JP4548040B2 - Furnace material erosion amount calculation method and furnace material erosion amount calculation program - Google Patents

Description

  The present invention relates to a furnace material erosion amount calculation method for calculating an erosion amount of a furnace material of a glass melting furnace by molten glass by a mathematical simulation.

  A glass melting furnace used for melting glass is generally formed of a furnace material such as brick. This furnace material is eroded as the glass is melted. Knowing how long the glass melting furnace is operated and how much the furnace material is eroded is important in designing the glass melting furnace and controlling the quality of the glass.

  Conventionally, in order to obtain the amount of erosion of the furnace material, molten glass is put in a container, the furnace material is immersed in the molten glass, the furnace material is taken out every predetermined time, and the amount of erosion of the furnace material is measured with a ruler or the like. (For example, refer nonpatent literature 1).

E.A Thomas, “33rdAnnual Conference on Glass Problems”, 1972

  According to the conventional method for determining the amount of erosion of the furnace material, the amount of erosion of the furnace material can be quantitatively determined, but the work takes time. Further, the conventional method cannot quantitatively determine the furnace material erosion amount in the long term (for example, 10 years) near the life of the glass melting furnace. Therefore, it was necessary to determine the amount of furnace material erosion without using a special tool.

  The present invention has been made in view of the above circumstances, and a furnace material erosion amount calculation method and a furnace material erosion amount calculation program capable of calculating the erosion amount of a glass melting furnace by molten glass by mathematical simulation. The purpose is to provide.

The furnace material erosion amount calculation method of the present invention is a furnace material erosion amount calculation method for calculating the erosion amount of a glass melting furnace furnace material by molten glass by mathematical simulation, wherein the molten glass in the glass melting furnace model and The glass melting furnace showing the structural data indicating the thickness of the furnace material, the temperature of the furnace material surface portion at a position directly above the portion where the furnace material and the surface of the molten glass are in contact, and the cooling condition of the furnace material Based on the operation data, and the input step of inputting the physical properties data of the molten glass and the furnace material, the structure data, the operation data, and the physical property data, using the unsteady heat conduction equation, Find the temperature change of the boundary temperature over time under the assumption that the furnace material is not eroded, repeat the process of adding the temperature change and updating the boundary temperature, the temperature The boundary temperature calculation step for calculating the boundary temperature in the steady state (hereinafter referred to as the steady boundary temperature) when the crystallization is reduced below a predetermined value, and the furnace material erosion rate data obtained in advance experimentally, A furnace material erosion amount calculating step of obtaining a mass transfer flux as a function of temperature, substituting the steady boundary temperature into the temperature, and obtaining an erosion amount of the furnace material after a predetermined time.

  By this method, it becomes possible to quantitatively calculate the amount of erosion of the furnace material of the glass melting furnace by molten glass.

The furnace material erosion amount calculation method of the present invention includes an update step of updating the structure data based on the erosion amount of the furnace material obtained in the furnace material erosion amount calculation step, and the update step until the predetermined condition is satisfied. The boundary temperature calculation step and the furnace material erosion amount calculation step are repeated in this order.

  By this method, it becomes possible to quantitatively calculate the erosion amount of the furnace material eroded over a long period of time.

In the furnace material erosion amount calculation method of the present invention, the model is a one-dimensional model. In the boundary temperature calculation step, the structure data, the physical property data, the operation data, and the one-dimensional unsteady heat conduction equation are discretely obtained. by using the is turned into obtain differential equations, and calculates the steady boundary temperature.

The furnace material erosion amount calculation method of the present invention includes a division step of dividing at least one of the molten glass and the furnace material into a plurality of grids prior to the boundary temperature calculation step, and in the boundary temperature calculation step, Using the structure data, the physical property data, and the operation data and the difference equation, in a situation where the furnace material is assumed not to be eroded, the boundary temperature between the grids when a certain time has passed is obtained, and the boundary The steady boundary temperature is determined using the temperature.

  By this method, the calculation accuracy of the amount of erosion of the furnace material of the glass melting furnace by molten glass can be improved.

  In the furnace material erosion amount calculation method of the present invention, the boundary temperature calculation step includes a monochrome absorption coefficient calculation step for obtaining a monochrome absorption coefficient of the molten glass from the physical property data of the molten glass, and the monochrome absorption coefficient and radiation transport equation. And a calorific value calculation step for obtaining a calorific value due to radiation used in the difference equation.

  In the furnace material erosion amount calculation method of the present invention, the calorific value calculation step calculates an average absorption coefficient that is an average of a predetermined wavelength region of the monochromatic absorption coefficient, and uses the average absorption coefficient and the radiation transport equation, Find the amount of heat generated by radiation.

