CN112949132A - Method for acquiring internal temperature distribution of ceramic body - Google Patents

Method for acquiring internal temperature distribution of ceramic body Download PDF

Info

Publication number
CN112949132A
CN112949132A CN202110248462.5A CN202110248462A CN112949132A CN 112949132 A CN112949132 A CN 112949132A CN 202110248462 A CN202110248462 A CN 202110248462A CN 112949132 A CN112949132 A CN 112949132A
Authority
CN
China
Prior art keywords
ceramic
temperature
ceramic body
model
flue gas
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202110248462.5A
Other languages
Chinese (zh)
Inventor
胡罗克
印四华
项星玮
龙时雨
徐康康
贾顺
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Zhejiang University ZJU
Original Assignee
Zhejiang University ZJU
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zhejiang University ZJU filed Critical Zhejiang University ZJU
Publication of CN112949132A publication Critical patent/CN112949132A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Mathematical Optimization (AREA)
  • Data Mining & Analysis (AREA)
  • General Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computer Hardware Design (AREA)
  • Operations Research (AREA)
  • Evolutionary Computation (AREA)
  • Algebra (AREA)
  • Geometry (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • Waste-Gas Treatment And Other Accessory Devices For Furnaces (AREA)
  • Tunnel Furnaces (AREA)

Abstract

The invention discloses a method for acquiring internal temperature distribution of a ceramic blank, which comprises the following steps: s1, establishing a heat conduction model inside the ceramic body in the firing process; s2, establishing a heat transfer process model of the ceramic body based on energy conservation and mass conservation to obtain the external surface temperature of the ceramic body as a boundary condition; and S3, solving the established heat transfer model and the heat conduction model by using a finite difference method to obtain the temperature distribution in the ceramic body. The invention establishes a one-dimensional unsteady state model between the process parameters and the ceramic body temperature and a heat transfer model of the ceramic body to obtain the relationship between the process parameters and the ceramic temperature, combines the input process parameters with the ceramic temperature model, simultaneously solves the defect that the kiln temperature is directly used as the boundary condition of the ceramic body in the traditional mechanism model, and carries out temperature analysis on the ceramic body to realize energy conservation and consumption reduction.

