KR920010528B1 - Method for deciding the amount of absorbing heat of the heat furnace - Google Patents

Abstract

(1) measuring actual temperature (Tn-m) of the inside of steel and atmosphere temperature (Tg) of heating furnace, (2) deducing pre-estimated temperature (T1) of the sample volume with the temperature distribution estimating equation, (3) calculating and minimizing evaluated function (P) as an equations of (I) and (II), (4) calculating the total thermal absorption ratio of heating furnace (φCG) by an equation of (III) [Where qK,; = heat flow rate, Ts, i = surface temperature of steel .

Description

Determination method of overall heat absorption rate of furnace

1A is a schematic diagram showing the position of the data logger, (b) is an enlarged view of the main part of (a) in which the data logger is enlarged, and (c) is a schematic diagram showing the temperature measuring point position.

2 is a schematic diagram showing selection of representative volume for predicting steel temperature distribution.

3 is a graph showing the temperature change according to the material time (minutes) for the skid portion.

4 is a graph showing the temperature change according to the idle time (minutes) for the non-skid part.

5 is a graph showing the change in the overall heat absorption rate according to the idle time (minutes) for the skid portion.

6 is a graph showing the change in the overall heat absorption rate for the idle time (minutes) for the non-skid part.

7 is a graph showing the temperature deviation according to the idle time (minutes) for the skid portion.

8 is a graph showing a temperature deviation with respect to minutes of non-skid parts.

The present invention relates to a method of determining the heat flux of the steel surface for accurately predicting the internal temperature of the steel when the steel is heated, and more particularly, to determine the heat flux of the heating furnace to determine the heat flux of the steel surface It is about how to decide.

In general, the method of estimating the internal temperature distribution of steel in the heating furnace is to solve the internal temperature by solving the thermal conductivity equation in the following equation 1) by using the ambient temperature and the heat absorption of the steel surface when the temperature of the steel is not measured directly. How to predict.

Where ρ: steel density, C _P : steel specific heat, T: temperature, T: time, (x, y, z): thickness, length, widthwise displacement, λ: thermal conductivity.

In other words, this method predicts the internal temperature by solving the equation given the boundary and initial conditions of Eq. (1). In this case, considering the representative volume for the forced internal temperature prediction in the thickness direction as shown in FIG. 2, the boundary condition and initial condition of Equation (1) can be represented as follows.

Where H represents the thickness of the steel. However, in this method, since the furnace conditions change from time to time, the heat absorption rate, which is a function of temperature, gas component, gas layer thickness, etc., is continuously changed, making it difficult to determine accurate surface heat flux, and therefore, it is more difficult to obtain accurate steel internal temperature.

Therefore, in the present invention, in order to find a more accurate internal temperature of the steel, the present invention was to find a method of directly measuring the temperature in the steel and determining the surface heat flux satisfying the temperature distribution in the measured steel.

In addition, in order to verify the reliability of the obtained surface heat flux, the measured temperature distribution and the obtained surface heat flux are substituted into the boundary conditions of equations (1-1) to (1-4), and the equation (1) is solved. The results were compared.

The overall heat absorption rate is an index that indicates the degree of absorption rate of heat input by radiation and convection to the steel surface according to the shape of the furnace, atmosphere temperature, gas composition, etc., and cannot be determined without directly measuring the internal temperature of the steel. As time goes by, the location and atmosphere of the steel are changed.

In order to determine the overall heat absorption rate, the temperature distribution in the steel is measured and the heat flux of the surface (upper and lower) satisfying the measured temperature distribution is determined. Hereinafter, the method for determining the surface heat flux according to the present invention will be described in detail.

분포를 측정한다. 이때, 내부 측정점은 가능한한 수채해석적으로 풀기위해 정한 절점(node)과 유사한 위치에 정한다. 가열로(1)내의 강재(2)내부 온도측정방법은 제1a도 및 제1b도와 같이 설치하고 온도이력은 내열데이터로거(3)를 이용하여 받은 다음 로밖으로 강재(2)가 추출된 후 데이터로거의 메모리기판을 온도이력 독출장치에 걸어서 온도를 알 수 있다.1) First, the temperature inside the steel

Measure the distribution. At this time, the internal measurement point should be located at the position similar to the node defined for solving the problem as possible. The internal temperature measurement method of the steel (2) in the furnace (1) is installed as shown in Figs. 1a and 1b, and the temperature history is received using the heat-resistant data logger (3), and then the steel (2) is extracted out of the furnace. The temperature can be obtained by hanging the logger's memory board on the temperature history reader.