  By this method, the calculation amount required for calculating the furnace material erosion amount can be reduced, and the calculation of the furnace material erosion amount can be speeded up.

  In the furnace material erosion amount calculation method of the present invention, the predetermined wavelength region is a region between wavelengths of 0.31 μm and 16.5 μm.

In the furnace material erosion amount calculation method of the present invention, the predetermined time for obtaining the erosion amount of the furnace material in the furnace material erosion amount calculation step is 1000 hours or less.

  By this method, the calculation accuracy of the furnace material erosion amount can be maintained satisfactorily.

  The furnace material erosion amount calculation program of the present invention is a program for causing a computer to execute each step of the furnace material erosion amount calculation method.

  ADVANTAGE OF THE INVENTION According to this invention, the furnace material erosion amount calculation method and furnace material erosion amount calculation program which can calculate the erosion amount of the furnace material of the glass melting furnace by molten glass by mathematical simulation can be provided.

Embodiments of the present invention will be described below with reference to the drawings.
In the embodiment of the present invention, a furnace material erosion amount calculation program for calculating the erosion amount of a glass melting furnace by a molten glass by a computer using a mathematical simulation will be described. The method for calculating the furnace erosion amount according to the present invention is the same as the processing steps of the computer operated by the program, and is included in the description of the processing of the program.

FIG. 1 is a diagram showing a schematic configuration of a glass melting furnace that is a simulation target for obtaining an erosion amount of a furnace material by a furnace material erosion amount calculation program for explaining an embodiment of the present invention.
As shown in FIG. 1, molten glass 12 exists in a glass melting furnace formed of a furnace material 11 such as brick. Generally, when operating the glass melting furnace, the furnace material 11 is cooled by applying air 13 from the outside of the glass melting furnace in order to reduce the erosion amount of the furnace material 11. The performance of the glass melting furnace is determined by various factors (operation conditions, shape, etc.). In this embodiment, in order to simplify the calculation, the temperature of the portion 14 that is a part of the surface of the furnace material 11 is used. the T _1, treated as data representing the operating conditions of the glass melting furnace. The part 14 is not particularly limited as long as it is a part of the surface of the furnace material 11, but it has the most influence on erosion, and the temperature is measured in an actual glass melting furnace, so that the calculation accuracy is easy to check. In consideration of the above, the portion 14 is a point directly above the portion where the furnace material 11 and the surface of the molten glass 12 are in contact, specifically, the portion 14 is more than the portion where the furnace material 11 and the surface of the molten glass 12 are in contact with each other. It is preferable that it is a part of the surface of the furnace material 11 on mm.

In the furnace material erosion amount calculation program of the present embodiment, the glass melting furnace shown in FIG. 1 is modeled as a one-dimensional model in order to simplify the calculation. FIG. 2 is a one-dimensional model of the glass melting furnace shown in FIG.
As shown in FIG. 2, the furnace material 11 and the molten glass 12 are one-dimensionally modeled with a thickness in the X direction in the figure. A major factor that causes the furnace material 11 to be eroded by the molten glass 12 is the temperature at the boundary between the furnace material 11 and the molten glass 12. There are several factors other than this temperature, but the temperature of the boundary is considered to have the greatest influence on the erosion. Therefore, in the furnace material erosion amount calculation program of this embodiment, the boundary of the boundary in the one-dimensional model shown in FIG. The amount of erosion of the furnace material 11 is obtained based on the temperature. Further, the temperature of this boundary is roughly affected by three factors of convection, thermal radiation, and heat conduction of the molten glass 12, but in the furnace material erosion amount calculation program of this embodiment, among these, thermal radiation and By considering heat conduction, it is possible to calculate the amount of erosion of the furnace material quantitatively. The operation of the computer that executes the furnace material erosion amount calculation program will be described below.

FIG. 3 is a diagram showing a processing flow of a computer that is operated by a furnace material erosion amount calculation program for explaining an embodiment of the present invention.
First, the computer operating by the furnace material erosion amount calculation program shows the structural data indicating the thickness of the furnace material 11 and the molten glass 12 in the one-dimensional model, the temperature T ₁ that determines the performance of the glass melting furnace, the cooling conditions, and the like. Operation data, physical property data (density ρ, specific heat c, thermal conductivity k, etc.) of the furnace material 11 used in the one-dimensional model, and physical property data (density ρ, specific heat c, monochromatic refractive index, monochromatic complex refraction) of the molten glass 12 The imaginary part of the rate, the thermal conductivity k) is input by the user (S1). In the following description, the thickness of the furnace material 11 is 250 mm, and the thickness of the molten glass 12 is 10 mm.