Description

Method for acquiring internal temperature distribution of ceramic body
Technical Field
The invention relates to the technical field of energy, in particular to a method for acquiring internal temperature distribution of a ceramic body.
Background
With the rapid increase of global economy, the demand for diversification of ceramics is increasing day by day. In 2017, the weight of Ceramic products worldwide reaches 135 million square meters, wherein the main production in Asia and Europe occupies 94 million square meters and 20 million square meters respectively (World production and con dition of Ceramic tiles [ J ]. Ceramic World review, 2018.), and China belongs to the most important Ceramic production place in Asia.
The glaze-coated ceramic manufacturing process mainly comprises the following steps: preparing raw materials, extrusion forming, drying, glazing, firing and other stages (CO)2emission calculation and reduction options in ceramic tile manufacture-the Foshan Case[J]Energy Procedia 2012 (16): 467-476). Wherein the spray drying process occupies about 30 percent of the total energy consumption (the current situation and the technical measures of energy conservation and emission reduction in the construction and sanitation porcelain industry [ J)]China ceramics, 2009 (1): 33-38.), the burning stage occupies more than 50% of the heat Energy consumption in the whole process (Energy saving in ceramic kilns: coin gas heat recovery [ J ]]Applied Thermal engineering.2014 (65): 102-110), and the carbon emission of the firing process in the whole manufacturing process is more than 90%. Meanwhile, in terms of resource utilization rate, China has a large gap with foreign countries, and some developed countries can reach more than 50 percent, even moreNearly 60 percent, but only about 30 percent in China (the current energy consumption and energy-saving technical analysis of ceramic industry [ J ]]Science and technology propagation, 2014: 94-96), it can be seen that the extensive, energy inefficient, high emission patterns are restricting the development of the enterprise.
With the change of global climate and the promotion of energy saving and emission reduction measures (the design and algorithm research of a glass kiln control system [ D ]. Qingdao science and technology university, 2013.) on the green and low carbon development of the kiln in the document [2012]44 issued by the State Council in 2012, how to reduce the energy consumption level in the ceramic production process and improve the energy utilization rate are problems to be solved urgently in the industry.
The temperature field inside the kiln and the temperature distribution of products are closely related to the quality of the products, but the internal temperature has the characteristic of immeasurability, so that the performance optimization difficulty of an enterprise on the kiln is high, and the energy consumption of the enterprise is restricted. At present, scholars at home and abroad make certain research on the research of the distribution of the temperature field of the kiln. Two main aspects are focused on: mechanism modeling and a mechanism and data combined modeling mode.
A Numerical analysis of an incident ceramic area operating conditions for the energy impact improvement [ J ]. Journal of Environmental Management, 2017, 203: 1026-. A Numerical modeling of a rotation center kit with improvements to shell coating [ J ]. International Journal of Heat and Mass Transfer, 2016, 102: 610 and 621, a practical one-dimensional kiln body model is established by combining a composite resistance model and a forced convection model, and the model is verified and researched to obtain reasonable quantitative and qualitative results of temperature distribution and mass fraction of substances.
Although scholars at home and abroad do a lot of work on the mechanism modeling of the temperature field, most scholars focus on the aspects of kilns such as tunnel kilns and rotary kilns, the mechanism modeling of the temperature field in the aspect of ceramic roller kilns is less, and most scholars do not have a model combining input with the temperature of ceramic. For such a typical thermal plant, the internal temperature field is not only related to the energy consumption of the whole process, but also related to the quality of the product phase. Therefore, the establishment of a temperature mechanism model of the ceramic roller kiln is a necessary requirement.
Disclosure of Invention
Aiming at the problems that the temperature of a ceramic body in a kiln cannot be measured and the ceramic quality of the ceramic body cannot be judged, the invention establishes a one-dimensional unsteady state model between a process parameter and the temperature of the ceramic body and a heat transfer model of the ceramic body to obtain the relation between the process parameter and the ceramic temperature, combines the input process parameter and the ceramic temperature model, and solves the problem that the kiln temperature is directly used as the boundary condition of the ceramic body in the traditional mechanism model, so that the defects exist, and the ceramic body is subjected to temperature analysis to realize energy conservation and consumption reduction.
In order to solve the technical problems, the application provides a method for acquiring the internal temperature distribution of a ceramic blank, which has the following specific technical scheme:
s1, establishing a heat conduction model inside the ceramic body in the firing process;
s2, establishing a heat transfer process model of the ceramic body based on energy conservation and mass conservation to obtain the external surface temperature of the ceramic body as a boundary condition;
and S3, solving the established heat transfer model and the heat conduction model by using a finite difference method to obtain the temperature distribution in the ceramic body.
Compared with the prior art, the invention has the following beneficial effects:
1. establishing a one-dimensional unsteady state model between the process parameters and the temperature of the ceramic body, analyzing the temperature of the ceramic body in the kiln, and judging the quality of the ceramic body;
2. obtaining the relation between the process parameters and the ceramic temperature, and combining the input process parameters with the ceramic temperature model;
3. the energy conservation and consumption reduction of ceramic enterprises are realized.
Drawings
Fig. 1 is a schematic diagram of a method for obtaining the internal temperature distribution of a ceramic body according to the present invention.
Fig. 2 is a schematic diagram of the movement of the ceramic body.
FIG. 3 is a distribution diagram of preheating and sintering sections of the roller kiln.
FIG. 4 shows the micro-element division of the preheating section.
FIG. 5 is a schematic diagram of the calculation of the angular coefficients of two perpendicular surfaces.
FIG. 6 is a layout view of a burner firing zone.
FIG. 7 is a micro-element division diagram of a firing stage.
Fig. 8 is a numerical calculation flowchart.
Fig. 9 is a one-dimensional unstable thermal conductive grid division diagram.
FIG. 10 shows the solution time for the catch-up method.
Fig. 11 is the gaussian seidel iterative solution time.
FIG. 12 is a graph of the internal and external temperature of the ceramic.
FIG. 13 is a temperature difference curve.
Detailed Description
The invention establishes a one-dimensional unsteady temperature distribution model of the ceramic body in the firing process based on mechanism analysis, obtains the temperature distribution of the ceramic in the preheating section and the combustion section during operation, and provides judgment basis for the quality in the firing process of the kiln.
As shown in fig. 1, the present invention provides a method for obtaining the internal temperature distribution of a ceramic body.
S1, establishing a heat conduction model inside the ceramic body in the firing process;
s2, establishing a heat transfer process model of the ceramic body based on energy conservation and mass conservation to obtain the external surface temperature of the ceramic body as a boundary condition;
and S3, solving the established heat transfer model and the heat conduction model by using a finite difference method to obtain the temperature distribution in the ceramic body.
And S1, establishing a heat conduction model in the ceramic body in the firing process.
Because the internal heat transfer and the physicochemical reaction of the ceramic are quite complicated in the firing process, the following assumptions are firstly made: (1) the two end faces of the ceramic are insulated, the temperature distribution is uniform along the width direction and the length direction of the kiln, and the heat conduction in the ceramic only occurs in the thickness direction; the air flow and temperature of the kiln roller way are the same, and the blackness of the surface of each section of the kiln body is the same. The ceramic green body is symmetrically heated on the upper and lower surfaces in the ceramic roller kiln.
The boundary condition of the ceramic body adopts the first class of boundary condition, and the temperature of the ceramic body at different positions in the kiln can be finally calculated by considering that the temperature error of the surface of the ceramic body directly replaced by a firing curve is large and the heat transfer process of the ceramic in the kiln needs to be established to obtain the temperature of the surface of the ceramic.
The heat conduction model is a one-dimensional unsteady heat conduction equation, which is specifically shown as the following formula:
Figure BDA0002964293670000041
Figure BDA0002964293670000042
in the formula: t represents the internal temperature of the ceramic blank, and the unit is;
τ represents time in units of s;
x represents the thickness direction of the ceramic blank and has the unit of mm;
lambda represents the thermal conductivity of the blank, and the unit is W/(m DEG C);
rho represents the density of the blank in kg/m3；
c represents the specific heat capacity of the blank body, and the unit is J/(kg DEG C);
f (l) represents the ceramic surface temperature as a function of the kiln length in degrees Celsius.
S2, establishing a heat transfer process model of the ceramic body based on energy conservation and mass conservation, and obtaining the external surface temperature of the ceramic body as a boundary condition.
And obtaining the boundary condition of the ceramic body through the ceramic body heat transfer process model.
Regarding the upper and lower boundaries of the ceramic body, the upper boundary is mainly subjected to flue gas heat transfer and wall surface radiation, and an input established ceramic heat transfer model in the kiln is considered as the upper boundary; the contact heat transfer between the lower boundary of the ceramic body and the roller way is mainly heat conduction. From the temperature curves of the upper part and the lower part of the roller kiln in actual production and research, the temperature difference between the upper part and the lower part in the kiln is not large. Therefore, only the upper part of the kiln is built, and the lower part is replaced by the heat transfer model of the upper part.
As shown in fig. 2-3, the ceramic body enters the kiln from the kiln head and moves relative to the heat medium between the preheating zone and the burning zone, is heated to the temperature required by the process through high-temperature flue gas, completes a series of physical and chemical reactions, enters the cooling zone, is cooled to a certain temperature by the cooling medium, and leaves from the kiln tail.
Combustion of natural gas in kiln
Figure BDA0002964293670000043
