KR100698740B1 - Wall temperature prediction method - Google Patents

Abstract

A modeling method for more accurately predicting only temperature of a wall used in wall radiation that accounts for most of radiant energy under circumstances in which an atmospheric temperature or gas temperature model is constructed is provided. In a method for predicting the temperature of a wall within a reheating furnace, the temperature of the wall modeling method comprises predicting the temperature of the wall by applying the temperature of the wall prediction algorithm, dTW(t)/dt=aTW(t)+bTG(t-tau)+c, suggested using the gas temperature from coefficients a, b and c having constant values determined by an experiment, and a time delay constant tau determined by response time of the reheating furnace as values that are concerned in, the temperature of the wall TW(t), gas temperature TG(t), and capacity and flux of the reheating furnace to be predicted at an arbitrary time point(t).

Description

Wall temperature prediction method

1 is a schematic diagram of atmospheric temperature estimation (linear approximation) showing a method of predicting an atmospheric temperature in a conventional heat treatment furnace.

2 is a graph illustrating the in-furnace atmosphere temperature prediction profile improved by the present invention.

Figure 3 is a graph showing the change characteristics over time of the gas temperature (T _G ) / atmosphere temperature (T _∞ ) (shown in dashed lines) and wall temperature (T _W ) (shown in solid lines) that can be deduced in the furnace.

The present invention relates to a method for predicting the wall temperature in the process in which the wall temperature governing the heat transfer in the furnace is generally obtained from the atmospheric temperature modeling results.

The thermal flows governing the slab temperature of the furnace are radiative heat transfer and convective heat transfer. Among them, the slab temperature is raised by the radiant heat transfer, since the furnace conditions are high temperature (1000-1300 ° C). The slab temperature governing equations in this series are represented by the following general partial differential equations (three-dimensional rectangular coordinate system) obtained from the law of energy conservation.

--------- 일반식(1)

--------- Formula (1)

Where T: temperature, t: time,

:슬라브내부 위치, ρ : 밀도,

Position inside the slab, ρ: density,

Cp: heat capacity, k: thermal conductivity.

The amount of heat entering and exiting through the surface at which the temperature of the slab changes due to the phenomenon of heat energy entering or exiting from the outside of the slab through the surface (boundary plane) of the slab (mathematical boundary condition (BC)) In mathematical terms:

--------- 일반식(2)

--------- Formula (2)

Here, q : heat flux, n : normal direction from the surface to the outside of the slab. Equation (2) is a mathematical expression that is actually surfaced in a form suitable for physical heat governing phenomenon. In our case, it is expressed as follows.

--------- 일반식(3)

--------- Formula (3)

: 분위기에서 슬라브로 전달되는 heat flux,

: 흑체 복사(전열)량이고

는 슬라브(slab)의 표면(surface)온도이고,

는 분위기온도(슬라브를 둘러싼 공간의 온도)이다. 흑체 복사량으로 전열량을 결정하면 일반적인 물체가 흑체가 아니므로 실제 전달량보다 많은 에너지가 출입하므로 이를 실제와 유사한 량으로 보정하기위해서 비례값을 도입하는데 위의 경우에는

으로 표현되고, 이를 총괄열흡수율이라 한다. here,

: Heat flux transferred from the atmosphere to the slab,

: Amount of black body radiation

Is the surface temperature of the slab,

Is the ambient temperature (the temperature of the space surrounding the slab). When the amount of heat is determined by the amount of black body radiation, since a general object is not a black body, more energy enters and exits than the actual amount of transfer. Therefore, a proportional value is introduced to correct it to a similar amount.

This is referred to as the overall heat absorption rate.

In practice, the radiation associated with the slab inside the furnace reveals a variety of radiative heat transfer types that are not represented in a simplified manner as in the simple equation (3).

If it is difficult to express them separately in actual application (actually, it is not easy to consider their effects separately), they are simply expressed as in the general formula (3), and thus the temperature to be used is also the wall temperature, Representative values (representative temperature) other than flame temperature, gas temperature and neighboring slab temperature should be used. Generally, there is no way to measure temperature except gas temperature, so it is used to estimate the temperature of other objects based on gas temperature. do.
1 is a graph showing a measurement temperature of each installation location of a thermocouple of a heating furnace, which is proposed to explain a method of estimating an atmosphere temperature in a furnace by a general linear approximation method. It is a method of estimating the temperature at the arbitrary position point (x) by the following formula by using the measured value of the control thermocouple 100 provided for each temperature control of 300.

라고 가정하여 경계면에서의 열유속을 계산하여 슬라브온도를 추론하는 방식을 택한다.In general, the wall temperature cannot be obtained.