  Next, when the user gives an instruction for dividing the grid of the furnace material 11 and the molten glass 12 of the one-dimensional model set by the structure data, the computer seems to have specified at least one of the furnace material 11 and the molten glass 12. Is divided into a plurality of grids (S2). For example, the computer equally divides the furnace material 11 into a grid of 50 mm units. That is, the whole molten glass 12 becomes one grid, and the furnace material 11 is divided into five grids. Thus, the furnace material 11 and the molten glass 12 are divided into a total of 6 grids, and preparations for calculating the furnace material erosion amount are completed. The molten glass 12 and the furnace material 11 may be divided into more grids in terms of calculation accuracy.

The image at this time is shown in FIG. As shown in FIG. 4, the one-dimensional model of the glass melting furnace is divided into grids 1 to 6 in order from the molten glass 12 side. In this one-dimensional model, the X coordinate is set in the thickness direction of each grid from the origin O set at the left end of the molten glass 12. The physical property data input in S1 is set in each grid. The physical property data of the molten glass 12 is set in the grid 1, and the physical property data of the furnace material 11 is set in each of the grids 2 to 6. In the following, for the sake of explanation, the coordinates of the origin are X ₁ (= 0 mm), the coordinates of the boundary between the grid 1 and the grid 2 are X ₂ (= 10 mm), and the coordinates of the boundary between the grid 2 and the grid 3 are X _3. (= 60 mm), the coordinate of the boundary between the grid 3 and the grid 4 is X ₄ (= 110 mm), the coordinate of the boundary between the grid 4 and the grid 5 is X ₅ (= 160 mm), and the boundary between the grid 5 and the grid 6 The coordinate is X ₆ (= 210 mm), and the coordinate of the right end of the grid 6 is X ₇ (= 260 mm). Further, i = 2 to 6, and the temperature at the boundary X _i between the grid i−1 and the grid i is defined as the boundary temperature T _i .

After S2, the computer assumes that the furnace material 11 is not eroded based on the structure data, operation data, and physical property data input in S1, and when a certain period of time has passed and a steady state is reached. The process proceeds to a boundary temperature calculation process for calculating a boundary temperature T ₂ (steady boundary temperature) between the molten glass 12 and the furnace material 11 (S3).

Next, the principle of calculating the boundary temperature will be described.
The furnace material erosion quantity calculation program of the present embodiment, in order to determine the boundary temperature T _i of each grid between the 1-dimensional model shown in FIG. 4, a one-dimensional non-illustrated heat transport by thermal radiation in Equation 1 below Considering A steady heat conduction equation is used.

Here, c: specific heat, ρ: density, T: temperature, t: time, k: thermal conductivity, x: coordinates, q _v : calorific value due to radiation.

Calorific value q _v by radiation of formula 1, shown in Equation 2 below, the radiation - can be determined by the radiation transport equation in one dimension parallel plate system in the absorbent medium.

Here, μ: zenith angle, I _λ : monochromatic radiation intensity, κ _λ : monochromatic absorption coefficient of molten glass at wavelength λ, x: coordinate, I _λ (x, μ): incident at coordinate zenith angle μ Coming monochrome radiation intensity, I _bλ {T (x)}: Monochromatic black body radiation intensity at a temperature T [K] at a coordinate x.

The monochromatic absorption coefficient κ _λ of Formula 2 can be obtained by the following Formula 3 using physical property data of the molten glass 12 used in the one-dimensional model (imaginary part of the monochromatic complex refractive index).

Here, λ: wavelength, k _λ : imaginary part of monochromatic complex refractive index at wavelength λ.

Κ _λ obtained by Equation 3 is used in the radiation transport equation shown in Equation 2, but if all wavelengths are calculated, the calculation load increases. Therefore, in this program, the monochromatic absorption coefficient κ obtained by Equation 3 is used. An average absorption coefficient κ _i obtained by averaging _λ is calculated and used for the radiation transport equation. The average absorption coefficient κ _i can be obtained by the following equation 4. Integrating wavelength region of monochromatic absorption coefficient kappa _lambda (wavelength region to be averaged) is black at a temperature (above T _{1 =} 700 ℃ ~1700 ℃) as the furnace material erosion is especially problematic in operating the glass melting furnace In order to consider 99% or more of the body radioactivity, the region has a wavelength of 0.31 μm to 16.5 μm. By averaging the monochromatic absorption coefficient κ _λ within this region, it becomes possible to calculate the amount of erosion of the furnace material in all glass melting furnaces used in practice while reducing the calculation load.

Here, I _bλ : Monochromatic blackbody radiation intensity at a certain temperature T [K], σ: Stefan Boltzmann constant.

Also, in this program, the radiation transport equation shown in Equation 2 is not used as it is, but is transformed into the following Equation 5 by gray approximation using the average absorption coefficient κ _i .