The losses are large in the whole process, so the invention takes the natural gas as an optimization target, wherein the natural gas combustion mainly occurs in a burning zone of the roller kiln, the ceramic physical and chemical reactions mainly occur in a preheating zone and the burning zone, and therefore the heat transfer model is positioned to the preheating section and the burning zone without considering a cooling zone. From the actual physical structure of the roller kiln, a fire baffle is arranged between the burning zone and the cooling zone to prevent cooling air from entering the burning section. The positioning is therefore also reasonable.
Basic assumption premise:
1. the system is steady, and the ceramic continuously runs.
2. The temperature of the surfaces of the kiln top, the kiln bottom and the kiln wall is uniform and the blackness is the same on each section of the roller kiln.
3. The ceramic flows counter-current to the gas, taking into account only the temperature variations along the length of the kiln, and not the temperature and gas flow variations in the vertical direction.
4. The external air can be completely mixed with the internal air flow into uniform air flow immediately after entering.
5. Neglecting the heat transfer of the roller way, the gas flow velocity, the composition and the temperature are the same above and below the roller way.
6. The longitudinal heat transfer of the kiln body due to temperature is neglected.
7. Neglecting kiln body air leakage.
S21, establishing a heat transfer process model of the ceramic body in the preheating section based on energy conservation and mass conservation.
In order to prevent the ceramic product from generating thermal shock due to overhigh temperature of the flue gas, the preheating section can not utilize the flue gas directly generated in the combustion process, but utilizes the pressure system in the kiln to enable the high-temperature flue gas in the combustion section to flow into the firing section to preheat the ceramic body. Or the clean hot air in the slow cooling stage is adopted for recycling and preheating. The ceramic evaporates free water and combined water in a preheating section, and the micro-element division of the preheating section is shown in figure 4.
Since the flue gas moves in the opposite direction to the ceramic, the smaller amount of ceramic mass in the preheating zone due to the amount of water evaporated is equal to the mass increase in the flue gas.
The flue gas mass conservation formula is as follows:
Figure BDA0002964293670000051
the ceramic conservation of mass formula is as follows:
Figure BDA0002964293670000052
wherein the content of the first and second substances,
Figure BDA0002964293670000053
which is representative of the mass flow of the flue gas,
Figure BDA0002964293670000054
represents the mass flow of the ceramic, w represents the amount of water evaporated, and Y represents the position of the ceramic body.
The flue gas energy conservation formula is as follows:
Figure BDA0002964293670000055
wherein the content of the first and second substances,cfgrepresents the specific heat capacity of the flue gas; t isfgRepresents the flue gas temperature; t isbRepresents the ceramic temperature; t iswRepresenting the temperature of the inner wall of the kiln wall;
Figure BDA0002964293670000066
represents the latent heat of vaporization of water;
Figure BDA0002964293670000067
represents the specific heat capacity of moisture; h isbRepresenting the convective heat transfer coefficient between the flue gas and the ceramic; h iswRepresenting the heat convection coefficient between the flue gas and the inner wall of the kiln; sbRepresenting the heat transfer area between the flue gas and the ceramic; swRepresenting the heat transfer area between the flue gas and the inner wall of the kiln.
The heat dissipated by the flue gas in the preheating zone is equal to the heat transferred to the ceramic and the kiln wall by the flue gas through convection, and the heat required by the evaporation of water in the ceramic body.
The ceramic energy conservation formula is as follows:
Figure BDA0002964293670000061
Figure BDA0002964293670000062
wherein Q iswbRepresenting radiation from the kiln wall to the ceramic, QbwRepresenting the radiation of the ceramic to the wall of the kiln, epsilonbRepresenting the emissivity between the ceramic and the kiln wall, epsilonwRepresenting the emissivity between the ceramic and the kiln wall; a. thebIs the emission area between the ceramic and the kiln wall, AwThe emission area between the ceramic and the kiln wall; σ represents Boltzmann constant of 5.67X 10-8w/(m2·k4)，FijRespectively, the radiation angle coefficient between the ceramic and the kiln wall.
The heat transfer of the ceramic body mainly comprises heat transfer from flue gas to ceramic, radiation from the wall surface to the ceramic and radiation from the ceramic to the wall surface.
According to the geometrical structure of the roller kiln and the ceramic green bodies, every two of the green bodies and the inner surface of the kiln wall are mutually vertical. Therefore, as shown in fig. 5, the radiation angle coefficient is calculated as follows:
Figure BDA0002964293670000063
integrating the above equation for surfaces I, J yields:
Figure BDA0002964293670000064
namely, it is
Figure BDA0002964293670000065
Due to the symmetry of the angular coefficients:
Figure BDA0002964293670000071
i represents the abscissa, and J represents the x and y abscissas of the contact position of the blank and the inner surface of the cellar wall respectively.
For the steady-state heat conduction process, the temperature of the inner wall surface of the kiln can be obtained by calculating heat loss, and the sum of the obtained heat of the inner wall surface and the convection heat transfer of the flue gas to the inner wall surface and the radiation of the ceramic to the ceramic in a section of the inner wall surface radiation is obtained. The heat loss on the outside of the wall is equal to the convection and radiation between the outer wall and the ambient air, and for a steady state process, the input heat flow is equal to the output heat flow.
hw·sw·(Tfg-Tw)+Qbw-Qwb＝R·sw·(Tw-Tenv)
