Study on Flow and Heat Transfer Characteristics of Reheating Furnaces Under Oxygen-Enriched Conditions

Abstract

A computational fluid dynamics (CFD) numerical simulation methodology was implemented to model transient heating processes in steel industry reheating furnaces, targeting combustion efficiency optimization and carbon emission reduction. The effects of oxygen concentration (O₂%) and different fuel types on the flow and heat transfer characteristics were investigated under both oxygen-enriched combustion and MILD oxy-fuel combustion. The results indicate that MILD oxy-fuel combustion promotes flue gas entrainment via high-velocity oxygen jets, leading to a substantial improvement in the uniformity of the furnace temperature field. The effect is most obvious at O₂% = 31%. MILD oxy-fuel combustion significantly reduces NOx emissions, achieving levels that are one to two orders of magnitude lower than those under oxygen-enriched combustion. Under MILD conditions, the oxygen mass fraction in flue gas remains below 0.001 when O₂% ≤ 81%, indicating effective dilution. In contrast, oxygen-enriched combustion leads to a sharp rise in flame temperature with an increasing oxygen concentration, resulting in a significant increase in NOx emissions. Elevating the oxygen concentration enhances both thermal efficiency and the energy-saving rate for both combustion modes; however, the rate of improvement diminishes when O₂% exceeds 51%. Based on these findings, MILD oxy-fuel combustion using mixed gas or natural gas is recommended for reheating furnaces operating at O₂% = 51–71%, while coke oven gas is not.

1. Introduction

With the intensification of global warming, the reduction of greenhouse gas CO₂ emissions has become a major international concern. According to reports from the International Energy Agency, the primary source of increased CO₂ emissions is fossil fuel combustion [1]. The steel industry is recognized as one of the largest CO₂ emitters within China’s industrial sector [2,3]. Reheating furnaces, which are widely used for heating slabs prior to rolling, are identified as key energy-consuming units in the steel production process [4,5,6]. Moreover, these furnaces constitute a significant source of CO₂ emissions in steelmaking operations. Therefore, reducing energy consumption and improving the thermal efficiency of reheating furnaces are considered critical steps toward achieving China’s “Dual Carbon” goals.

In traditional reheating furnaces, combustion is typically carried out using air, in which nitrogen accounts for approximately 79%. This nitrogen does not participate in the combustion process but is instead discharged as flue gas, leading to significant heat loss and, consequently, low combustion efficiency [7,8]. Moreover, it contributes to the formation of pollutants such as NOx [9]. Oxygen-enriched combustion (OEC) is a greenhouse gas reduction technology. It uses oxygen-enriched air (O₂% > 21%) or pure oxygen as an oxidant, which greatly reduces flue gas volume and exhaust heat loss. Consequently, the fuel consumption is reduced, leading to high efficiency and low emissions [10]. A number of studies have been conducted on the application of OEC in reheating furnaces [11,12,13,14,15,16,17,18]. For example, Han et al. [15] numerically compared thermal efficiency and fuel consumption in the air and pure oxygen condition for a reheating furnace. Wu et al. [17] experimentally studied heating rate, temperature distribution, and fuel consumption in a burner at O₂% = 21~30%. These studies show that OEC greatly improves furnace combustion efficiency and energy saving rate.

However, existing studies also show that NO_x emissions increase significantly with the elevated oxygen concentration [19]. To reduce NO_x generation, combining Moderate or Intense Low-Oxygen Dilution (MILD) combustion with OEC is proposed by researchers. MILD combustion is known for high thermal efficiency and low NO_x emission [20]. There is no flame front and uniform temperature field for MILD combustion, which is due to high-temperature exhaust gas recirculation [21]. Many scholars have studied MILD combustion in reheating furnaces. Ehab et al. [22] and Tu et al. [23,24] performed 3D numerical simulations on an experimental furnaces. The NO_x generation was explored under different fuels in MILD combustion. Results confirmed the NOx emission is low in MILD combustion. Tu et al. [25] and Pormehr et al. [26] studied the effects of furnace shape and baffle on the MILD combustion characteristics in experimental furnaces. Results show that enhancing internal gas recirculation by changing geometry positively affects the MILD combustion process. Environmental factors affecting MILD combustion were also studied. Tu et al. [27] used a 0.3 MW industrial furnace to study the performance of MILD and traditional burners. They found that MILD combustion reduced NO emissions by over 80% and improved the furnace temperature uniformity. Tu et al. [28] also studied the effects of elevated pressure (1–8 atm) on the combustion process. Results show that increased operating pressure disrupts sustained MILD combustion.