In Equation 5, q _i corresponds to q _v in Equation 1, and is the amount of heat generated by radiation at the coordinate X _i . I _b (T _i ) is the black body radiation intensity obtained by integrating the monochromatic black body radiation intensity I _bλ {T (x)} with respect to the wavelength in the wavelength range of 0.31 μm to 16.5 μm, and the boundary temperature The value is determined by T _i . I _i−1 is the radiation intensity incident on the boundary X _i from X _i−1 , and I _{i + 1} is the radiation intensity incident on the boundary X _i from X _{i + 1} . κ _i-1 is an average absorption coefficient at the boundary temperature T _i-1 , and κ _i is an average absorption coefficient at the boundary temperature T _i .

According to Equation 5, the calorific value q _i due to radiation at the coordinate X _i can be obtained as an equation including the boundary temperature T _i .

1 dimensional unsteady heat conduction equation shown in Equation 1 is an equation which can obtain the temperature change over time, in the form of this state, obtains the boundary temperature T _i of each grid each other shown in FIG. 4 In this program, the one-dimensional unsteady heat conduction equation is discretized by the forward difference method and used. When the one-dimensional unsteady heat conduction equation is approximated to the difference equation by the forward difference method, the following equation 6 is obtained.

Here, c _i-1 : specific heat of the material set on the grid i-1, ρ _i-1 : density of the material set on the grid i-1, k _i-1 : set on the grid i-1 The thermal conductivity of the material, c _i : the specific heat of the material set in the grid i, ρ _i : the density of the material set in the grid i, k _i : the thermal conductivity of the material set in the grid i.

Temperatures T ₁ is a fixed value determined by the operational data as described above, the temperature T ₇ is a fixed value determined by the cooling conditions of operation data. Further, the boundary temperature T _i (i = 2 to 6) between the grids is a fixed value (hereinafter referred to as an initial value) in a state where the glass melting furnace is not operating (hereinafter referred to as an initial state). This initial value can be set to an arbitrary value. For example, it may be set to room temperature, it may be set to the same temperature as the temperature T ₁ of a input operation data. In the present embodiment, the initial value of the boundary temperature T _i is set to the same value as the temperature T ₁ . For this reason, if there is physical property data of the molten glass 12 and the furnace material 11, operation data of the glass melting furnace, and structural data of the glass melting furnace, the glass melting furnace is assumed under the condition that the furnace material 11 is not eroded. The temperature change ΔT _i of the boundary temperature T _i after elapse of time Δt (for example, 1/100 second) from the operation of can be obtained using Equation 6. After determining the [Delta] T _i updates the boundary temperature T _i by adding the boundary temperature T _i to _(a fixed value in the initial state) [Delta] T _i, using the boundary temperature T _i of the updated, after further Δt of by repeating the operations such updates boundary temperature T _i seeking temperature change [Delta] T _i, can be determined the temperature distribution in the X-direction of the one-dimensional model shown in FIG. The boundary temperature T _i is in a steady state that hardly changes when a certain amount of time has passed under the condition that the furnace material 11 is not eroded. This program calculates the amount of erosion of the refractory lining 11 with boundary temperature T _i of the steady state. Therefore, when determining the boundary temperature _{T i,} repeated operation until [Delta] T _i <0.000001, the boundary temperature _{T 2} at the time of a [Delta] T _i <0.000001, treated as boundary temperature _{T 2} of the steady-state I will decide.

FIG. 5 is a flowchart for explaining the flow of the boundary temperature calculation process by the computer.
Computer is the mean of monochromatic absorption coefficient to calculate the kappa _lambda (S31), the calculated monochromatic absorption coefficient kappa _lambda using the imaginary part of the single-color complex refractive index of the molten glass 12 that is input in S1, the formula 3 The average absorption coefficient κ _i is calculated using Equation 4 (S32). An initial value is used as a value to be substituted for the boundary temperature T _i in Equation 4. The average absorption coefficients κ _{2 to} κ ₆ are calculated by the process of S32.

Next, the computer uses the calculated average absorption coefficients κ _{2 to} κ ₆ , the coordinate data based on the input structure data, and the radiation transport equation (Equation 5) to generate the heat generated by the radiation at the coordinates X _i. q _i is calculated (S33). An initial value is used as a value to be substituted for the boundary temperature T _i in Equation 5. By treatment S32, the heating value _q 2 to q ₆ are calculated.