Wherein, TenvRepresenting the outside ambient temperature and R representing the equivalent thermal resistance of a wall composed of different materials and ambient air.
Figure BDA0002964293670000072
Wherein, deltaiRepresents the thickness delta of each layer of heat-insulating material of the wall of the kilniRepresenting the thickness and the thermal conductivity of each layer of heat insulation material of the kiln wall; h isenvThe heat transfer coefficient of the external convection is represented and specifically shown in tables 1-2.
TABLE 1 Heat transfer coefficient between the outer surface of the wall of the ceramic kiln and the air
Figure BDA0002964293670000073
TABLE 2 insulating Material Performance parameters
Wall thermal insulation material Density (kg/m)3) Thermal conductivity (W/m. degree. C) Maximum temperature (. degree. C.)
Mullite brick 800 0.31+0.000176T 1450
Refractory clay brick 1800-2000 0.698+0.000582T 1350-1450
Mineral wool fiber 80-200 0.035+0.00015T 600
Glass wool raw cotton board 80-100 0.038+0.00017T 300
Light refractory clay brick 270-330 0.058+0.00017T 1100
S22, establishing a heat transfer process model of the ceramic body in the sintering section based on energy conservation and mass conservation.
The invention adopts a simplified mode, and only considers the input variable of the main pipe and distributes the burners of each group according to a fixed proportion by considering that the parameters of each controller are input by the main pipe.
As shown in fig. 6, the layout of the burners is such that the internal mass flow rate changes due to the presence of the burners at different positions in the firing zone, and the temperature also changes due to the combustion of the fuel. Therefore, the firing zone still needs to be divided into micro-elements for calculating the temperature distribution of the ceramic, as shown in fig. 7.
The ceramic conservation of mass formula is as follows: since the ceramic has already completed the evaporation of water and the conversion of the corresponding crystals in the preheating zone, the quality of the ceramic is not considered to change in the firing zone.
Figure BDA0002964293670000081
The flue gas mass conservation formula is as follows: the inlet mass flow of natural gas and combustion air is increased at the location of the burners compared to the preheating section.
Figure BDA0002964293670000082
Figure BDA0002964293670000083
Wherein the content of the first and second substances,
Figure BDA0002964293670000084
indicating the input quantity due to fuel and combustion air at position Y.
The ceramic energy conservation formula is as follows: the heat transfer from the flue gas to the ceramic, the radiation of the ceramic to the wall, and the radiation of the wall to the ceramic.
Figure BDA0002964293670000085
The flue gas energy conservation formula is as follows: compared with the preheating section, the position of the kiln with the burner can increase the heat quantity of the area due to the combustion of natural gas and the sensible heat brought by combustion air.
Figure BDA0002964293670000086
Wherein Q iswbRepresenting the radiation of the kiln wall to the ceramic. QfaMeans the heat input at the position with the burner,
Figure BDA0002964293670000091
wherein, caRepresents the specific heat capacity of combustion air; t isainRepresents the temperature of the combustion air input;
Figure BDA0002964293670000092
indicating the heating value of the fuel.
And S3, solving the established heat transfer model and the heat conduction model by a finite difference method to obtain the temperature distribution in the ceramic body.
And solving the ceramic body heat transfer model in the roller kiln and the ceramic body heat conduction model by adopting numerical calculation. And (3) performing programming solution on the differential equation by using a finite difference method and using MATLAB. The length L of the kiln of the preheating section and the firing section is discretized into N intervals which are mutually connected, and the discrete mass conservation and energy conservation equations are arranged at nodes, and the system calculation framework is shown in figure 8.
S31, inputting mass flow, extracted position, boundary, input condition, total node number of the blank, time step length and blank size data;
s32, solving the established heat transfer model by a finite difference method to obtain the temperature of the outer surface of the blank as a boundary condition;
and S33, solving the established heat conduction model by a finite difference method to obtain the temperature distribution in the ceramic body.
For one-dimensional unsteady heat conduction of the ceramic body, the temperature is a function of time and a function of position, and a finite difference method can be used for solving. Therefore, when equation dispersion is performed, not only the space nodes but also the time nodes are divided. Because the ceramic body is assumed to be symmetrically fired and the temperature is symmetrically distributed, only half of the thickness needs to be solved.
As shown in fig. 9, the ceramic heat conducting mesh division divides the mesh along the direction of the ceramic thickness X according to the space step Δ X; starting from τ equal to 0, the grid is divided by a time step Δ τ. The coordinates for each dimension are as follows:
xi＝iΔx i＝0，1，2，...I
τ＝kΔτ k＝0，1，2，...J
Δx＝1/I
the basic idea of finite difference is based on taylor series, and taylor expansion is as follows:
Figure BDA0002964293670000093
Figure BDA0002964293670000101
Figure BDA0002964293670000102
therefore, the differential equation of the heat conduction of the internal nodes of the ceramic can be expressed by the differential equation. The partial differential format includes several discrete methods such as a classical explicit format, a classical implicit format, a Crank-Nicolson format, a Richardson format, a compact differential format, and the like, and in order to more visually display the application of the partial differential format, a difference format of a corresponding one-dimensional unsteady heat transfer equation is given as the following table 3.
