Introduction

Glass fibers have become essential materials in various critical fields due to their excellent insulation, heat resistance, corrosion resistance, and mechanical strength1,2. With the increase in the market demand, the requirements for furnace technology are continuously increasing, which makes large-capacity and high-efficiency furnaces the new standard for industry development3. However, in traditional air-fuel combustion processes, the presence of nitrogen results in significant heat loss and the formation of NOx, which adversely affects the environment. In order to solve this issue, the oxy-fuel combustion process was developed. By utilizing high-purity oxygen as the oxidizer, it not only reduces nitrogen oxide emissions, but also improves the combustion temperature and heat transfer efficiency of the glass melt. Bělohradsky et al.4 conducted a combustion experiment with two modes (single-stage and two-stage combustion) via using a low-NOx experimental dual-fuel staged burner under a thermal input of 750 kW. The available heat at 46% oxygen was 20% higher than that at 21% oxygen. Because of its advantages, this process has been widely adopted in the glass industry, which demonstrates its potential in many studies to enhance combustion efficiency, reduce environmental pollution, and meet sustainable development goals.

Currently, the application of numerical simulation technology offers strong support for performance prediction and structural optimization of glass melting furnaces5,6. Through accurate numerical calculations and intuitive visual displays, researchers can thoroughly understand the application of oxy-fuel combustion technology in furnaces, which can enable them to optimize designs. For instance, Feng et al.7,8simulated float glass furnaces with varying production capacities, and revealed the significance of consistent glass surface temperature distribution in ensuring product quality. This work also showed that with increasing production, glass uniformity decreases, and the consistency between glass product side stripes. Simultaneously, the simulation results further validated the effectiveness of numerical simulation in predicting and optimizing furnace performance. Furthermore, in terms of the CFD model study of oxy-fuel combustion, Li et al.9 established a 3D mathematical model based on the actual conditions of a 20,000-ton per year glass fiber furnace, analyzed the defects in the combustion space, and proposed structural improvements to maintain a reasonable temperature field, reduce heat load on the crown, and enhance flow field distribution. Dong et al.10 creatively integrated a burner and flue on one side of the furnace, and their study validated the simulation results of high-temperature flue gases generated by natural gas oxy-combustion, significantly reducing energy consumption. Meanwhile, different burner nozzle widths allowed for flame width adjustment, better meeting the requirements of the glass melting system, and then it could significantly improve the flue gas waste heat utilization. Filho et al.11 selected the vortex dissipation model, weighted gray gas model, and a 5% turbulent intensity k-epsilon model as the combustion, participating medium absorption, and turbulence models. Actually, in terms of numerical simulations, the combustion chamber and glass melt were solved independently. But the iterative process was coupled and it could enhance the iterative stability and reduce computation costs. More scholars have conducted in-depth research on the selection of combustion models. Chen, Xuelei et al.12 tested PDF model, multi-flame model, eddy-dissipation model and finite-rate / eddy-dissipation model with two different global rates. The simulation results show that the finite rate / eddy dissipation model is most consistent with the BERL data. Gallegos-Munoz et al.13 carried out a study on low-pressure gas combustion of baked ceramics in an atmospheric burner. The study included different models of combustion and turbulence to find the best chemical-turbulence interaction. The turbulent-chemical results of each combination were compared with the experimental measurements of the temperature in the furnace. The results show that the combustion finite rate / eddy dissipation and laminar flamelet model obtain the best experimental results. Lezcano-Benitez et al.14 studied and simulated a flame atmospheric premixed burner that burns methane under high pressure. A total of nine simulations were performed on different regulator openings of primary and secondary air. The standard k-epsilon model is used for turbulence, the P1 model for radiation and the finite rate / eddy dissipation model for simulation. The model has a simplified two-step combustion reaction mechanism. HUANG Wei et al.15 numerically simulated the combustion flow field of a typical strut scramjet combustor by using two-dimensional coupled implicit Reynolds-averaged Navier-Stokes equations, shear stress transfer k-w turbulence model and finite rate / eddy dissipation reaction model. The effects of hydrogen-air reaction mechanism, fuel injection temperature and pressure on the parameter distribution in the combustion chamber were studied. The results show that the numerical results are in good agreement with the experimental data. Katare, S et al.16 studied the flame retention mechanism of the wedge strut in supersonic flow. The two-dimensional coupled implicit RANS equation, the standard k-ε turbulence model and the finite rate / eddy dissipation model were introduced to simulate the flow field of the scramjet combustor with strut under different working conditions. In order to improve the combustion characteristics of non-premixed double-jet inlet, Mohamed M. S. Yaseen et al.17 studied the effects of fuel and inlet shape on the component transport and finite rate / eddy current dissipation process at different speeds by using ANSYS finite element analysis software. The results show that the change of inlet velocity and geometry will affect the behavior and intensity of the flame, thus affecting the temperature, heat release rate, combustion efficiency and equivalence ratio. In the circular-circular inlet, the optimal air / fuel velocity is 2.5 / 1.5.