In FIG. 1B, 3a represents a cooling device, 3b represents a data storage element, 3c represents a vapor evaporation port, 3d represents a short material, 3e represents a thermocouple, and 3f represents a temperature measurement point. 1C shows the position of the internal measurement point.

2) Representative volume for predicting the temperature distribution inside the steel considering the skid and non-skid parts of the steel when the steel is heated in a walking beam type furnace ( control volume) was the hatched portion of FIG. The predicted temperature (T ₁ ) at the two boundary surfaces in the thickness direction of the representative volume is estimated one-dimensionally by the differential equation of the steel temperature distribution prediction equation model used in the furnace combustion control.

For example, when the steel internal defect is 5 points in the thickness direction, the differential equation of the steel temperature distribution prediction equation model is given by the following equation (2).

: 시간 t에서의 강재온도. T

^-1: 시간t+△t에서의 강재온도, λ : 강재의 열전도도, r : 강재의 밀도Where D is the distance between nodes, Δt is the time increment, T

: Steel temperature at time t. T

^-1 : steel temperature at time t + Δt, λ: thermal conductivity of steel, r: density of steel

3) Since the measurement point for steel temperature measurement and the position used for calculation in the actual mathematical model are different, the temperature of the temperature measurement point, that is, the estimated measurement temperature (using the predicted temperature T ₁ obtained from the differential equation) T _n ^m ) is expressed as follows.

Where T _n ^m : estimated temperature

T ₁ : Defective temperature (predicted temperature) in model calculation

F _mi : correction factor

At this time, the defect of F _mi is performed as follows.

First, the temperature distribution inside the steel is assumed to be a second function (T (x) = ax ² + bx + c) and the upper surface (x = H / 2), center (x = 0), and lower surface (x = 2H / If the temperature at 2) is T (H / 2) = T ₁ , T (0) = T ₃ , T (-H / 2) = T ₅ , the coefficients a, b, and c are respectively a = 2 (T ₁ -2T ₃ + T ₅ ) / H, b = (T ₁ -T ₅ ) / H, C = T ₃ Therefore, if the temperature distribution function in steel is x ₁ ^m , x ₂ ^m , x ₃ ^m , x ₄ ^m ,

Comparing Equations 3) and 4),

와의 편차제곱을 평가함수 P로 정의하고 P를 최소로 하는 조건을 구비한다.4) Estimated measuring temperature (T _n ^m ) and actual measuring temperature

The deviation square with is defined as the evaluation function P, and the condition that minimizes P is provided.

1 is the number of actual points

The conditions under which the evaluation function is minimum are as follows.

Q is the heat flux of the steel surface.

Substituting the above formula (3) into the above formula (7),

Becomes

5) If the equation (2) and the equation (8) are assembled, the determinant can be written as the equation (9).

Solving the above formula (9), T (i = 1, 5) and q (k = 1, 2) are obtained. Q is the upper and lower surface heat flux satisfying T, the steel internal temperature distribution.

T₁/

q_k), 열유속변화에 대한 강재내부특정절점에서의 온도변화의 비는 상기 식(2)를 q(k=1, 2)로 편미분하여 구한다.6) the strength used in the calculation of equation (9)

T ₁ /

q _k ), the ratio of the temperature change at the specific internal point of the steel to the heat flux change is obtained by partial derivative of equation (2) with q (k = 1, 2).

Where k is 1, A is the same as the coefficient matrix of Equation (2), T is (T ₁ , T ₂ , T ₃ , T ₄ , T ₅ ), and D is (2D / λ ₁ , 0, 0, 0, 0) ^T , and when k is 2, D becomes (0, 0, 0, 0, 2D / λ ₅ ) ^T.

7) q _k , _j (k = 1 (top), 2 (bottom), j = 1 (skid part), 2 (non-skid part)) obtained through the process 1) -6) and steel surface temperature T _{s The} overall heat absorption rate, which is the intrinsic coefficient of the heating furnace, is determined using _{, i} (T _1,1 , T _1,2 , T _5,1 , T _5,2 ) and the ambient temperature (Tg) at the furnace steel position.

8) Since the total heat absorption rate obtained in 7) changes from time to time depending on the furnace location, it is usually obtained by dividing the interval according to the specifications and the thermocouple position for measuring the atmosphere temperature in the furnace. In general, the overall heat absorption is obtained by dividing the preheating zone, the heating zone, and the crack.