Recently, combining OEC and MILD combustion has been attempted in industrial application. Currently, the research about MILD oxy-fuel combustion (MOFC) mostly focuses on the burner [29,30,31,32,33] and the furnace-scale research is scarce. Yu et al. [30] conducted a study on the impact of introducing H₂ and CO into syngas on the characteristics of MOFC. The critical oxygen concentration required to sustain MILD combustion was obtained for various H₂/CO/CH₄ blending ratios. Fordoei et al. [31] studied heat transfer, ignition delay, flame color, flame structure, and CO/NO_x emissions of natural gas MILD flames in air, oxygen-enriched, and pure oxygen conditions. Mario et al. [33] investigated the effect of oxygen concentration on the performance of a regenerative MILD combustion furnace. At O₂% = 30%, NO_x emissions are below 5 ppm, the thermal efficiency of the furnace increases by 5%, and the energy recovery rate of self-regenerative burners exceedes 80%. In addition to these studies, there are few studies about the MOFC in the reheating furnaces.

To address the gap in the application of MOFC in reheating furnaces, a CFD numerical model was developed in this study, incorporating slab movement and multi-zone heat transfer, to study the flow and heat transfer behavior under both OEC and MOFC modes. The effects of oxygen concentration (31–91%) and fuel types on flow and heat transfer characteristics were investigated. The temperature distribution, flue gas emissions, and slab heating performance in the furnace were analyzed. Furthermore, thermal efficiency and energy-saving rates were calculated for each condition. The applicable oxygen concentration ranges for both OEC and MOFC modes in reheating furnaces are clarified, providing valuable insights for practical retrofitting aimed at energy conservation and emission reduction in industrial reheating processes.

2. Methods

2.1. Physical Model

As shown in Figure 1, the reheating furnace is structured into 5 sequential zones: the preheating zone, heating zone 1, heating zone 2, heating zone 3, and the soaking zone. Further details regarding the furnace geometry and burner layout are provided in

Table 1. Detailed parameters and burner arrangement of the reheating furnace.

Reheating Furnace Section	Length/m	Width/m	Height/m	Number of Burners
Preheating zone	11.6	11.66	4.25	0
First heating zone	9.982	11.66	5.25	16
Second heating zone	9.076	11.66	5.25	16
Third heating zone	8.483	11.66	5.25	16
Soaking zone	7.75	11.66	4.25	40

.

The reheating furnace in this study adopts an end-in and end-out charging/discharge configuration, with a fuel gas outlet located in the preheating zone. Burners are installed in both the heating and soaking zones, specifically arranged in the following section.

The burners in the heating zone are located on the side furnace walls and are symmetrically arranged relative to the horizontal centerline at the slab entry. The burners in the soaking zone are primarily positioned on the furnace roof and side walls. On the side walls of both the heating and soaking zones, axial flame burners are adopted under OEC mode, while MILD burners are adopted under MOFC mode. Flat flame burners are installed on the roof of the soaking zone.

The axial flame burners feature a concentric sleeve structure, with the inner tube serving as the fuel inlet and the annular gap of the outer sleeve acting as the oxidizer inlet. Within the MILD burners, the oxidizer is injected into the furnace chamber via an oxygen lance. This design aims to generate a strong internal recirculation effect through the high-velocity injection of oxygen into the furnace chamber. Consequently, the reactants become continuously diluted by the inert components present in the flue gas, thus achieving the MILD combustion regime.

The reheating furnace is used for heating low carbon steel. The slab dimensions are 230 mm × 1285 mm × 8960 mm. Slabs are charged at 30 °C and are discharged at 1250 °C, with a permissible discharge temperature fluctuation of ±50 °C. The maximum allowable temperature difference across the slab cross-section is 30 °C.