Nowadays, the electric melting process achieves efficient auxiliary melting by directly inserting electrodes into the glass melt, using Joule heat to act directly on the molten glass18,19. This method leverages the electrical conductivity of the glass melt, and compared to traditional combustion methods, electricity as a clean energy source offers significant benefits in energy saving and consumption reduction20. The use of the electric power, not only reduces pollutant emissions, but also plays an important role in reaching carbon peak and carbon neutrality goals21. Although all-electrical glass melting furnaces are mainly suitable for small-scale specialty glass production due to their small size and simple structure, significant progress has been made in the study of all-electric and electric boosting furnaces. Through the establishment of a physical model of the furnace, Bansal et al.22 explored the relationship between macro and micro aspects of all-electrical glass furnaces and provided relevant findings. Li et al.23 simulated and analyzed two all-electrical furnaces of different scales, uncovering the features of electric power density distribution, temperature fields, and velocity fields. They discovered that the power density and temperature increase firstly and then decrease in the horizontal direction from the center to the sidewalls, with a similar trend observed vertically from top to bottom. Li et al.24,25,26 developed an integrated glass furnace model that combines the combustion space and glass tank, and analyzed the effects of electric boosting systems on a 600t/d float glass furnace. Through analyzing temperature fields, velocity fields, and glass trajectories, they found that the electric boosting system enhanced the average melting efficiency, glass melting quality, and the uniformity of the glass melt. However, in the case of electric boosting, the melting quality of the fastest particles might be inferior. By optimizing the design of the electric boosting system, better glass melting quality, more uniform melting, and higher melting efficiency could be achieved. Further research explored the impact of increasing fuel supply and introducing electric boosting on enhancing glass production. The results showed that although increasing fuel supply was an effective method, the introduction of electric power was the superior choice when ensuring glass quality and furnace lifespan. The study also revealed that electrode positioning had a significant effect on the glass melting process. When electrodes were installed beneath the batch blanket, they accelerated the melting process of the batch and stabilize convection, and then it improved glass quality and melting efficiency.

In a word, in the current research field, the simulation of glass fiber melting furnaces has mainly centered on several types, such as all-electrical furnaces, oxy-fuel furnaces, or air-fuel electric boosting furnaces. However, the research on the oxy-fuel electric boosting furnace model, which combines oxy-fuel combustion with electric boosting, is relatively scarce. And then, this situation indicates that this field requires further exploration and development. In this study, the computational fluid dynamics (CFD) method was used to carry out the simulation analysis of a 200-ton-per-day oxy-fuel electric boosting glass fiber melting furnace by using ANSYS Fluent2022R1. The simulation not only encompasses the operating conditions of the furnace, but also particularly compares the performance of air-fuel and oxy-fuel combustion methods. During the actual simulation process, data exchange between simulations was realized through the coupling interface (glass melt surface) between the combustion chamber and the glass tank, and this simulation method can reduce computational costs. In evaluating the performance and production quality of the glass melting furnace, several key quality indicators, including residence time distribution, melting factor, and mixing factor, were utilized. These indicators offered a comprehensive perspective for evaluating and optimizing furnace operational efficiency and product quality. Through this comprehensive simulation and evaluation approach, we can gain an in-depth understanding of the performance of oxy-fuel electric boosting furnaces in practical applications, and this work can provide scientific evidence for further technological improvements and innovations. This research not only adds to the literature on glass fiber furnace simulation, but also offers new insights and methods for the sustainable development of the glass fiber industry. Next, the process strengthening simulation of different process conditions and furnace structure will be continued to explore, aiming to play a guiding role in actual production.

