winding was predicted.
【００５９】冷却条件は、搬送速度580ｍ／分、圧延終
了温度＝850℃、冷却水温度＝33℃とした。また、冷却
制御は熱延冷却ライン上下面の分割されている冷却ゾー
ンの稼働数を逐次変更して行った。The cooling conditions were as follows: transport speed 580 m / min, rolling end temperature = 850 ° C., cooling water temperature = 33 ° C. The cooling control was performed by sequentially changing the number of operating cooling zones divided into upper and lower surfaces of the hot rolling cooling line.
【００６０】本発明の発明方法ではＱ＝−30、ＴM＝500
を用い、さらに前述の方法で補正を行って得られた熱
流束を用いて予測を行った結果、450 ℃であった。In the method of the present invention, Q = −30 and T M = 500
The temperature was 450 ° C. as a result of performing prediction using the heat flux obtained by performing the above-mentioned correction and further performing the correction by the method described above.
【００６１】比較例として、鉄鋼協会推奨式(a)および
(b)式を用いて熱伝達率の鋼板表面温度に対する関数式
で予測を行った結果、560 ℃であった。As comparative examples, the formula (a) recommended by the Iron and Steel Institute
As a result of predicting the heat transfer coefficient by a function formula with respect to the steel sheet surface temperature using the formula (b), it was 560 ° C.
【００６２】このときの実測巻取り温度は440 ℃であっ
たので、予測誤差は、本発明方法では２％［（450−44
0)÷440×100］、比較例では27％［（560−440）÷440
×100］であった。Since the measured winding temperature at this time was 440 ° C., the prediction error was 2% [(450−44) in the method of the present invention.
0) ÷ 440 × 100], 27% in the comparative example [(560−440) ÷ 440
× 100].
【００６３】実機においては、ＴMは前述のように冷却
水量、鋼板の搬送速度、材質、スケールの厚さの関数と
して求めておき、また、Ｑに関しても同様の諸条件に対
する関数を予め用意しておくことで、極めて高精度な冷
却制御が可能となる。In the actual machine, T M is obtained as a function of the amount of cooling water, the conveying speed of the steel sheet, the material, and the thickness of the scale as described above. For Q, functions for the same various conditions are prepared in advance. By doing so, extremely accurate cooling control becomes possible.
【００６４】[0064]
【発明の効果】本発明の熱伝達（熱流束）予測方法は、
水冷面に濡れが発生した時の鋼板表面温度（遷移沸騰開
始温度）を取り入れたので、遷移沸騰領域および核沸騰
領域の鋼板の温度を正確に予測することができる。この
方法を使用した鋼板の制御冷却では、得られる鋼質のバ
ラツキを少なくできる。The heat transfer (heat flux) prediction method of the present invention is as follows.
Since the steel sheet surface temperature (transition boiling start temperature) when wetting occurs on the water-cooled surface is adopted, the temperature of the steel sheet in the transition boiling region and the nucleate boiling region can be accurately predicted. The controlled cooling of the steel sheet using this method can reduce the variation in the obtained steel quality.
【図１】高温鋼材を水冷却したときの冷却特性（熱流束
曲線）を示す図である。FIG. 1 is a diagram showing cooling characteristics (heat flux curves) when a high-temperature steel material is water-cooled.
【図２】厚さの異なる高温鋼板を水スプレーによる冷却
を行ったときの鋼板温度の時間経過（冷却曲線）を示す
図である。FIG. 2 is a diagram showing a time course (cooling curve) of a steel sheet temperature when a high-temperature steel sheet having different thicknesses is cooled by water spray.
【図３】加熱された鋼板を水で冷却するときの試験装置
を示す図である。FIG. 3 is a diagram showing a test apparatus when a heated steel plate is cooled with water.
【図４】試験によって得られた冷却曲線（鋼板温度の経
時変化）を示す図である。FIG. 4 is a diagram showing a cooling curve (temporal change in steel sheet temperature) obtained by a test.
【図５】補正の方法を説明するための模式図である。FIG. 5 is a schematic diagram for explaining a correction method.
１．鋼板 ２．熱電対 ３．冷却ノズル ４．温度記録計 1. Steel plate 2. Thermocouple 3. Cooling nozzle 4. Temperature recorder
Claims (2)
する方法であって、鋼板の遷移沸騰開始温度ＴMを冷却
条件から予め設定し、遷移沸騰開始から核沸騰終了領域
までの冷却面における熱流束ｑを下記(3)〜(5)式により
求めることを特徴とする熱流束予測方法。 【数１】 ただし、ｑは冷却面における熱流束(W/m2)、λは鋼の熱
伝導率［W/(m・K)］、ｃは鋼の比熱［Ｊ／(kg・K)］、ρ
は鋼の密度(kg/m3)、Ｑは冷却の強さを表すパラメータ
(℃／秒)、Ｔは鋼板の表面温度(℃)、ａはＱ2／［4(ＴM
−ＴS)］、ＴSは核沸騰が終了する温度(℃)およびｔは
(5)式から求まる時間（遷移沸騰が開始してからの時
間、秒）である。1. A method for predicting a heat flux when a high-temperature steel sheet is water-cooled, wherein a transition boiling start temperature T M of the steel sheet is set in advance from cooling conditions, and cooling from a transition boiling start to a nucleate boiling end region is performed. A heat flux prediction method, wherein a heat flux q on a surface is obtained by the following equations (3) to (5). (Equation 1) Here, q is the heat flux on the cooling surface (W / m 2 ), λ is the thermal conductivity of the steel [W / (m · K)], c is the specific heat of the steel [J / (kg · K)], ρ
Is the density of the steel (kg / m 3 ), Q is the parameter indicating the cooling strength
(° C./second), T is the surface temperature of the steel sheet (° C.), and a is Q 2 / [4 (T M
−T s )], where T s is the temperature at which nucleate boiling ends (° C.) and t is
This is the time (time from the start of transition boiling, seconds) obtained from equation (5).