TABLE 3 five exemplary differential formats
Figure BDA0002964293670000103
The Richardson format is a completely unstable differential format, and no matter how many step sizes are taken, if a small error occurs in the calculation, the final numerical solution of the whole calculation may generate a large error. The classical display format belongs to a condition stable form, and only if
Figure BDA0002964293670000104
The calculation is reasonable, and the classical display format is obviously not suitable for the situation that the heat conductivity coefficient and the specific heat capacity of the ceramic are changed along with the temperature in the practical production process. The classical hidden format, the Crank-Nicolson format and the compact differential grid are unconditionally stable, but the truncation errors are o (tau + h)2)、o(τ2+h2) And o (τ)2+h4). It is clear that the latter is more accurate than the first two.
In order to ensure the solving precision and the operation time, the Crank-Nicolson format and the compact differential cells are respectively put under different grid numbers for comparison of the operation time. From the above table difference format it is clear that the difference equation can be written in the form of a tri-diagonal matrix at the temporal level.
Figure BDA0002964293670000111
Where a, b, c are related to λ and can be obtained from the time step, space step and heat transfer coefficient, and u represents the value to be solved in each time layer. f represents the product of the known quantity, which has been determined for the previous time horizon, and the correlation coefficient, which can also be determined in relation to λ.
The tri-diagonal matrix can be solved by catch-up in numerical analysis and gaussian seidel iteration. An example of a parabolic equation is used.
Figure BDA0002964293670000112
The analytic solution of the fixed solution problem is that u (x, t) is equal to gx+t。
The invention provides a heat transfer model of a ceramic blank in a roller kiln and a heat conduction model of the ceramic blank. And (3) solving by adopting numerical calculation, and programming and solving by adopting a finite difference method and MATLAB aiming at a differential equation.
The finite difference method is adopted for differential equations, and MATLAB is utilized for programming solution, so that solution time of a catch-up method and a Gauss Seidel iteration method is obtained, and the solution time is shown in table 4.
TABLE 4 solving time of catch-up method and Gauss Seidel iteration method
Figure BDA0002964293670000121
From table 4 above, fig. 10 and 11 show that the running time of the Crank-Nicolson format and the compact difference format solved by the catch-up method increases with the increase of the number of grids, the running time rises steeply after the number of grids exceeds 20000, and it takes almost 30 minutes when the number of grids reaches 40000 or so. While the time for both differential runs for the gaussian seidel iterative solution remains substantially within 0.3 seconds. The speed of adopting Gaussian Seidel to solve by using compact difference dispersion is about 10000 times of that of the solution by using a catch-up method.
Therefore, in terms of stability and precision of the differential format, the Crank-Nicolson format and the compact differential format are superior to the other two formats, and the Gauss Seidel iterative solution speed is superior to the solution speed of the catch-up method. Therefore, in this chapter, the equations are dispersed by a compact difference format and a differential equation is solved by a Gauss-Seidel iteration method.
Analysis of the ceramic temperature: in order to analyze the ceramic temperature by the finite difference method, the physical properties of the ceramic body were calculated as shown in table 5. The spatial step size is taken to be 0.5 and the temporal step size is taken to be 0.05.
TABLE 5 thermal Property parameters of ceramic bodies
Figure BDA0002964293670000122
From fig. 12 to 13, it can be seen that there is an obvious hysteresis relationship between the surface temperature of the ceramic body and the central section temperature of the ceramic body in the temperature rising process, so that the temperature difference is gradually increased at the beginning, the internal temperature gradually follows the surface temperature when the temperature reaches about 200s, and the internal and external temperature differences are gradually reduced. When the temperature reaches 900 ℃, the relation that physical property parameters change appears in the ceramic, and the fluctuation of the temperature difference between the inner surface and the outer surface of the ceramic is large when the temperature reaches 900 ℃ as can be seen in a temperature difference diagram. The trend of the temperature difference of the ceramic after 900 ℃ due to the influence of the variable coefficient is similar to that before 900 ℃, but the amplitude is reduced, the temperature difference of the inner and outer sections is gradually reduced when the ceramic enters the heat preservation process of the kiln at the later stage, and the ceramic is discharged from the kiln at the sintering section and enters the cooling section after the temperature reaches 0 ℃.
Therefore, for ceramics with different physical parameters, enterprises need to adjust different parameters to enable the interior of the kiln to have different temperature distributions, so that the quality of the ceramics is ensured. The change of the mechanical properties of the ceramic is researched according to the conditions of different ceramic products, and if the performance of the ceramic is measured by adopting a traditional experimental method, a large amount of manpower and material resources are wasted. Therefore, the establishment of the temperature distribution model of the ceramic body has great significance for the evaluation of the ceramic quality of enterprises.