Numerical simulation

Geometric model

This study examines an oxy-fuel glass fiber melting furnace with electric boosting. Figure 1 is a three-dimensional schematic diagram of the furnace. The furnace consists of a combustion chamber and a glass tank. The height of the glass melt is set at 1.2 m.

Fig. 1
figure 1

Three-dimensional schematic diagram of glass fiber furnace.

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Due to the complexity of the physical field changes in the glass fiber furnace, and the strong correlation between the combustion space and the glass tank, a complete three-dimensional integrated numerical model is needed to predict the furnace’s operating conditions.

Figure 2 shows a schematic of the sectional views of the 3D numerical model of the glass fiber furnace, with the furnace dimensions shown in Table 1.

Fig. 2
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Schematic diagram of each section of 3D glass furnace. (a) horizontal plane of glass tank. (b) section of glass tank side.

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Table 1 The main structure parameters of the orifice plate glass fiber melting furnace.
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Mesh generation and simulation boundary conditions

Figure 3 shows a schematic of the full mesh. The minimum mesh size is set to 5 mm. The computational domain includes a glass tank and a combustion space. Polyhedral meshes and refined meshes are used at the inlet and outlet, with a total of 1,358,950 cells.

Fig. 3
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Schematic diagram of glass furnace grid division.

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Combustion chamber

In this study, each side of the combustion chamber has 7 burners and 1 flue outlet. Under oxy-fuel operation, the burners supply a constant fuel input of 2209 m³/h, and the natural gas has a heating value of 33,235 kJ/m³. Unlike regenerative furnaces, these burners do not preheat the fuel or oxidizer. The fuel supply for each burner is detailed in Table 2. The natural gas used as fuel consists of 96%v CH4, 3%v higher hydrocarbons (ethane and propane), 0.34%v CO2, and 0.66%v N2. The oxidizer is either 99.5%v pure oxygen or air.

Table 2 Fuel ratio in each port.
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Glass melt section

The production target is typical soda-lime-silica glass. The furnace has a melting capacity of 200 t/d. To facilitate raw material melting and mixing, six rows of electrodes are vertically installed evenly at the bottom of the furnace, with each row having six electrode rods. Every two rows of electrode rods form a group, with the input power ratio of the three groups being 25:20:14. The diameter of the electrode rods is 70 mm, with an insertion depth of 350 mm into the glass melt.

Material properties

The combustion gas is a mixture. Properties such as viscosity, thermal conductivity, and specific heat, are defined by calculating the mass-fraction averages of the pure substances. The density is determined by the ideal gas law. The study uses typical Na-Ca-Si glass, and the thermal properties of the molten glass are listed in Table 3.

Table 3 Thermophysical properties of molten glass27.
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Numerical settings

Coupled simulation methods

In the calculation of the glass fiber furnace, the combustion chamber and glass tank are coupled through data exchange. The coupling interface is the bottom of the combustion chamber, i.e., the glass melt surface. The glass melt and combustion chamber exchange heat flux densities at the coupling interface to couple the two spaces.

Governing equations

A model incorporating the combustion space and glass melt is established. In the combustion chamber, the k-ε model, species transport, and radiation model (DO) are used to analyze the flow behavior in this space. In the glass tank, modeling is performed using laminar flow, the radiation model (DO), and Joule heating for electric boosting. Data exchange between the combustion chamber and glass tank is realized through the coupling interface (glass melt surface) to enable numerical simulation.

Combustion chamber simulation

Fluid flow simulation in the combustion chamber

In this study, the realizable k-ε model was chosen for steady-state turbulent combustion simulation28,29. To ensure that the model performs well for certain standard flows, the default values of the model constants were maintained during the model setup. The standard wall function was applied to handle the near-wall transition layer.

Combustion simulation

For modeling the combustion reaction of natural gas, the species transport volumetric reaction model was chosen. The finite-rate/eddy-dissipation model was employed to handle the influence of turbulence on the chemical reaction rate. ANSYS Fluent models the mixing and transport of chemical species by solving the conservation equations for convection, diffusion, and reaction sources for each species.