Using the total heat absorption rate (ø _CG ) obtained through the process 1) to 8), the temperature distribution inside the steel according to the change in the atmosphere temperature in the furnace and the residence time of the steel in the heating furnace can be obtained. In fact, the overall heat absorption rate is an essential factor to obtain the temperature rise curve of a specific steel for optimum combustion of the furnace. Once the intrinsic overall heat absorption rate of the furnace is obtained, it is possible to predict the temperature distribution of another steel as long as there are no significant changes in operating conditions, such as atmospheric temperature, steel size, residence time, etc. It is also very important to determine the overall heat absorption for other performance analysis. In the above process 3), the correction factor was obtained by assuming that the temperature distribution in the steel was second, but the correction factor was calculated differently even when the actual measured internal temperature distribution fits well other than the second, that is, the third or fourth equation. Can be reprinted. In this case, if the internal temperature distribution is assumed to be cubic, at least 4 points in thickness direction are required, and at least 5 in cubic.

Therefore, it is also possible to determine the overall heat absorption rate through the above detailed process 1) to 8) by looking at the shape of the measured temperature distribution in the steel and assuming that the internal temperature distribution curve is either 2nd or 3rd order.

Hereinafter, the present invention will be described through examples.

EXAMPLE

를 측정하였다. 다음에 측정된 온도이력을 이용하여 본 발명에 따라 가열로의 고유한 값인 총괄열흡수율을 구하였다.In the working beam type steel furnace, which has an effective length of 36m consisting of preheating table, heating table, and cracking bar, the heat resistant data logger is mounted on the steel as shown in Fig.

Was measured. Next, using the measured temperature history, the overall heat absorption rate, which is a unique value of the heating furnace, was obtained according to the present invention.

That is, FIG. 3 is a graph of temperature change of the calculated node assuming that the temperature distribution in the steel is a quadratic function using the result (T _n ^m ) of the temperature of the skid at the temperature measurement position of the steel as in FIG. 1c. to be.

4 is the result for the non-skid part. Atmosphere temperature was made into the temperature of each thermocouple for control of a measurement heating furnace.

5 and 6 show the results of calculating the overall heat absorption at the upper and lower surfaces of the skid part and the non-skid part according to the furnace position of the steel by the method according to the present invention.

와의 편차를 나타낸 결과로서, 약 5℃ 정도의 편차로 상당히 잘 일치함을 보여주고 있다.7 and 8 show the steel temperature distribution and the actual temperature measured by calculating the heat flux using the overall heat absorption rate obtained above and solving the differential equation (2) of Eq.

As a result of the deviation from and, it shows a good agreement with the deviation of about 5 ° C.

As a result of this embodiment, if the overall heat absorption rate is calculated by the method of the present invention and the temperature distribution in the furnace is predicted by using the method of the present invention, it is expected that the degree of measurement of the temperature distribution of the steel can be significantly improved. Precise steel temperature prediction is expected to contribute not only to energy saving of furnace but also to improvement of plate quality.

Claims (1)

The heat flux of the steel surface is calculated from the overall heat absorption rate of the furnace, and the actual temperature inside the steel located in the furnace is used to estimate the internal steel temperature in the furnace using the heat flux.

And measuring the atmosphere temperature (Tg) in the furnace; Estimated temperature (T _i ) at both interfaces in the thickness direction with respect to the representative volume for predicting the internal temperature distribution in steel by one-dimensional differential equation of steel temperature distribution prediction equation used in furnace combustion control Doing; Estimated in the steel material temperature distribution predictive mathematical expression model used in the combustion control the furnace temperature measuring temperature (T _n ^m) the predicted temperature obtained in step (T _i) and the steel temperature model used in the calculation from the temperature detecting when the measurement point and the actual mathematical model Obtaining by the correction factor (F _mi ) for correcting the temperature deviation caused by the positional difference of the point as shown in the following formula (8);

Estimated measured temperature (T _n ^m ) and actual measured temperature obtained in the above step as shown in Equation (6)

Obtaining a condition for minimizing the evaluation function P expressed by the square of the deviation as shown in Equation (8);

The steel temperature (T _i ) and the heat flux of the upper and lower surface parts of the steel are determined by a matrix equation combining the differential equation of the steel temperature distribution prediction equation model used for the combustion furnace control described above and the minimization condition equation (8) described above. q _{k, j} ); And the steel surface temperature (T _{s, i} ) of the atmosphere temperature (Tg) measured in the above, and the heat flux (q _{k, j} ) and the steel temperature (T _i ) of the steel phase, the lower surface portion obtained above. (11)

Obtaining the total heat absorption rate (ø _CG ) by substituting to the total heat absorption rate determination method of the furnace, characterized in that it comprises a.

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