We assume that the slab temperature is inferred by calculating the heat flux at the interface.

)들 간의 동적인 특성들(dynamic properties)이 무시되어 있다. 즉, 시간적인 측면에서 보면 유량이 변동하면 제일먼저 변화하는 것은 가스온도(

)이고 분위기온도(

)는 가스온도와 운전조건들(

:연료유량,공기유량,노내 압력)을 근거로 함수 근사된 것으로 얻어지고, 가스온도의 변화에 의해서 벽체온도(

)가 최종적으로 변화를 보일 것이다.However, in this temperature approximation method, each temperature (

The dynamic properties between the elements are ignored. In other words, when the flow rate changes, the first thing that changes is the gas temperature (

) And ambient temperature (

) Is the gas temperature and operating conditions (

: It is obtained by approximating a function based on fuel flow rate, air flow rate, and furnace pressure.

) Will finally change.

In the case of the furnace, due to the difficulty of operating conditions, it is almost impossible to measure the internal temperature of the slab as an object, and the operation is performed based on the method of inferring the internal temperature by mathematical modeling technique.

There is a problem that the accuracy of the mathematical modeling technique used to adopt the above inference method is low.

)만을 더욱 정밀하게 예측하기 위한 모델링 기법을 제공하는데 목적이 있다.Accordingly, the present invention has been made in order to solve the above-described problems, and the wall temperature used for wall radiation, which occupies most of the radiant energy under the condition in which the atmosphere temperature or gas temperature model is constructed,

) Aims to provide a modeling technique to predict more precisely.

을 적용하는 것을 특징으로 한다. The present invention for achieving the above technical problem is a method of predicting the wall temperature inside the heating furnace, the wall temperature prediction algorithm proposed using the gas temperature (T _G ),

It is characterized by applying.

을 적용하는 것을 특징으로 한다.
이하, 첨부도면을 참조하여 본 발명의 열처리로에서의 벽체온도 예측방법을 더욱 상세히 설명한다. In addition, the wall temperature prediction algorithm presented using the ambient temperature (T _∞ ),

It is characterized by applying.
Hereinafter, with reference to the accompanying drawings will be described in more detail the wall temperature prediction method in the heat treatment furnace of the present invention.

로 나타낼 수 있으며,
예를 들어, 단순 다변수 선형 근사방식에 의하면,

로 나타내어진다. 여기서 α는 고정 계수이며, T_c,z는 대상 z번째 영역(zone)의 열전대 측정장치이고, F_c,z는 대상 z번째 영역(zone)의 연료유량이고, A_c,z는 대상 z번째 영역(zone)의 공기유량이다.
한편, 임의의 위치(x)에서의 분위기 온도예측은 선형근사방식 및 스플라인(spline) 방식에 의해 아래의 수식과 같이 나타낸다.
선형근사방식에 의하면,

로 나타내어지고,
스플라인(spline) 방식에 의하면,

로 나타내어진다.
도 3은 가열로에서 추론할 수 있는 가스온도(T_G)/분위기온도(T_∞)와 벽체온도(T_W)의 시간에 따라 변화특성을 나타낸 그래프로서, 가스온도(T_G)와 벽체온도(T_W)의 시간에 따른 변화를 시계열 그래프를 도시하고 있다. 도면에서처럼 항상 벽체온도(T_W)의 변화가 가스온도(T_G)의 변화를 시간차에 따라 변화한다는 것을 알 수 있다. 이러한 동적인 현상을 다루기 위해서 아래의 수학식 1, 2와 같은 상미분 방정식을 각각 세울 수 있다. 즉, 임의의 시점(t)에서 예측하고자 하는 벽체온도가 T_W(t), 로내의 열전대에서 측정되는 가스온도가 T_G(t), 상기 가스온도T_G(t)로부터 예측되는 로내 분위기 온도가 T_∞(t), 가열로의 응답 특성에 따른 지연시간(τ)이 반영된 가스온도가 T_G(t-τ) 및 그 가스온도 T_G(t-τ)로부터 예측되는 로내 분위기 온도가 T_∞(t-τ)라고 가정하는 경우, 아래의 각 수학식1,2으로 제시되는 벽체온도 예측 알고리즘을 형성 할 수 있으며, 이 각각의 상미분 방정식을 해석하므로 해서 가스온도 또는 로내 분위기 온도로부터 올바른 벽체온도를 추정할 수 있게 된다.

