Function optimization of ceramic firing process and reduction of energy consumption based on CFD simulation

Microwave sintering, as an efficient and energy-saving advanced sintering method, has advantages that traditional sintering methods cannot match, such as promoting ion diffusion and refining grains. This paper uses microwave heating equipment and solid-phase reaction method combined with microwave sintering technology to prepare ceramics. The treatment process of powders and the influence of microwave sintering parameters on the reduction of energy consumption in the ceramic firing process were studied, and the microwave sintering process was optimized. This article also uses computational fluid dynamics (CFD) as a tool to establish a numerical model of hydrodynamic sedimentation based on the Euler multiphase flow model, and it uses the established numerical model to conduct engineering scale research on the classification treatment process of processing waste. Finally, this article elaborates on the process of multi-process planning and optimizes relevant process parameters. This article builds on previous research by employing a BP neural network (BPNN) to determine the correlations between the many variables involved in the production of functional ceramics and their respective quality metrics. The experimental findings demonstrate the efficacy of the proposed methodology in performing intelligent tasks like process decision-making and optimizing process parameters.


Introduction
In the application field of functional ceramics, the processing quality of functional ceramics directly determines the performance of functional ceramic electronic components.During the sintering process of transparent ceramics, rotation and sliding occur between particles, causing particle rearrangement [1].At the same time, with the growth of grains and the increase of sample density, appropriate sintering processes can reduce the generation of impurities and defects inside the sample, effectively improving the permeability of the ceramics.In recent decades, with the research and exploration of ceramics by scientists, various methods of sintering transparent ceramics have continuously improved and matured, and high-quality transparent ceramics have been successfully prepared, achieving highpower laser output [2].Vacuum pressureless sintering is currently the most mature and effective sintering method for preparing transparent ceramics.
Generally, the densification process of ceramics is controlled through slow heating in a high vacuum environment.The driving force of sintering is mainly the change of free energy, which promotes the discharge of gas along grain boundaries and avoids the generation of second phases.After sintering, oxygen vacancies are eliminated through heat treatment and a transparent ceramic with high transmittance is obtained [3].In addition, researchers have prepared ideal ceramics using vacuum pressureless sintering in a hydrogen or oxygen atmosphere.This method requires simple equipment, low manufacturing cost, and can achieve the preparation of large-sized and structurally complex ceramics.However, the preparation of ceramics by this method requires a longer insulation time at high temperatures, which consumes more energy compared to other sintering methods, has a longer production cycle, and it is prone to abnormal grain growth and other phenomena.Spark plasma sintering is the process of placing a sample in a mold and applying axial pressure to heat the sample through a large amount of heat generated by Joule heat and pulse energy.This method can accelerate the densification process of the sample and obtain ceramics with fine grains at lower temperatures and in a short period of time [4].At present, high-quality ceramics have been prepared through this method, and their laser performance is similar to that obtained by traditional sintering methods.Due to the fastheating rate, internal stress can easily form inside the ceramic, leading to sample cracking.At the same time, it poses certain challenges in the accuracy of temperature measurement and the uniformity of temperature distribution [5].Hot pressing sintering is a method of quickly completing sintering by placing the mixed powder into a mold, applying pressure, and at high temperatures [6].
The heating rate of this method is relatively slow, and it can also obtain dense and transparent ceramics in a relatively short time, with small grains and excellent optical properties.However, due to mold limitations, it can only manufacture ceramic samples with simple structures.Microwave heating has an inverse temperature distribution, where the center temperature of the sample is the highest and the surface temperature is the lowest.This temperature distribution is conducive to the gas being expelled from the sample one by one along the grain boundaries.Microwave sintering of ceramics can also reduce additional contamination of the sample, such as the chemical elements evaporated in traditional heating equipment, which is beneficial for improving the purity of the sample.Compared with traditional heating methods, microwave heating is more uniform, fast, and energy-saving.At the same time, under the action of electromagnetic fields, it reduces the sintering activation energy and sintering temperature, improves the ion diffusion rate, and it helps to obtain high optical quality ceramics in a short period of time.This can effectively compensate for some shortcomings of the solid-state reaction method, avoid prolonged insulation at high temperatures, inhibit grain growth and weaken the impact of relatively large commercial powder particle sizes.Due to the complexity of ceramic membrane filtration and membrane fouling mechanisms, only macroscopic experimental data and qualitative or semi quantitative information on permeation, concentration polarization and membrane fouling phenomena can be obtained in a single filtration experimental study, making it difficult to judge and analyze the microscopic fluid flow inside the membrane.CFD is an important tool for developing membrane filtration processes, which can reduce resource consumption.Many scholars have used CFD simulation to intuitively and effectively simulate and predict the fluid flow inside the membrane, analyze and explore the mechanism of membrane filtration process.
This article analyzes the microwave firing process of ceramics, optimizes the heating parameters and applies CFD to analyze and optimize the flow mechanism of ceramic firing equipment flow field.Finally, a neural network is used to evaluate the effect of energy reduction after optimization, which has guiding significance for optimizing ceramic firing process and reducing energy consumption.