2.2. Meshing Details

2.2.1. Mesh Generation

The computational domain of the reheating furnace model was meshed using MESH software. Figure 2 shows the mesh schematic for the half-model. Due to the axisymmetric structure of the furnace, only half of the geometry was used for mesh generation and numerical simulation, thereby reducing computational cost. This approach was also applied during the mesh independence verification process. The primary meshing methodologies utilized included multi-zone partitioning and tetrahedral elements, with localized mesh refinement implemented specifically at burner locations and around slabs to enhance computational accuracy. The complete mesh comprises 420,000 cells, exhibiting a minimum orthogonality of 0.3 and an average orthogonality of 0.93, meeting all computational requirements.

2.2.2. Grid Independence Verification

Mesh quality and quantity critically affect simulation accuracy. To find optimal mesh, cases with 220,000, 420,000, 700,000, and 830,000 cells were tested. Figure 3 shows the flame center temperature at the same burner position for different mesh sizes. Above 420,000 cells, results show minor differences. The result with 220,000 cells has larger deviation. Balancing accuracy and resources, 420,000 cells were chosen in the following calculation.

2.3. Mathematical Model

2.3.1. Governing Equations

(1) Mass Conservation Equation

The mass conservation equation is fundamental in fluid dynamics and thermodynamics. It states that mass cannot be created or destroyed in a fixed control volume. Mass can only be transferred. Inflow mass flow rate must equal outflow plus mass change rate due to density variation. Under continuum assumption, for ideal-gas, it is usually written as follows:

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla \cdot (\rho \overrightarrow{v})=0$$

(1)

where $\rho$ is density; $t$ is time; and $\overrightarrow{v}$ is velocity.

(2) Momentum Conservation Equation

The momentum equation describes fluid momentum change versus external forces. It applies Newton’s second law to continuous media. Momentum change rate in a control volume equals the sum of all external forces. For an ideal-gas, it is expressed as follows:

$${\displaystyle \frac{\partial (\rho \overrightarrow{v})}{\partial t}}+\nabla \cdot (\rho \overrightarrow{v}\overrightarrow{v})=-\nabla p+\nabla \cdot \stackrel{=}{\tau }+\rho \overrightarrow{g}+\overrightarrow{F}$$

(2)

where $p$ is static pressure; $\stackrel{=}{\tau }$ is the stress tensor; $\overrightarrow{F}$ is external force; and $\rho \overrightarrow{g}$ is gravity.

(3) Energy Conservation Equation

During fluid flow, energy is transferred and converted in multiple ways. These include convection, conduction, radiation, and energy changes from pressure and viscosity. For a continuous medium (e.g., fluid or gas), the energy equation is usually as follows:

$${\displaystyle \frac{\partial (\rho T)}{\partial t}}+\nabla \rho \overrightarrow{v}T=\nabla ({\displaystyle \frac{\lambda }{c_p}}\nabla T)+S_T$$

(3)

where $c_p$ is specific heat capacity; $T$ is temperature; $\lambda$ is fluid thermal conductivity; and $S_T$ is internal heat source and viscous dissipation term.

(4) Species Transport Equation

$${\displaystyle \frac{\partial (\rho Y_i)}{\partial t}}+\nabla (\rho \overrightarrow{v}{Y}_i)=-\nabla \cdot \overrightarrow{J_i}+R_i+S_i$$

(4)

where $Y_i$ is mass fraction of species i; $R_i$ is net generation rate via chemical reaction; and $S_i$ is net generation rate from other sources and user-defined terms.

2.3.2. Combustion, Radiation, Turbulence, and NOx Generation Models

The Eddy Dissipation Concept (EDC) model [34] considers turbulence–chemistry interaction. It suits fast reaction systems and complex combustion that needs detailed chemistry. It models the combustion process. Additionally, according to the study by M. Vascellari et al. [35], the EDC model yields better results for MILD combustion.