Claims (6)

1. A method for obtaining the internal temperature distribution of a ceramic body is characterized by comprising the following steps:
s1, establishing a heat conduction model inside the ceramic body in the firing process;
s2, establishing a heat transfer process model of the ceramic body based on energy conservation and mass conservation to obtain the external surface temperature of the ceramic body as a boundary condition;
and S3, solving the established heat transfer model and the heat conduction model by using a finite difference method to obtain the temperature distribution in the ceramic body.
2. The method according to claim 1, wherein the thermal conductivity model is a one-dimensional unsteady thermal conductivity equation, as shown in the following formula:
Figure FDA0002964293660000011
Figure FDA0002964293660000012
in the formula: t represents the internal temperature of the ceramic body; τ represents time; x represents the thickness direction of the ceramic body; lambda represents the heat conductivity coefficient of the blank; rho represents the density of the blank; c represents the specific heat capacity of the green body; and f (l) represents the internal temperature of the ceramic as a function of the length of the kiln.
3. The obtaining method according to claim 1, wherein the step S2 of establishing a heat transfer process model of the ceramic body based on energy conservation and mass conservation to obtain an external surface temperature of the ceramic body as a boundary condition, specifically:
s21, establishing a heat transfer process model of the ceramic body in a preheating section based on energy conservation and mass conservation;
s22, establishing a heat transfer process model of the ceramic body in the sintering section based on energy conservation and mass conservation.
4. The acquisition method according to claim 3, wherein the heat transfer process model of the preheating section comprises a flue gas mass conservation formula, a ceramic mass conservation formula, a flue gas energy conservation formula and a ceramic energy conservation formula;
the flue gas mass conservation formula is as follows:
Figure FDA0002964293660000013
the formula for conservation of mass of the ceramic is as follows:
Figure FDA0002964293660000014
wherein the content of the first and second substances,
Figure FDA0002964293660000015
which is representative of the mass flow of the flue gas,
Figure FDA0002964293660000016
representing the mass flow of the ceramic, w representing the water evaporation capacity, and Y representing the position of the ceramic blank;
the flue gas energy conservation formula is as follows:
Figure FDA0002964293660000021
wherein, cfgRepresents the specific heat capacity of the flue gas; t isfgRepresents the flue gas temperature; t isbRepresents the temperature of the outer surface; t iswIn the representative kiln wallWall temperature;
Figure FDA0002964293660000022
represents the latent heat of vaporization of water;
Figure FDA0002964293660000023
represents the specific heat capacity of moisture; h isbRepresenting the convective heat transfer coefficient between the flue gas and the ceramic; h iswRepresenting the heat convection coefficient between the flue gas and the inner wall of the kiln; sbRepresenting the heat transfer area between the flue gas and the ceramic; swRepresenting the heat transfer area between the flue gas and the inner wall of the kiln;
the energy conservation formula of the ceramic is as follows:
Figure FDA0002964293660000024
Figure FDA0002964293660000025
wherein Q iswbRepresenting radiation from the kiln wall to the ceramic, QbwRepresenting the radiation of the ceramic to the wall of the kiln, epsilonbRepresenting the emissivity between the ceramic and the kiln wall, epsilonwRepresenting the emissivity between the ceramic and the kiln wall; a. thebIs the emission area between the ceramic and the kiln wall, AwThe emission area between the ceramic and the kiln wall; σ represents Boltzmann constant of 5.67X 10-8w/(m2·k4)，FijRespectively, the radiation angle coefficient between the ceramic and the kiln wall.
5. The acquisition method according to claim 3 or 4, wherein the heat transfer process model of the sintering section comprises a flue gas mass conservation formula, a ceramic mass conservation formula, a flue gas energy conservation formula and a ceramic energy conservation formula;
the ceramic conservation of mass formula is as follows:
Figure FDA0002964293660000026
the flue gas mass conservation formula is as follows:
Figure FDA0002964293660000027
Figure FDA0002964293660000028
wherein the content of the first and second substances,
Figure FDA0002964293660000029
indicating the input quantity due to fuel and combustion air at position Y;
the ceramic energy conservation formula is as follows:
Figure FDA00029642936600000210
the flue gas energy conservation formula is as follows:
Figure FDA0002964293660000031
wherein f isaRepresents the temperature of the outer surface; qwbRepresenting the radiation of the kiln wall to the ceramic. QfaThe specific calculation mode is as follows:
Figure FDA0002964293660000032
wherein, caRepresents the specific heat capacity of combustion air; t isainRepresents the temperature of the combustion air input;
Figure FDA0002964293660000033
watch with watchIndicating the heat value of the fuel.
6. The obtaining method according to claim 1, wherein the step S3 of solving the established heat transfer model and the heat conduction model by using a finite difference method to obtain the temperature distribution inside the ceramic body is specifically as follows:
s31, inputting data;
s32, solving the established heat transfer model by a finite difference method to obtain the external surface temperature of the ceramic blank;
and S33, solving the established heat conduction model by a finite difference method to obtain the temperature distribution in the ceramic blank.
CN202110248462.5A 2021-01-22 2021-03-05 Method for acquiring internal temperature distribution of ceramic body Pending CN112949132A (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN2021100936914 2021-01-22
CN202110093691 2021-01-22