Next, the computer uses the physical property data, the coordinate data, the operation data (T ₁ , T ₇ ), the calculated calorific value q _{2 to} q ₆ , and Equation 6 so that the furnace material 11 is not eroded. calculating a [Delta] T _i after time Δt has elapsed in assumed circumstances, the addition of calculated [Delta] T _i to the initial value of the boundary temperature T _i, and calculates the boundary temperature T _i after time Δt has elapsed (S34). An initial value is used as a value to be substituted for the boundary temperatures T _{2 to} T ₆ in Equation ₆ . By the process of S34, the boundary temperatures T _{2 to} T ₆ after the lapse of time Δt are calculated.

The computer repeats the processing of S32 to S34 until each of ΔT ₂ to ΔT ₆ calculated in S34 becomes smaller than 0.000001 (S35: YES), and when a certain period of time has elapsed and the steady state is reached. calculating the boundary temperature _{T 2} (S36). However, in the second and subsequent processing of S32 to S34, the latest boundary temperature T _i newly calculated in S34 is used instead of the initial value as the value to be substituted for the boundary temperature T _i in the equations 4, 5, and 6. . In the second and subsequent processing of S34, the calculated ΔT _i is not added to the initial value of the boundary temperature T _i , but the calculated ΔT _i is added to the latest boundary temperature T _i and the boundary after the time Δt has elapsed. to calculate the temperature _{T i.}

Next, the computer based on the boundary temperature T ₂ of the calculated steady-state S36, the transition to furnace material erosion quantity calculation processing for calculating the amount of erosion of the furnace material 11 after a predetermined time (eg, 500 hours) (S4).

Here, the principle of calculating the furnace material erosion amount will be described.
In order to calculate the amount of erosion of the furnace material 11, the mass transfer flux F of the furnace material 11 (the amount of material that passes through the unit area per unit time) is obtained. The mass transfer flux F is determined by the physical properties of the furnace material 11. The diffusion constant D of the furnace material 11 is expressed by the following formula 7.

  Here, A: diffusion frequency factor, ΔE: activation energy, R: gas constant, and T: temperature.

  Further, the mass transfer flux F is expressed by the following formula 8 using the diffusion constant D.

Here, c: concentration of the dissolved furnace material at the position where the furnace material is dissolved, c _∞ : concentration of the dissolved furnace material at a position sufficiently away from the position where the furnace material is dissolved, δc: concentration The boundary layer thickness.

  Taking the logarithm of both sides of Equation 8, the following Equation 9 is obtained.

According to Expression 9, it is possible to determine how much the furnace material 11 melts per unit time at a certain temperature T. However, since the values (A, ΔE, R, c, c _∞ , δc) on the right side of Equation 9 cannot be obtained from the physical property data input in S1, the computer eroded the furnace material obtained experimentally in advance. The above value is obtained using the speed data. The furnace material erosion rate data is experimental data indicating how much the furnace material is eroded per unit time (for example, 100 hours) at a certain temperature T, and is represented by a graph as shown in FIG. In the graph shown in FIG. 6, when a logarithm of the value on the vertical axis is taken and the reciprocal of the value on the horizontal axis is taken, a graph as shown in FIG. 7 is obtained. The graph shown in FIG. 7 has the same form as the function represented by Expression 9. Thereby, it turns out that the mass transfer flux F of a furnace material becomes a value equal to an actual furnace material erosion rate. Therefore, the mass transfer flux F is obtained by obtaining the above value from the graph of FIG. In other words, the mass transfer flux F of the furnace material can be obtained as a function of temperature by using the furnace material erosion rate data. The furnace material erosion rate data is stored in the memory in the computer for each type (physical property) of the furnace material when this program is installed.

FIG. 8 is a flowchart for explaining the flow of the furnace material erosion amount calculation processing by the computer.
The computer reads out the furnace material erosion rate data corresponding to the type of the furnace material 11 from the memory based on the physical property data of the furnace material 11 input in S1, and uses the furnace material erosion rate data to determine the material of the furnace material 11 The moving flux F is obtained as a function of the temperature T (S41). The computer then, a boundary temperature T ₂ in the steady state that is calculated in S36 is substituted into a function of temperature determined above, the unit time (100 hours) to calculate the furnace material erosion per (S42), In order to speed up the calculation while maintaining the calculation accuracy, the furnace material erosion amount is multiplied by 5 to calculate the furnace material erosion amount after 500 hours (S43).