The Discrete Ordinates (DO) model handles radiation heat transfer [36]. It is suitable for high-temperature, strong radiation scenarios like combustion. The DO model is applicable to a wide range of optical conditions, ranging from optically thin to optically thick media. It is capable of handling non-gray gas radiation and complex boundary conditions. Compared to other radiation models, the DO model offers significant advantages in terms of accuracy and versatility, particularly in combustion simulations involving high temperatures and intense radiative heat transfer. Although the DO model entails a relatively higher computational cost, its superior ability to resolve detailed radiative transport makes it an ideal choice for modeling combustion processes.

The standard k-ε model handles turbulence [37]. By solving the transport equations for turbulent kinetic energy (k) and its dissipation rate (ε), the model offers a good balance between computational efficiency, numerical stability, and broad applicability. These advantages make it a well-established choice for simulating complex turbulence phenomena commonly encountered in practical industrial and engineering settings.

The Weighted Sum of Gray Gases (WSGG) model calculates absorption coefficient [38]. It predicts radiative heat transfer from the medium. The WSGG model achieves a good balance between computational efficiency and accuracy by representing the radiative properties of non-gray gases as a weighted sum of contributions from multiple gray gas components.

A thermal NOx generation model is employed [39]. In the NOx generation mechanisms, there are mainly three types: fuel-NOx, thermal-NOx, and prompt-NOx. The dominant type depends on the fuel composition. According to

Table 2. Fuel composition.

Fuel Type	N2/%	H2/%	CH4/%	CO2/%	CO/%	Calorific Value/kJ/Nm3
MG	35.6	20.3	11.2	13.9	17.4	8360
NG	0	0	100	0	0	35,000
COG	11.7	52.9	25.4	2.7	6.9	17,500

, taking MG as an example, the generation of fuel-NOx is minimal, and the contribution of prompt-NOx typically accounts for less than 5%. Therefore, thermal-NOx becomes the primary source.

2.4. Boundary Conditions

Mixed gas (MG), natural gas (NG), and coke oven gas (COG) were used as fuels. Table 2 shows fuel composition and calorific values.

Table 3. Burner parameters (taking MG as an example).

Operating Conditions
Fuel inlet volumetric flow rate	40,416 m3/h
Fuel inlet temperature	303 K
Oxidant inlet volumetric flow rate	Changes with O2%
Oxidant inlet temperature	303 K
Excess air coefficient	1.1

shows the burner parameters. To ensure consistency in the flow field, the fuel inlet diameter was adjusted such that the inlet velocity remained nearly constant across different fuels under the same combustion mode, despite variations in total flow rate.

Table 4. Other boundary conditions.

Operating Conditions
Inlet temperature	303 K
Outlet temperature	303 K
Outlet pressure	20 Pa
Excess air coefficient	1.1
Furnace Wall Emissivity	0.8
Slab Surface Emissivity	0.8
Slab initial temperature at Non-firing zone	303 K
Slab initial temperature at Preheating zone	505 K
Slab initial temperature at First heating zone	1100 K
Slab initial temperature at Second heating zone	1100 K
Slab initial temperature at Third heating zone	1300 K
Slab initial temperature at Soaking zone	1520 K

shows main simulation boundary conditions. Sliding mesh technology simulated slab movement. Slabs and inter-slab air were defined as moving domains. The rest of the furnace was a stationary domain. Moving domain length was twice the furnace length. Data exchange between the moving and stationary domains was achieved through an interface surface. The SIMPLE algorithm solved the equations numerically.

Additional simplifications were made: Bottom water-cooling heat loss of slabs was neglected. Oxidation and decarburization during heating were neglected. Gas escape/suction at furnace ends was neglected. Wall radiation heat transfer coefficient per zone was constant. Slab oxidation loss was neglected.

These simplifications have an impact on the heating process of the slab. However, the focus of this work is on the overall flow, temperature distribution, and NOx formation mechanisms inside the furnace chamber—characteristics that are primarily governed by gas flow and combustion reactions. The effects of simplifications such as neglecting heat loss from water cooling and oxidation loss on the gas flow, flue gas recirculation, and temperature field distribution are considered to be minimal. While emissivity affects radiative heat transfer within the furnace, the radiative heat flux is predominantly determined by the participation of high-temperature combustion gases (CO₂ and H₂O). Compared with traditional combustion, the change in the contributions from radiation between the slab and the furnace walls are not in a significantly oxy-enriched condition. Furthermore, the key conclusions of this study—such as the effect of oxygen concentration on temperature uniformity and the NOx reduction mechanism under MOFC—are found to be insensitive to variations in emissivity. Therefore, the aforementioned simplifications do not compromise the general applicability of the results.

