JPH11309507A - Method for estimating thermal flux in cooling of steel and cooling control method using the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To exactly estimate a steel temperature in the range of transition boiling and nucleate boiling. SOLUTION: A method for estimating thermal flux when a high temperature steel plate is water-cooled in which a transition boiling starting temperature TM of a steel plate is previously set and thermal flux q on a cooling surface in a region from the starting of transition boiling to finishing of nucleate boiling is obtained by following formulas. In the formulas, q is thermal flux on the cooling surface (W/m<2> ), λ is heat conductivity of steel [W/(m.k)], c is specific heat of steel [J/(kg.k)], ρ is density of steel (kg/m<3> ), Q is a paremeter indicating cooling intensity ( deg.C/sec), T is a surface temperature of the steel plate ( deg.C), a is Q2 /[4(TM-TS)], TS is a temperature at finishing of mucleate boiling ( deg.C), t is a time obtained from formula (5) (time from starting of transition boiling, sec). The formulas are q=[8b/3π<0.5> ]a.t<1.5> +[2b/π<0.5> ]Q.t<0.5> , b=(λ.c.p)<0.5> and t=-Q- Q<2> +4a(T-TM)}<0.5> /2a.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

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]

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] 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.

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] 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)).

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]

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.

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.

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.

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]

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.

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.

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]

(Equation 3)

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] 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.

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]

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.

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.

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.

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.

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.

Next, the heat flux derivation formula in the transition boiling / nucleate boiling region of the present invention will be described.

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-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.

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]

(Equation 4)

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 ).

(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]

(Equation 5)

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] 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.

FIG. 5 is a schematic diagram for explaining a correction method.

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.

The first method is to find T _M ′ by using a computer by numerical analysis.

[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.

In the second method, T _M ′ is approximately obtained by the following equation.

[0038]

(Equation 6)

Equation (8) was obtained as follows.

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 .

By substituting this into equation (6) and expanding it, (8)
Get the expression. However, a at this time is obtained from equation (2).

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.

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.

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]

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

The prediction method of the present invention was applied to a hot rolling line.

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.

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.

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.

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.

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].

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]

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.

[Brief description of the drawings]

FIG. 1 is a diagram showing cooling characteristics (heat flux curves) when a high-temperature steel material is water-cooled.

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.

FIG. 3 is a diagram showing a test apparatus when a heated steel plate is cooled with water.

FIG. 4 is a diagram showing a cooling curve (temporal change in steel sheet temperature) obtained by a test.

FIG. 5 is a schematic diagram for explaining a correction method.

[Explanation of symbols]

 1. Steel plate 2. Thermocouple 3. Cooling nozzle 4. Temperature recorder

Claims (2)

[Claims] 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). 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).