Radiation simulation in the combustion chamber

The discrete ordinates radiation model (DO) was employed to solve the radiation transfer equation inside the combustion chamber.

Glass tank simulation

Glass tank fluid flow simulation

Due to the high viscosity and low speed of the glass melt, its flow in the glass tank is laminar. For laminar flow, the mass and momentum conservation equations are solved directly30.

Glass tank radiation simulation

In the radiation modeling of the glass melt, scattering is ignored, and the discrete ordinates (DO) radiation model is used to calculate radiative heat transfer inside the glass tank.

Glass tank electric boosting simulation

Since molten glass becomes conductive at high temperatures, applying an electric field generates electric potential and current. When the current flows through the medium, it produces heat, a phenomenon known as Joule heating. The generated Joule heat is included in the energy equation as an energy source term.

Mesh independence validation

According to the mesh division results, the total number of cells in the computational region is 1,358,950, with all meshes being polyhedral. Mesh refinement was applied at the inlet and outlet for combustion gas and glass. Considering the influence of mesh quantity on the calculation results, three mesh configurations, 980,019、1,358,950 and 1,686,138, were compared. As shown in Fig. 4, the error of the mesh results of 980, 019 is large, and the difference between the results of the 1,358,950 and 1,686,138 meshes is less than 3%. Therefore, the 1,358,950 mesh is considered suitable for the simulation.

Fig. 4
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Glass surface temperature.

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Results and discussion

Combustion space temperature distribution

Figures 5 and 6 display the temperature and streamline distribution contour plots for the oxy-fuel electric boosting process and the electric boosting process at the burner plane (a) and the plane of burner 4 (b). Compared to the oxy-fuel electric boosting process, the electric boosting process—where air is used as the oxidizer—shows a significantly lower overall temperature in the flame-covered zone, but the temperature difference in the non-flame zone is minimal. This is because the oxy-fuel electric boosting process uses high-concentration oxygen as the oxidizer, and as oxygen is a strong oxidizing agent, higher concentrations intensify chemical reactions, allowing the fuel to burn more completely and resulting in higher temperatures. In the non-flame-covered zone, the temperature is primarily influenced by the temperature of the glass melt. Figure 7 shows the temperature distribution across the planes of the burners in the combustion space, where the temperature difference between the two processes is most noticeable at burner 4, which has the highest gas flow, with a maximum temperature difference of around 378.5 K.

Fig. 5
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Temperature and streamline distribution of each burner plane (a) and No. 4 burner plane (b) in oxy-fuel electric boosting process.

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Fig. 6
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Temperature and streamline distribution of each burner plane (a) and No. 4 burner plane (b) in electric boosting process.

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In the oxy-fuel electric boosting process, oxygen reacts with natural gas to produce high temperatures as soon as it enters the combustion chamber. In the electric boosting process, however, the oxygen content in the air is only 28%, leading to lower combustion temperatures and a much smaller high-temperature zone, making heat transfer to the glass melt significantly less efficient compared to the oxy-fuel electric boosting process. By comparing Figs. 5 and 6b, one can observe a significant change in the temperature stratification of the glass melt. As the glass melt penetrates deeper, the high-temperature region expands, which aids in improving the melting efficiency of the glass melt.

Fig. 7
figure 7

Temperature distribution of each plane of burner in combustion space.

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Glass surface temperature distribution

Figure 8 illustrates the temperature and streamline distribution contour plots of the glass melt surface for the oxy-fuel electric boosting process (a) and the electric boosting process (b). Compared to the oxy-fuel electric boosting process, the glass melt surface temperature in the electric boosting process is lower, and the high-temperature zone is smaller. To provide a clearer comparison, the temperatures along the centerline of the glass melt surface were measured and compared. Figure 9 shows the centerline temperature distribution of the glass melt surface. Compared to the oxy-fuel electric boosting process, the glass melt surface temperature in the electric boosting process is slightly lower, but the temperature difference decreases along the length of the furnace, with a maximum difference of 20.19 K in the flame-covered region.

Fig. 8
figure 8

Oxy-fuel electric boosting process (a) and electric boosting process (b) glass surface temperature and streamline distribution.