2.5. Simulation Cases

Table 5. Simulation Cases.

Case	Combustion Mode	Fuel	Oxidizer Composition
1	Fuel-Air	MG	O2% = 21%, N2% = 79%
2	OEC	MG	O2% = 31%, N2% = 69%
3			O2% = 41%, N2% = 59%
4			O2% = 51%, N2% = 49%
5			O2% = 61%, N2% = 39%
6			O2% = 71%, N2% = 29%
7			O2% = 81%, N2% = 19%
8			O2% = 91%, N2% = 9%
9	MOFC	MG	O2% = 31%, N2% = 69%
10			O2% = 41%, N2% = 59%
11			O2% = 51%, N2% = 49%
12			O2% = 61%, N2% = 39%
13			O2% = 71%, N2% = 29%
14			O2% = 81%, N2% = 19%
15			O2% = 91%, N2% = 9%
16	MOFC	NG	O2% = 51%, N2% = 49%
17	OEC	COG	O2% = 51%, N2% = 49%

shows the simulation cases. To study the effects of oxygen concentration under both modes, MG was used as fuel. OEC and MOFC cases were set at O₂% = 31~91%. To study the effects of fuel type under both modes, NG and COG cases were set at O₂% = 51%.

3. Results and Discussion

3.1. Thermocouple Embedding Experiment and Model Validation

3.1.1. Thermocouple Embedding Experiment

The thermal process model for the reheating furnace was validated by comparing simulation results with the temperature measurement data obtained under actual operating conditions, thereby ensuring the reliability and accuracy of the numerical predictions. To accurately measure the flue gas temperature and minimize errors due to radiation, an aspirated thermocouple was adopted. S-type thermocouples and a heat-resistant temperature recorder were adopted to measure the slab temperature. Holes were drilled at different positions on the experimental slab, and S-type thermocouples were embedded to record temperature data. Based on the type of slab and the corresponding heating schedule, the charging and discharging times of the slab were controlled. After cooling, the temperature recorder was retrieved, and the surface and center temperatures of the slab were also obtained.

Figure 4 shows the thermocouple layout on the experimental slab. A total of nine thermocouple positions were arranged, with points three, four and five located at the center of the slab’s mid-section, while the remaining positions were placed on the top surface. The thermocouples were connected to heat-resistant temperature data loggers via insulated wires, which were wrapped in thermal insulation material to shield them from the flame. The data loggers were housed in an insulated box to ensure their safe operation under high-temperature conditions.

3.1.2. Model Validation

Figure 5 shows a comparison between the experimental and simulated values of the flue gas temperature, the top surface temperature of the slab, and the center temperature of the slab (see Appendix A for detailed data). The numerical results accurately capture the trend of flue gas temperature variation. The maximum error occurs at the slab inlet, with a deviation of 6.98%, which falls within the acceptable error range. For the validation of the slab’s top surface and center temperatures, the simulated values are generally higher than the experimental data. The maximum error reaches 11.34% for the top surface temperature and 7.17% for the center temperature. This discrepancy is mainly attributed to the fact that heat loss due to water cooling at the bottom of the slab is not considered in this study, and the emissivity of the furnace walls and the slab is assumed to be constant. As a result, the heating rate of the slab in the simulation is slightly higher than that observed in the experiment. Additionally, the experimental and simulated temperatures show good agreement shortly before the slab exits the furnace. Overall, the model demonstrates reasonable accuracy and meets the requirements of practical engineering applications.