Related work
Reference [7] used different polishing abrasives in the polishing of silicon nitride ceramics, observed the reactants and surface morphology of the polished specimen surface, and explored the relationship between polishing abrasives and surface roughness.Reference [8] explored the relationship between main process parameters such as polishing solution concentration, polishing solution flow rate, polishing wheel speed, and surface quality in experiments on the use of silicon nitride ceramics, and ultimately obtained the optimal combination of process parameters.Reference [9] optimized the polishing pressure, polishing speed, and other process parameters for CaAs substrate polishing using surface roughness and material removal rate as comprehensive evaluation indicators and obtained the best combination of results.
Reference [10] establishes a prediction model for surface roughness after cutting based on BPNN theory for ceramic material cutting, with an accuracy of over 97%, which can effectively predict.In order to optimize the structure and operating parameters of asymmetric single-channel ceramic membrane tubes, CFD calculations were conducted to simulate their permeability performance.Reference [12] established local two-dimensional simplified models for ceramic membranes with geometric configurations of circular and square channels, and studied the effect of permeability ratio between membrane separation layer and membrane support layer on fluid flow distribution.To study the flow field distribution of serial ceramic modules, the flow field, resistance, and permeation flux within components with different component positions and channels were studied.The infiltration of pure water over the cross-section of a ceramic membrane tube with 37 channels was analyzed in detail using a three-dimensional CFD model in reference [13].Six enhanced models were offered for the 37channel ceramic membrane configuration after theoretical analysis and simulation calculations were performed on its key structural features.The pressure distribution and fluid velocity distribution inside the membrane were obtained by numerical simulations under the assumption of pure water filtration via a ceramic membrane without a separating layer.
Compared to traditional heating methods, microwave heating is more uniform, rapid, and energyefficient.Additionally, under the influence of an electromagnetic field, it reduces the activation energy and sintering temperature, enhances ion diffusion rates, and helps achieve high optical quality ceramics in a short period of time.This effectively compensates for some drawbacks of solid-state reaction methods, avoiding prolonged insulation time at high temperatures, suppressing grain growth, and mitigating the influence of relatively large commercial powder particle sizes.However, CFD simulation of ceramic firing processes also has certain limitations.Ceramic firing involves multiple physical processes such as heat conduction, mass transfer, and chemical reactions, which need to be considered in CFD simulations, making the simulation process relatively complex.CFD simulations require various physical and chemical parameters, which may be difficult to accurately measure or estimate, including material properties and fuel combustion characteristics, potentially affecting the accuracy of simulation results.High-resolution CFD simulations require substantial computational resources, including computation time and computer storage space, which may not be suitable for all practical engineering applications.CFD simulations require the development of appropriate mathematical models to describe the physical phenomena of firing processes, and the accuracy and applicability of these models need to be validated and verified, as inaccurate models may lead to simulation results that deviate from reality.Validation and verification of CFD simulation results require experimental data as references, but sometimes obtaining experimental data can be challenging or costly.Overall, although CFD simulation has achieved success in many engineering fields, there are still challenges and limitations when simulating ceramic firing processes.