After calculating the furnace material erosion amount after 500 hours, the computer updates the structure data input in S1 based on the furnace material erosion amount (S5). Specifically, the thickness of the molten glass 12 of the one-dimensional model shown in FIG. 2 is increased by the amount of erosion of the furnace material 11, and the thickness of the furnace material 11 is decreased by the amount of erosion, thereby updating the structure data. . Then, the computer determines whether or not a predetermined condition is satisfied (S6). The predetermined conditions are, for example, conditions such as the operating time of the glass melting furnace for which the furnace material erosion amount set by the user is to be obtained and the remaining thickness of the furnace material 11. When the furnace material erosion amount after the operating time set by the user has not been calculated yet, or when the remaining thickness of the furnace material 11 exceeds the threshold value, the computer determines that the predetermined condition is not satisfied. (S6: NO), the process proceeds to S2. As the grid dividing method in S2, the method set first (only the furnace material 11 is equally divided into five) is repeatedly applied. By structural data is updated, since the boundary temperature T _i varies, the computer until a predetermined condition is satisfied, S5, S2, S3, S4 and by repeating in this order, obtains the furnace material erosion amount. Note that since this repetition is for updating only the structure data, the processes of S31 and S41 that are not affected by the structure data may be omitted after the second time. On the other hand, when the calculation of the furnace material erosion amount after the operating time set by the user is completed, or when the remaining thickness of the furnace material 11 is less than the threshold value, the computer determines that the predetermined condition is satisfied ( (S6: YES), various data obtained by the calculation by this program are output (S7), and the process is terminated.

Various data that can be output in S7 include, for example, the amount of erosion of the furnace material 11 at a certain time, the remaining thickness of the furnace material 11 at a certain time, the temperature at a coordinate X _i at a certain time, and the furnace material at a certain time 11 mass transfer fluxes F and the like. It is also possible to obtain the heat flux and the amount of heat released from the outer wall of the furnace material by using the data obtained by the calculation of this program. Further, by using the average absorption coefficient κ, the radiation property value can be obtained.

Hereinafter, an example of data (graph) output from the computer is shown.
Figure 9 is a graph showing the relationship between the operating time and the boundary temperature T ₂ of the glass melting furnace, the horizontal axis running time and the vertical axis represents the boundary temperature T _2. In FIG. 9 shows the results when a simulation by changing the temperature T ₁ of determining the performance of a glass melting furnace to eight values. As shown in FIG. 9, when the operating time is 0, that is, in the initial state, as the boundary temperature T ₂ has become the initial value (1300 ° C. to 1600 ° C.), respectively, the time has passed, the value is changed You can check the status. According to this graph, it is possible to know what value the temperature T ₁ should be used to decrease the boundary temperature T ₂ , which can be used for designing a glass melting furnace.

  FIG. 10 is a graph showing the relationship between the operating time of the glass melting furnace and the remaining thickness of the furnace material 11, where the horizontal axis is the operating time and the vertical axis is the remaining thickness. In FIG. 10, in the same glass melting furnace, the initial thickness of the furnace material 11 is 250 mm, the initial thickness of the furnace material 11 is 300 mm, and the initial thickness of the furnace material 11 is 250 mm. The simulation results are shown for three cases, that is, when a 50 mm furnace material is laid on the way. As shown in FIG. 10, there is a difference of one year in the period until the remaining thickness reaches 50 mm between the case of using the furnace material of 250 mm from the beginning and the case of using the furnace material of 300 mm from the beginning. From this, it can be seen that the life of the furnace material can be extended by using the furnace material having a large thickness. It can also be seen that using a 250 mm furnace material and then applying the roof tile later will extend the life rather than using a 300 mm furnace material from the beginning. For this reason, the data shown in FIG. 10 can be used for the design of the glass melting furnace, and the timing of the roof tile can be determined appropriately.

As described above, according to this program, the amount of erosion of the furnace material can be obtained quantitatively, which can be used for designing a glass melting furnace and controlling the quality of glass. Further, in this program, since the glass melting furnace to be simulated is converted into a one-dimensional model and various calculations are performed, the calculation load on the computer can be reduced and high-speed processing can be performed. Moreover, maintenance because they perform processing in consideration of the influence of heat radiation and heat conduction Request boundary temperature T _i, in spite of the one-dimensional model of a glass melting furnace, the calculation accuracy of the furnace material erosion rate can do.

  In addition, according to this program, it is possible to quantitatively predict the furnace material erosion amount over a long period of time, which was impossible in the past. For example, the process of S2 to S6 in FIG. 3 can be repeated to obtain the furnace material erosion amount after 15 years, which is suitable for prediction of the long-term erosion quantity and can know the life of the glass melting furnace. .

In the above, as shown in FIG. 4, the furnace material erosion amount is calculated after dividing at least one of the molten glass 12 and the furnace material 11 of the one-dimensional model into a plurality of grids. The furnace material erosion amount may be calculated without dividing the furnace material 11 into the grid. That is, the calculation may be performed with the entire molten glass 12 as the grid 1 and the entire furnace material 11 as the grid 2. In this case, by calculating with the coordinate X ₇ as X ₃ and the temperature T ₇ as temperature T ₃ , the amount of erosion of the furnace material can be quantitatively obtained as described above, and the processing is performed at higher speed. It is also possible. When at least one of the molten glass 12 and the furnace material 11 is divided into a plurality of grids, the processing is somewhat slow, but the internal temperature of the molten glass 12 and the furnace material 11 can be taken into account finely. There is an advantage that the calculation accuracy of the quantity can be improved.