から核沸騰領域までの熱流束を予測する方法であって、
鋼板の遷移沸騰開始温度ＴMを冷却条件から予め設定
し、遷移沸騰開始から核沸騰終了までの冷却面における
熱流束ｑを下記(3)〜(5)式により求め、該熱流束に従い
鋼板温度変化を予測し、鋼板温度が目標温度になるよう
冷却水量、鋼板速度を調整することを特徴とする冷却制
御方法。 【数２】 ただし、ｑは冷却面における熱流束(W/m2)、λは鋼の熱
伝導率［W/(m・K)］、ｃは鋼の比熱［Ｊ／(kg・K)］、ρ
は鋼の密度(kg/m3)、Ｑは冷却の強さを表すパラメータ
(℃／秒)、Ｔは鋼板の表面温度(℃)、ａはＱ2／［4(ＴM
−ＴS)］、ＴSは核沸騰が終了する温度(℃)およびｔは
(5)式から求まる時間（遷移沸騰が開始してからの時
間、秒）である。2. A method for predicting a heat flux from a transition boiling region to a nucleate boiling region when cooling a high-temperature steel sheet with water,
The transition boiling start temperature T M of the steel sheet is set in advance from the cooling conditions, the heat flux q on the cooling surface from the start of transition boiling to the end of nucleate boiling is obtained by the following equations (3) to (5), and the steel sheet temperature is calculated according to the heat flux. A cooling control method comprising predicting a change and adjusting a cooling water amount and a steel sheet speed so that the steel sheet temperature becomes a target temperature. (Equation 2) Here, q is the heat flux on the cooling surface (W / m 2 ), λ is the thermal conductivity of the steel [W / (m · K)], c is the specific heat of the steel [J / (kg · K)], ρ
Is the density of the steel (kg / m 3 ), Q is the parameter indicating the cooling strength
(° C./second), T is the surface temperature of the steel sheet (° C.), and a is Q 2 / [4 (T M
−T s )], where T s is the temperature at which nucleate boiling ends (° C.) and t is
This is the time (time from the start of transition boiling, seconds) obtained from equation (5).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP10118637A JPH11309507A (en) | 1998-04-28 | 1998-04-28 | Method for estimating thermal flux in cooling of steel and cooling control method using the same |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP10118637A JPH11309507A (en) | 1998-04-28 | 1998-04-28 | Method for estimating thermal flux in cooling of steel and cooling control method using the same |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPH11309507A true JPH11309507A (en) | 1999-11-09 |
Family
ID=14741477
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP10118637A Pending JPH11309507A (en) | 1998-04-28 | 1998-04-28 | Method for estimating thermal flux in cooling of steel and cooling control method using the same |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH11309507A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2010079452A1 (en) * | 2009-01-09 | 2010-07-15 | Fives Stein | Method and section for cooling a moving metal belt by spraying liquid |
| JP2013076593A (en) * | 2011-09-30 | 2013-04-25 | Nippon Steel & Sumitomo Metal | Method for predicting temperature distribution in metal plate and method of manufacturing metal plate |
| CN110834032A (en) * | 2019-10-10 | 2020-02-25 | 中冶南方连铸技术工程有限责任公司 | Method and device for tracking temperature of casting blank in continuous casting and rolling temperature field |
-
1998
- 1998-04-28 JP JP10118637A patent/JPH11309507A/en active Pending
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2010079452A1 (en) * | 2009-01-09 | 2010-07-15 | Fives Stein | Method and section for cooling a moving metal belt by spraying liquid |
| FR2940978A1 (en) * | 2009-01-09 | 2010-07-16 | Fives Stein | METHOD AND COOLING SECTION OF A METAL BAND THROUGH A PROJECTION OF A LIQUID |
| CN102272338A (en) * | 2009-01-09 | 2011-12-07 | 法孚斯坦因公司 | Method and section for cooling a moving metal belt by spraying liquid |
| US8918199B2 (en) | 2009-01-09 | 2014-12-23 | Fives Stein | Method and section for cooling a moving metal belt by spraying liquid |
| JP2015083719A (en) * | 2009-01-09 | 2015-04-30 | フイブ・スタン | Method of cooling moving metal belt by spraying liquid and section |
| JP2013076593A (en) * | 2011-09-30 | 2013-04-25 | Nippon Steel & Sumitomo Metal | Method for predicting temperature distribution in metal plate and method of manufacturing metal plate |
| CN110834032A (en) * | 2019-10-10 | 2020-02-25 | 中冶南方连铸技术工程有限责任公司 | Method and device for tracking temperature of casting blank in continuous casting and rolling temperature field |
| CN110834032B (en) * | 2019-10-10 | 2021-06-29 | 中冶南方连铸技术工程有限责任公司 | Method and device for tracking temperature of casting blank in continuous casting and rolling temperature field |
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