Basic principles of computational fluid dynamics
Using numerical computations and visual representations, CFD analyzes systems with physical phenomena like fluid flow and heat conduction.Computer fluid dynamics (CFD) numerical simulation using computers to do theoretical analysis and computations on objects, with the outcome being shown visually.The analysis results are objective, reliable, and vivid.The working principle and process of CFD are as follows: Step 1, establish the control equation.This is the primary step in the CFD solution process.Knowing the fundamentals of fluid mechanics and being able to express control equations and mathematical models that are appropriate for the research object will help users when it comes time to select the appropriate parameters in commercial software that converts control equations into controls.The second stage entails fixing the starting and boundary states.In order for the control equation to have a unique solution, the initial and boundary conditions must be specified.Together, the control equation and the beginning and boundary conditions describe the entire physical process.At the outset of the procedure, the boundary condition describes how the variables or their derivatives solved at the area's edge change with respect to place and time, while the starting condition describes the geographical distribution of each solution variable of all research items.The next step is to separate the computational grid.To use numerical approaches to the solution of control equations, one must first discretize the equations in the spatial domain.There are a number of grid generating technologies available now.Although the grids required by various numerical solutions for various problems might vary, the fundamental approach to constructing grids remains the same.There are now two types of grids, organized and unstructured.Nonstructural grids do not have apparent row and column lines in spatial distribution, but structural grids are more uniform in space, such as for a quadrilateral region, where the grid is frequently dispersed in rows and columns.Triangles and quadrilaterals are frequent mesh components for 2D challenges.Tetrahedra, hexahedra, triangular prisms, and other shapes are all employed as mesh elements for 3D issues.Grids are interconnected by nodes over the entirety of the computational domain.Figure 1 depicts a typical CFD process.Creating a discrete equation is the fourth stage.Within the solution domain, there exists a theoretically solvable partial differential equation.However, it is typically challenging to develop analytical answers due to the intricacy of the problem being addressed.Therefore, it is necessary to establish a set of algebraic equations about these unknowns via numerical methods in order to obtain these node values, and then to treat the dependent variable values of a finite number of positions within the computational domain as basic unknowns.Based on the values at the node position, the values at other places within the computational domain are calculated.Different types of discretization methods have developed as a result of the distribution assumptions of the added dependent variables between nodes and the various approaches to generating discretization equations.The fifth step is to make the beginning and boundary conditions discrete.Since the specified beginning and boundary conditions are continuous, they must be discretized into values on the nodes of the created mesh, and the established discrete control equation must also be used.Sixth, adjust the parameters of the solution.After a discrete space is defined and an algebraic equation system is used, the physical parameters of the fluid and the empirical coefficients of the turbulence model must be supplied.After that, the output frequency, the realistic step size of the transient problem, and the control accuracy of the iterative calculation should be provided.Seventh, determine the numerical answer to the discrete equation.Computation relies on discretizing the control equation into an algebraic system and developing a set of procedures that can be carried out by a computer to solve the algorithm.The infinite information system is reduced to a finite one by discretizing and algebraizing partial differential equations.After discretizing the partial differential equations into algebraic equations, the flow field may be solved numerically.Step 8, determine the convergence of the solution.This part is empirical and needs to be analyzed for different situations.Step 9, post processing and visualization process.The purpose of post-processing is to effectively observe and analyze the flow calculation results.At present, general CFD software is equipped with a post-processor, providing relatively complete post-processing functions.By utilizing the post-processing function, the obtained data can be processed, and vector maps, contour maps, streamline maps, cloud maps, and other methods can be used to more intuitively express CFD calculation results.