Furthermore, in this program, in S4 of FIG. 3, seeking furnace material erosion amount after a predetermined time using a boundary temperature T ₂ when it becomes constant. Actually, since the boundary temperature T ₂ changes with the erosion of the furnace material, an accurate amount of the erosion of the furnace material cannot be obtained at the constant boundary temperature T ₂ . However, since the erosion of the furnace material is very slowly performed, in this program, it is to a certain time by obtaining the furnace material erosion amount using a constant boundary temperature T _2, maintaining the calculation accuracy of the furnace material erosion rate ing. In order to maintain this calculation accuracy, the certain amount of time (the predetermined time) is preferably 1000 hours or less.

In the above, the average absorption coefficient κ _i is calculated as a numerical value in S32, the calorific value q _i is calculated as a numerical value in S33, and ΔT _i is calculated by substituting these numerical values into Equation 6. Substituting structural data, physical property data, operation data, and initial values of the boundary temperature T _i simultaneously into an equation including the boundary temperature T _i obtained by substituting the equations 3 to 5 into the equation 6, and ΔT _i It may be calculated.

  Hereinafter, the effect of this program will be proved by examples.

In this example, the glass melting furnace shown in FIG. 1 is used as a model, and only the temperature T ₁ is changed to eight values (1300 ° C. to 1600 ° C.), and simulation is performed by the furnace material erosion amount calculation program described in the embodiment. The result was output as a graph (FIG. 11) showing the relationship between the operating time and the furnace material erosion amount. Various data set in the simulation are as follows.
<Structural data>
Thickness of molten glass 12 = 10 mm
Thickness of furnace material 11 (made brick) = 250 mm
Number of grid divisions of molten glass 12 = 30
Number of grid divisions of furnace material 11 = 10
<Operation data>
Temperature T ₁ : 8 types of 1300 ° C, 1350 ° C, 1400 ° C, 1450 ° C, 1500 ° C, 1550 ° C, 1580 ° C, 1600 ° C Cooling condition of furnace material 11: Using wind of temperature 30 ° C, wind speed is 10m / s Ambient temperature around cooling glass melting furnace = 30 ° C
<Physical property data>
Thermal conductivity k of molten glass 12 = 1.2 [W / m / K]
Density of molten glass 12 ρ = 2500 [kg / m ³ ]
Specific heat c of molten glass 12 = 1400 [J / kg / K]
Imaginary part data of the monochromatic birefringence of the molten glass 12: see literature “M. Rubin, Solar Energy Materials, 12, 275-288 (1985)”. Thermal conductivity k of furnace material 11 = 4.1 [W / m / K]
Density of furnace material ρ = 3600 [kg / m ³ ]
Specific heat of furnace material c = 1000 [J / kg / K]
<Other conditions>
Initial value = T ₁
Operation period (predetermined condition): 3 years or until the remaining thickness of the furnace material 11 is less than 0.5 mm Time Δt = 0.001 [s]
Conditions for obtaining the steady-state temperature of the boundary temperature T _i : | ΔT _i | <0.0000001 [° C.]
Predetermined time = 500 hours (unit time 100 hours x 5)

The data when the temperature T ₁ is 1300 ° C. is Example 1, the data when the temperature T ₁ is 1350 ° C. is Example 2, the data when the temperature T ₁ is 1400 ° C. is Example 3, and the temperature T ₁ is 1450 data of embodiment in case of ° C. 4, the data in example 5 when the temperature _{T 1} is the 1500 ° C., the data in example 6 when the temperature _{T 1} is the 1550 ° C., the data at the temperature _{T 1} is 1580 ° C. Is Example 7, and the data when the temperature T ₁ is 1600 ° C. is Example 8. Further, as a reference example, a curve obtained by actually measuring the relationship between the operation time and the amount of erosion of the furnace material for a glass melting furnace having the same structure as the glass melting furnace shown in FIG. Indicated. In Reference Example 1, measurement data of a glass melting furnace (physical property data, structure data, operation conditions, and other conditions are all the same as described above) in which the temperature T ₁ was 1600 ° C. was used. In Reference Example 2, the temperature T ₁ Measurement data of a glass melting furnace having a temperature of 1560 ° C. (physical property data, structure data, operating conditions, and other conditions are all the same as above) were used.

  As can be seen from FIG. 11, when Example 8 and Reference Example 1 are compared, the two curves are almost the same, and it has been found that the amount of erosion of the furnace material can be quantitatively calculated by this program. Further, when Example 6 and Reference Example 2 were compared, the two curves were almost the same, and it was found that the amount of furnace material erosion could be calculated quantitatively by this program.