단, 상기 제시된 수학식1,2의 알고리즘에서, T_W(t)는 임의의 시점(t)에서 예측하고자 하는 벽체온도, T_G(t)는 가스온도, T_∞(t)는 분위기 온도이고, 계수 a,b,c 및 α,β,δ는 가열로의 용량, 유량 등에 관여하는 값들로서 실험에 의해 결정되는 상수값이고, τ는 가열로의 응답특성에 의해 결정되는 시간지연(time delay)상수이다. FIG. 2 is a graph illustrating an in-furnace atmosphere temperature prediction profile improved by the present invention, by a singular point temperature estimation method for estimating a temperature Tp at a singular point 700 (a point at which a peak value or inflection point occurs). The improved prediction norm profile 600 is shown.
2, the singular point temperature estimation method,

Can be represented by
For example, according to a simple multivariate linear approximation,

It is represented by Where α is a fixed coefficient, T _{c, z} is a thermocouple measuring device in the z-th zone, F _{c, z} is the fuel flow rate in the z-zone, and A _{c, z} is the z-th target The air flow rate in the zone.
On the other hand, the ambient temperature prediction at an arbitrary position (x) is expressed by the following equation by the linear approximation method and the spline method.
According to the linear approximation,

Represented by
According to the spline method,

It is represented by
3 is a graph showing the change characteristics according to the time of gas temperature (T _G ) / atmosphere temperature (T _∞ ) and wall temperature (T _W ) which can be inferred from the heating furnace, and gas temperature (T _G ) and wall temperature. A time series graph of the change over time of (T _W ) is shown. As shown in the figure, it can be seen that the change in the wall temperature T _W always changes with the time difference in the gas temperature T _G. In order to deal with these dynamic phenomena, ordinary differential equations such as Equations 1 and 2 can be established. In other words, the wall temperature to be predicted at an arbitrary time t is T _W (t), the gas temperature measured at the thermocouple in the furnace is T _G (t), and the furnace atmosphere temperature is estimated from the gas temperature T _G (t). Is T _∞ (t), and the gas temperature reflecting the delay time (τ) according to the response characteristics of the furnace is T _G (t-τ) and the atmosphere temperature in the furnace is estimated from T _G (t-τ). If we assume _∞ (t-τ), we can form the wall temperature prediction algorithm represented by the following equations (1, 2), and by interpreting each of the ordinary differential equations, It is possible to estimate the wall temperature.

However, in the algorithm of Equations 1 and 2, T _W (t) is the wall temperature to be predicted at any time t, T _G (t) is the gas temperature, and T _∞ (t) is the ambient temperature. , Coefficients a, b, c and α, β, δ are constants determined by experiments as values related to the capacity, flow rate, etc. of the furnace, and τ is a time delay determined by the response characteristics of the furnace. Is a constant.

The best embodiments have been disclosed in the drawings and specification above. The specific terminology used herein is for the purpose of describing the present invention only and is not intended to be limiting of meaning or the scope of the invention as set forth in the claims. Therefore, those skilled in the art will understand that various modifications and equivalent other embodiments are possible from this. Therefore, the true technical protection scope of the present invention should be determined by the technical spirit of the present invention without being limited to the literary meaning described in the specification.

As described above, through the present invention, it is possible to predict the wall temperature necessary for calculating the wall radiation amount that governs the radiant heat amount in the furnace more closely to the phenomenon occurring in the real furnace, and consequently, the degree of slab temperature prediction is improved. Based on this, various operation optimizations (Slave temperature prediction must be accurate so that extraction temperature and crack of slab can be predicted according to various virtual operating condition combinations. ) And activities to improve productivity (derivation of operating conditions to increase productivity can also proceed with accurate slab temperature prediction).

Claims (3)

In the method of predicting the wall temperature inside the furnace, Coefficients a having constant values determined by experiments as values related to wall temperature T _W (t), gas temperature T _G (t), gas furnace capacity, flow rate, etc. to be predicted at an arbitrary time point t, b, c, from the time delay constant τ determined by the response characteristic of the heating furnace, Wall temperature prediction algorithm presented using the gas temperature

Wall temperature modeling method characterized in that for predicting the wall temperature by applying a. In the method of predicting the wall temperature inside the furnace, The values related to the wall temperature T _W (t) to be predicted at an arbitrary time point t, the ambient temperature T _∞ (t) predicted by the gas temperature measured at the thermocouple, and the capacity and flow rate of the heating furnace are included in the experiment. From the coefficients α, β, δ having a constant value determined by time, and the time delay constant τ determined by the response characteristics of the heating furnace, Wall temperature prediction algorithm using the furnace atmosphere temperature predicted from the gas temperature

Wall temperature modeling method characterized in that for predicting the wall temperature by applying a. delete

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