Microwave sintering process of ceramics
The sintering process of ceramics is divided into pre sintering, mid sintering, and post sintering, mainly completing the densification process through mutual diffusion between materials, accompanied by phenomena such as particle bonding, rearrangement, and continuous grain growth.Solid state reaction synthesis is usually considered to be controlled by the diffusion of Al.The decrease in the generation temperature of each phase indicates that electromagnetic fields can effectively promote the diffusion of Al and accelerate the reaction between various substances.Analyzing the transformation process between phases is of great significance for optimizing sintering parameters.There are three phases in the Al₂O₃-Y₂O₃ system: monoclinic phase, perovskite phase, and cubic phase.The solid-state reaction during the sintering process is shown by the following equation: After calcination at 800℃, only Al2O3 and Y2O3 substances still exist in the ceramic body.After calcination at 900℃, a small amount of YAM is generated.The main temperature range for YAM formation is between 900℃ and 1000℃.At 1000℃, there is a large amount of YAM present, while a small amount of YAP and YAG coexist.When the temperature rises to 1100℃, the content of YAM gradually decreases, accompanied by a large amount of YAP generation.After calcination at 1200℃, YAP phase gradually transforms into YAG phase, but YAM, YAP, Al2O3, and Y2O3 also exist simultaneously.As the sintering temperature increases, YAM and Y2O3 disappear at 1300℃, while a small amount of YAP and Al2O3 exist.When the calcination temperature is 1400℃, all are converted into YAG phase.Research has shown that compared with traditional sintering methods, the exothermic reaction temperature of YAM and YAP occurs below 150℃-200℃.Based on the above experimental results, it can be concluded that the temperature at which YAM phase is generated under microwave sintering conditions is 50°C-100°C lower, while the temperature at which the characteristic peaks of YAP and YAG appear is reduced by 100°C-150°C.There is a difference between these two temperature differences.
The sintering temperature has a direct effect on optimizing the internal structure of ceramics.When the temperature is low, the diffusion process is mainly surface diffusion.The rate of mass transfer through this diffusion method is slow, and the migration rate of pores and the densification rate of the sample are relatively slow, making it difficult to obtain an ideal sample.When the temperature is too high, the migration rate of grain boundaries is greater than that of pores, which can form closed pores or large-sized grains in the ceramic.At the same time, ceramic samples are prone to thermal runaway during the single mode cavity microwave sintering process, resulting in uneven heating or burning loss of the samples.Microwave sintering of YAG ceramics can achieve volume heating and enhance densification kinetics, which differs from the traditional pressureless sintering process.Analyzing the influence of temperature on the densification process of ceramics is beneficial for optimizing microwave sintering parameters.
At 1300℃, there are still a large number of pores, but through the rotation and sliding of particles, the initial particles rearrange and form submicron sized particles.At the same time, it is also found that YAG phase grain boundaries have begun to form.Compared with traditional heating methods, the particle size change after this rearrangement is more significant, due to the volume heating characteristics of microwave sintering promoting particle rearrangement.As the temperature increases to 1400℃, the number of spherical particles decreases and with the increase of size, microwave sintering accelerates the coarsening of particles.The densification behavior of ceramics mainly occurs at 1400℃-1500℃.As the sintering temperature increases, there are still a small number of pores in the grains, and intergranular fractures gradually disappear.
Shortening the sintering time and considerably improving the preparation efficiency are two major benefits of microwave sintering clear ceramics, both of which are directly connected to the faster heating rate.Liquid Al-Y-Si-O can absorb a lot of microwave energy and generate high temperatures in localized areas because the Esposito wave accelerates the development of this phase at lower temperatures.Exothermic reactions of YAM and YAP occur simultaneously with the sintering process.Overheating the sample causes the liquid phase's viscosity to drop, leading to the formation of a second phase at the grain boundary and a subsequent decrease in the ceramic's optical transparency.Optimizing microwave sintering parameters is necessary to enhance the internal structure of YAG transparent ceramics, where the second phase and pores are the primary variables impacting the sintering process.Taking into account the influence of sintering temperature and heating rate on the internal structure of the ceramic, the optimal heating rate of microwave sintering was determined by analyzing the above phase and densification process.Microwave sintering increases the reaction rate of the material, resulting in the formation of an Al-Y-Si-O liquid phase at lower temperatures accompanied by exothermic reactions of YAM and YAP.Unlike conventional sintering techniques, the initial heating temperature of a sample in a single mode cavity can reach 800°C when a high density electromagnetic field is combined with it.Experiments, however, have shown that this makes little difference to the microwave sintering of transparent ceramics.

Structure and design of BP neural network
The characteristic of the BP algorithm is that it includes forward signal transmission and reverse error transmission.The following are introduced from three aspects: weight adjustment, signal flow direction, and program implementation.When the output signal is different from the expected signal, the network error is recorded as E, and its formula is as follows.
where   represents the expected output of the k-th item, and   represents the output of the k-th item.Reducing the error value is the goal of adjusting the weight value, so there is the following relationship: where ∆ and ∆ respectively represent the weight adjustment amounts of the output layer and the hidden layer.