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Fig. 9
figure 9

Temperature distribution of glass surface centerline.

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Temperature distribution in glass tank

Figure 10 presents the temperature and streamline distribution contour plots at a height of 0.35 m in the glass melt plane for both the oxy-fuel electric boosting process and the electric boosting process. Compared to the oxy-fuel electric boosting process, the glass melt temperature in the electric boosting process is slightly lower, especially at the front end of the flame-covered area. The glass melt temperature reaches its highest point near the feed inlet because the maximum voltage is applied to the first two rows of electrodes located near the feed inlet, generating Joule heat as current and voltage act on the glass melt. However, since the temperature of the glass feed is lower, the temperature near the center of the inlet is reduced, while higher temperatures are observed at both ends. This helps accelerate the melting of the glass batch, thereby enhancing the overall melting efficiency. Figure 11 shows contour plots of temperature and streamlines at the symmetry plane of the glass furnace for the oxy-fuel electric boosting process (a) and the electric boosting process (b). In the combustion chamber, apart from the gas vortices generated near the burners, the high temperature in the non-flame-covered zone induces a large recirculating vortex, promoting gas circulation and creating a more uniform temperature distribution. Additionally, glass melt circulation can be observed in the melting zone after feeding, driven by the combined effect of the high flame temperatures and the maximum voltage applied to the electrodes, increasing the residence time of the glass in the melting zone and improving melting efficiency. Figure 12 illustrates the centerline temperature at the bottom of the glass furnace. Compared to the electric boosting process, the oxy-fuel electric boosting process shows a slightly higher bottom centerline temperature, as the oxy-fuel combustion generates higher temperatures, leading to greater heat transfer from the combustion space to the glass melt, thereby increasing the temperature of the glass melt.

Fig. 10
figure 10

Oxy-fuel electric boosting process (a) and electric boosting process (b) temperature and streamline distribution of Y = 0.35 m liquid glass horizontal plane.

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Fig. 11
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Oxy-fuel electric boosting process (a) and electric boosting process (b) temperature and streamline distribution on symmetrical plane of glass furnace.

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Fig. 12
figure 12

Bottom Centerline Temperature of glass furnace.

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Evaluation of furnace performance

In order to accurately describe and assess the performance of the glass furnace, a batch of particles is introduced into the furnace, with their trajectories and residence times recorded from the feed inlet to the outlet. The residence time distribution of the glass melt is then calculated, and the furnace performance is evaluated using the melting factor and mixing factor31,32. The melting factor and mixing factor are used to evaluate the melting quality, fining quality, and mixing quality of the glass. The melting factor, IMel, is driven by the ratio of the glass melt temperature T along the particle trajectory to the dynamic viscosity µ. Starting from the batch inlet, where the temperature is low and the melt viscosity is high, the ratio increases continuously and reaches its maximum at the hotspot in the glass tank. Overall, a higher IMel value indicates a faster phase transition of the glass from the solid state to the molten state.

$$I_{{Mel}} = \mathop \smallint \limits_{L}^{~} \frac{T}{\mu }dt$$
(1)

In the equation, T and µ represent the temperature and dynamic viscosity of the glass melt at the particle’s position, L is the particle’s trajectory in the furnace, and t is the travel time.

IMix represents the degree of mixing between the glass melt and the surrounding glass during movement, with a higher value indicating better mixing quality in the furnace.

$$I_{{Mix}} = \mathop \smallint \limits_{L}^{~} \frac{{4\nabla U^{{2/3}} D_{r}^{{1/3}} }}{{3\left( {0.01^{{2/3}} } \right)}}dt$$
(2)

In the equation, U represents the velocity of the glass melt at the particle’s position, Dr is the diffusion coefficient (for standard float glass, 1.5 × 10–12 m2/s), L is the particle’s path in the furnace, and t is the travel time.