Publications (1)

Publication Number Publication Date
CN112949132A true CN112949132A (en) 2021-06-11

Family

ID=76228615

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110248462.5A Pending CN112949132A (en) 2021-01-22 2021-03-05 Method for acquiring internal temperature distribution of ceramic body

Country Status (1)

Country Link
CN (1) CN112949132A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113627064A (en) * 2021-09-03 2021-11-09 广东工业大学 Roller kiln sintering zone temperature prediction method based on mechanism and data hybrid driving

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20180118626A1 (en) * 2016-10-28 2018-05-03 XiangTan QUFO Technology Material CO., Ltd Method for synthesizing ceramic composite powder and ceramic composite powder
CN111931417A (en) * 2020-07-21 2020-11-13 广东工业大学 Method for analyzing and optimizing technological parameters of roller kiln
CN111931419A (en) * 2020-07-30 2020-11-13 广东工业大学 Improved particle swarm algorithm-based ceramic roller kiln process parameter optimization method

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20180118626A1 (en) * 2016-10-28 2018-05-03 XiangTan QUFO Technology Material CO., Ltd Method for synthesizing ceramic composite powder and ceramic composite powder
CN111931417A (en) * 2020-07-21 2020-11-13 广东工业大学 Method for analyzing and optimizing technological parameters of roller kiln
CN111931419A (en) * 2020-07-30 2020-11-13 广东工业大学 Improved particle swarm algorithm-based ceramic roller kiln process parameter optimization method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
龙时雨: "基于GO--NP--PSO算法的辊道窑燃烧㶲损失优化研究", 《万方学位论文》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113627064A (en) * 2021-09-03 2021-11-09 广东工业大学 Roller kiln sintering zone temperature prediction method based on mechanism and data hybrid driving
CN113627064B (en) * 2021-09-03 2023-11-21 广东工业大学 Roller kiln firing zone temperature prediction method based on mechanism and data mixed driving

Similar Documents

Publication Publication Date Title
Jouhara et al. Investigation on a full-scale heat pipe heat exchanger in the ceramics industry for waste heat recovery
CN102748942B (en) Wide-bodied energy-saving and environment-friendly tunnel kiln
CN104480300B (en) A kind of based on the Pellet production method of pellet comprcssive strength in prediction rotary kiln
CN202675857U (en) Wide-body energy-saving and environment-friendly tunnel kiln
Yin et al. Design requirements and performance optimization of waste heat recovery systems for rotary kilns
Delpech et al. A review on waste heat recovery from exhaust in the ceramics industry
Refaey et al. Influence of fuel distribution and heat transfer on energy consumption in tunnel kilns
CN208059546U (en) The box atmosphere roller furnace of ternary
CN112949132A (en) Method for acquiring internal temperature distribution of ceramic body
CN107445156A (en) A kind of graphitizing furnace with quick cooling and function of recovering waste heat
Filkoski et al. Energy optimisation of vertical shaft kiln operation in the process of dolomite calcination
CN107867868A (en) A kind of super fine and close high heat conduction silica brick and preparation method thereof
CN207850033U (en) A kind of energy-saving tunnel oven
CN107723006A (en) A kind of heater and technique of long flame dry distillation of coal complete alternation gas
Balli et al. Experimental study and numerical modeling of the thermal behavior of an industrial prototype ceramic furnace: energy and environmental optimization
CN202792964U (en) Small-sized external heating type sintering interruption experiment furnace
CN204514019U (en) A kind of novel high-efficiency and energy-saving preparing heat-accumulating ceramic roller kilns
CN203403121U (en) Device for achieving high blast temperature by virtue of low calorific value coal gas and high temperature combustion-supporting air
CN204574837U (en) Roller kilns waste heat combustion air heating apparatus
CN206755585U (en) Organic heat carrier furnace
CN206001892U (en) Rotary reaction furnace hot air heating system
CN207525187U (en) A kind of heating unit of long flame dry distillation of coal complete alternation gas
Ma et al. Transient heat transfer analysis in packed beds: Entropy generation model and multi-objective optimization
CN106091672B (en) Rotary reaction furnace hot air heating system
CN201805891U (en) Flue gas channel of heater for dense tobacco flue-curing house

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20210611

RJ01 Rejection of invention patent application after publication