Experimental preparation
This article constructed an experimental dataset with a total of 500 sets of data for the experiment.Part of the data is shown in Table 1.Due to the physical and dimensional differences in the input and output quantities of networks, in order to have the same status in network input and output, it is necessary to normalize the input and output samples.The specific calculation formula is as follows.

Experimental results and analysis
Figure 2 shows the training error curve of a network with a hidden layer neuron count of 2-12.

Figure 2.
Training of the number of hidden layer neurons.As shown in figure 2, when the number of hidden layer units is 12, the neural network has good accuracy and convergence, so the number of hidden layer units is taken as 12.
To verify the correctness and effectiveness of the BPNN prediction model with a hidden layer unit number of 12, six additional sets of test samples were selected in this paper.Figure 3 shows a comparative analysis of the predicted and experimental results of sintering energy consumption of silicon carbide ceramics.From figure 3, it can be seen that the BPNN with a hidden layer unit number of 12 has a prediction accuracy of 96%, proving that the prediction model established in this paper can effectively predict the sintering energy consumption of silicon carbide ceramics.This article has established prediction models for silicon carbide and alumina ceramics, with the prediction accuracy shown in figure 4. The prediction accuracy refers to the relative error between the predicted values of each prediction model and the experimental values.From figure 4, it can be seen that the average relative error between the predicted values and experimental values of the prediction model established for silicon carbide and alumina ceramics is below 5%.Therefore, the BPNN prediction model established in this article for silicon carbide and alumina ceramics is correct and effective.

Conclusion
On the basis of summarizing the current research status of ceramic sintering process optimization and energy consumption prediction both domestically and internationally, in order to further reduce energy consumption, a mapping relationship between process flow and energy consumption was established using BP neural network.A multi process intelligent process flow for ceramic sintering was proposed, and the following main results were obtained.Based on the multi process theory, this article optimized the process route and parameters for the ceramic firing process, and the effectiveness of the optimization results was verified through experiments.Based on the BP neural network, this article establishes mapping relationships between various process parameters and evaluation indicators in a multi process ceramic firing process.Experiments have shown that the prediction accuracy of the established mapping relationships is over 96%.Due to constraints, the intelligent process database established in this article for the ceramic firing process needs to be further enriched.

Figure 1 .
Figure 1.Working flow chart of CFD.Creating a discrete equation is the fourth stage.Within the solution domain, there exists a theoretically solvable partial differential equation.However, it is typically challenging to develop analytical answers due to the intricacy of the problem being addressed.Therefore, it is necessary to establish a set of algebraic equations about these unknowns via numerical methods in order to obtain these node values, and then to treat the dependent variable values of a finite number of positions within the computational domain as basic unknowns.Based on the values at the node position, the values at other places within the computational domain are calculated.Different types of discretization methods have developed as a result of the distribution assumptions of the added dependent variables between nodes and the various approaches to generating discretization equations.The fifth step is to make the beginning and boundary conditions discrete.Since the specified beginning and boundary conditions are continuous, they must be discretized into values on the nodes of the created mesh, and the established discrete control equation must also be used.Sixth, adjust the parameters of the solution.After a discrete space is defined and an algebraic equation system is used, the physical parameters of the fluid and the empirical coefficients of the turbulence model must be supplied.After that, the output frequency, the realistic step size of the transient problem, and the control accuracy of the iterative calculation should be provided.Seventh, determine the numerical answer to the discrete equation.Computation relies on discretizing the control equation into an algebraic system and developing a set of procedures that can be carried out by a computer to solve the algorithm.The infinite information system is reduced to a finite one by discretizing and algebraizing partial differential equations.After discretizing the partial differential equations into algebraic equations, the flow field may be solved numerically.Step 8, determine the convergence of the solution.This part is empirical and needs to be
on Applied Physics and Mathematics Journal of Physics: Conference Series 2729 (2024) 012003

Figure 4 .
Figure 4.The prediction accuracy of the model for two types of ceramics.From figure4, it can be seen that the average relative error between the predicted values and experimental values of the prediction model established for silicon carbide and alumina ceramics is below 5%.Therefore, the BPNN prediction model established in this article for silicon carbide and alumina ceramics is correct and effective.
on Applied Physics and Mathematics