Residence time

Residence time refers to the time it takes for glass particles to move from the glass melt feed inlet to the outlet. In the glass fiber furnace, sufficient residence time is required to ensure that the glass particles fully melt, but excessive residence time can lead to substantial energy loss. As a result, residence time is a critical parameter in glass fiber furnace performance. In this study, the distribution of glass particle residence times is shown in Table 4, with the x-axis values representing ten-hour intervals. As shown in Fig. 13, the fastest glass particles reached the outlet 5–10 h after release at the feed inlet. In the oxy-fuel electric boosting process, the majority of particles reached the outlet between 50 and 60 h, whereas in the electric boosting process, most particles reached the outlet between 30 and 40 h. The majority of particles reached the outlet within 100 h, and nearly all particles arrived at the outlet after 250 h. According to Table 4, the average residence time is 62.5 h for the oxy-fuel electric boosting process and 55.9 h for the electric boosting process. In the oxy-fuel electric boosting process, the residence time distribution within the first 100 h is more uniform, which enhances the melting efficiency and improves the quality of the glass melt. The minimum residence time for the oxy-fuel electric boosting process is 8.0 h, compared to 9.0 h for the electric boosting process. The shorter minimum residence time in the oxy-fuel electric boosting process is attributed to the higher temperature, lower viscosity, and faster flow of the glass melt in this process.

Fig. 13
figure 13

Residence time distribution of glass.

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Table 4 Average and minimum residence time.
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To ensure thorough melting and mixing of the glass melt, a longer minimum residence time for larger glass particles is typically desired. As shown in Table 4, the minimum residence time in the oxy-fuel electric boosting process is shorter than in the electric boosting process, suggesting that the shorter minimum residence time in the oxy-fuel electric boosting process might result in reduced glass melting quality.

Glass melting factor and mixing factor

The average and minimum values of the melting factor and mixing factor under both processes are shown in Table 5. In Table 5, the melting factor and mixing factor in the oxy-fuel electric boosting process are higher than those in the electric boosting process, due to the increased glass melt temperature, indicating that the phase transition of glass from solid to molten state is faster in the oxy-fuel electric boosting process, leading to an improvement in mixing quality. This is due to the higher glass melt temperature improving the melting efficiency of raw glass material at the feed inlet. Additionally, as the temperature increases, the fluidity of the glass melt improves, making the mixing effect more pronounced.

Table 5 Melting factor and mixing factor of glass particles.
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In conclusion, the oxy-fuel electric boosting process enhances the melting efficiency of glass. Furthermore, the improved fluidity of the glass melt promotes better uniformity. However, it also shortens the minimum residence time, which can lead to reduced melting quality for faster-moving particles.

Conclusion

In the process of studying a 200 t/d glass fiber furnace, an integrated glass furnace model, incorporating both the combustion space and glass tank, was developed to better understand the impact of heat transfer and glass flow within the furnace. The model features six evenly distributed rows of electrodes at the bottom to examine the varying impacts of oxy-fuel and air-fuel combustion on the performance of the electric boosting furnace. Indicators such as residence time, melting factor, and mixing factor were used to conduct a comprehensive evaluation of the melting quality and efficiency of the glass furnace. The main conclusions of the study are as follows:

(1) The impact of oxidizer gases on furnace heat transfer: In electric boosting furnaces, the difference in oxidizer gases leads to a decrease in flame zone temperature and a reduction in the size of the high-temperature region. This change helps extend the furnace’s lifespan, as smaller high-temperature areas reduce thermal stress and wear on the furnace materials. However, this also reduces heat transfer efficiency to the glass melt, which may affect the melting rate and uniformity.

(2) Enhanced heat transfer and flow with the oxy-fuel process: The oxy-fuel process significantly improves heat transfer to the glass melt and promotes melt flow. By supplying purer oxygen, this process increases the intensity and efficiency of the combustion reaction, thereby raising the furnace’s thermal efficiency. However, it also shortens the minimum residence time within the furnace, meaning some glass particles may not have sufficient time to fully melt, which could impact the melting quality.

(3) Melting efficiency and quality of the oxy-fuel electric boosting process: By combining oxy-fuel combustion with electric boosting technology, the oxy-fuel electric boosting process enhances glass melting efficiency. This process accelerates the melting process and improves glass melt flow, increasing the mixing and improving the final product’s quality. However, the shorter minimum residence time may affect the melting quality of the fastest-moving particles. Therefore, optimizing the oxy-fuel electric boosting process is essential to achieve a balance between high melting efficiency and quality.