The figure which shows schematic structure of the glass melting furnace used as the object which calculates | requires the amount of erosion of a furnace material with the furnace material erosion amount calculation program for describing embodiment of this invention A one-dimensional model of the glass melting furnace shown in FIG. The figure which shows the processing flow of the computer which operate | moves with the furnace material erosion amount calculation program for describing embodiment of this invention An image of the one-dimensional model shown in Fig. 2 divided into grids Flowchart for explaining the flow of boundary temperature calculation processing by a computer Graph showing furnace material erosion rate data Graph re-plotted by changing the vertical and horizontal axes of the graph shown in FIG. Flowchart for explaining the flow of furnace material erosion amount calculation processing by a computer The figure which shows an example of the graph output by the furnace material erosion amount calculation program for demonstrating embodiment of this invention The figure which shows an example of the graph output by the furnace material erosion amount calculation program for demonstrating embodiment of this invention The figure for demonstrating the Example of this invention

Explanation of symbols

11 Furnace material 12 Molten glass

Claims (9)

A furnace material erosion amount calculation method for calculating an erosion amount of a glass melting furnace material by molten glass by a mathematical simulation,
Structural data indicating the thickness of the molten glass and the furnace material in the model of the glass melting furnace, the temperature of the furnace material surface portion at a position directly above the portion where the furnace material and the surface of the molten glass are in contact, An input step for inputting operation data of the glass melting furnace indicating cooling conditions of the furnace material, and physical property data of the molten glass and the furnace material,
Based on the structural data, the operation data, and the physical property data, the temperature change of the boundary temperature with the passage of time is obtained under the condition that the furnace material is not eroded using an unsteady heat conduction equation. , Repeating the process of adding the temperature change and updating the boundary temperature to calculate the boundary temperature in the steady state (hereinafter referred to as the steady boundary temperature) when the temperature change falls below a predetermined value Steps,
Using the furnace material erosion rate data obtained experimentally in advance, the mass transfer flux of the furnace material is obtained as a function of temperature, and the steady boundary temperature is substituted for the temperature, and the amount of erosion of the furnace material after a predetermined time. A furnace material erosion amount calculation method including a furnace material erosion amount calculation step. A furnace material erosion amount calculation method according to claim 1,
An update step of updating the structure data based on the erosion amount of the furnace material obtained in the furnace material erosion amount calculation step ,
A furnace material erosion amount calculation method in which the updating step, the boundary temperature calculation step, and the furnace material erosion amount calculation step are repeated in this order until a predetermined condition is satisfied. A furnace material erosion amount calculation method according to claim 1 or 2,
The model is a one-dimensional model;
In the boundary temperature calculation step, a furnace material for calculating the steady boundary temperature using the structure data, the physical property data, the operation data, and a differential equation obtained by discretizing a one-dimensional unsteady heat conduction equation. Erosion amount calculation method. A furnace material erosion amount calculation method according to claim 3,
Prior to the boundary temperature calculating step, including a dividing step of dividing at least one of the molten glass and the furnace material into a plurality of grids,
In the boundary temperature calculation step, using the structure data, the physical property data, the operation data, and the difference equation, the grids when a certain period of time has passed, assuming that the furnace material is not eroded. The furnace material erosion amount calculation method for determining the steady boundary temperature using the boundary temperature. A furnace material erosion amount calculation method according to claim 3 or 4,
The boundary temperature calculating step includes:
A monochrome absorption coefficient calculating step for obtaining a monochrome absorption coefficient of the molten glass from physical property data of the molten glass;
A furnace material erosion amount calculation method including a calorific value calculation step for obtaining a calorific value due to radiation used in the difference equation based on the monochromatic absorption coefficient and radiation transport equation. A furnace material erosion amount calculation method according to claim 5,
The calorific value calculation step includes:
A furnace material erosion amount calculation method for obtaining an average absorption coefficient that is an average of a predetermined wavelength region of the monochromatic absorption coefficient and obtaining a heat generation amount due to the radiation using the average absorption coefficient and the radiation transport equation. A furnace material erosion amount calculation method according to claim 6,
The furnace material erosion amount calculation method, wherein the predetermined wavelength region is a region between a wavelength of 0.31 μm and 16.5 μm. The furnace material erosion amount calculation method according to any one of claims 1 to 7, wherein the predetermined time for obtaining the erosion amount of the furnace material in the furnace material erosion amount calculation step is 1000 hours or less. Method.   A furnace material erosion amount calculation program for causing a computer to execute each step of the furnace material erosion amount calculation method according to claim 1.

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