3.2. Effect of O₂ Concentration

3.2.1. Temperature and Velocity Distribution

Figure 6a,c,e,g show the temperature distribution at the lower burners under OEC mode. As the oxygen concentration increases, the flame temperature near the burner rises from 1700 K to 2000 K, and the overall furnace temperature increases significantly. Figure 6b,d,f,h show the temperature distribution at lower burners under MOFC mode. Flame temperature rises from 1500 K at O₂% = 31% to 2000 K at O₂% = 91%. Under both modes, the flame color changes from yellow to bright red with increasing oxygen concentration, indicating a rise in flame temperature. At the same oxygen concentration, MOFC results in a more uniform temperature distribution compared to OEC, particularly at O₂% = 31%. However, as the oxygen concentration increases, flame visibility under MOFC mode becomes more pronounced. The high-temperature zone expands toward the center of the furnace, and the flame shape becomes increasingly distinct. The increase in oxygen concentration significantly reduces the flue gas volume, which in turn decreases internal flue gas recirculation and dilution. Consequently, the extent of the MILD combustion zone is reduced, and the uniformity of the temperature field deteriorates.

To quantify the uniformity of temperature distribution within the furnace, the temperature gradient [40] was introduced as an evaluation index. A smaller temperature gradient indicates better temperature uniformity. The expression for the temperature gradient is as follows:

$$R_T=\sqrt{{\displaystyle \sum _{i=1}^N{\left(\frac{T_i-\overline{T}}{\overline{T}}\right)}^2}}$$

(5)

where $T_i$ represents the temperature at the i-th measurement point, and $\overline{T}$ is the average temperature. When $R_T=0$, there is no gas temperature gradient inside the furnace.

Figure 7 shows the $R_T$ under OEC and MOFC modes at different oxygen concentrations. Under OEC mode, as the oxygen concentration increases, the $R_T$ fluctuates significantly, reaching a peak value of approximately 0.308 at O₂% = 51%. As the oxygenation concentration continues to increase, the $R_T$ briefly decreases before rising again, eventually stabilizing at around 0.306. In contrast, under the MOFC mode, the variation in $R_T$ is much smoother, with no distinct peak observed. The overall trend follows a pattern of “gradual increase—slight decrease—gradual increase”, maintaining a consistently lower $R_T$ compared to the OEC system throughout the range of oxygen concentrations. At an oxygen concentration of 31%, the $R_T$ under the MOFC mode reaches its lowest point, at 0.24, corresponding to the most uniform temperature distribution within the furnace.

Figure 8 shows the velocity distribution under OEC and MOFC modes at different oxygen concentrations. As shown in Figure 8a,c,e,g, the maximum flow velocity is 11.2 m/s at O₂% = 31% and decreases to 6.4 m/s at O₂% = 91%. The velocity range narrows as oxygen concentration increases under OEC mode. High flow velocities are observed near the burners and the flue gas outlet, which is attributed to the strong driving forces in these regions. The preheating and soaking zones have lower heights compared to the heating zones, resulting in reduced flow velocities in those areas. Pronounced recirculation zones are formed in these regions. As shown in Figure 8b,d,f,h, the velocity range also narrows with increasing oxygen concentration under MOFC mode. The oxidant injection velocity exceeds 200 m/s. The velocity range depicted in the figures is intentionally set to clearly distinguish the velocity distributions across different sections of the furnace. At the same oxygen concentration, the flow velocities are significantly higher under MOFC mode than under OEC mode, this is because oxidant enters the furnace as high-speed jets via oxygen lance under MOFC mode. Strong recirculation occurs in heating zones due to the high-speed injection of O₂ and recirculation zones are expanded in preheating and soaking zones. Furthermore, recirculation zones shrink with increasing oxygen concentration under MOFC mode, which hinders the MILD combustion state.

3.2.2. Emission Analysis

Figure 9 shows the average NOx mass fraction at the furnace outlet. NOx emissions increase significantly with rising oxygen concentration under both OEC and MOFC modes. The high oxygen concentration environment accelerates the combustion rate, which also prolongs high-temperature residence time. This strengthens thermal NOx formation pathways. Under OEC mode, NOx mass fraction rises sharply from 9.98 × 10⁻⁶ at O₂% = 31% to 2.67 × 10⁻³ at O₂% = 91%, representing a 267-fold increase. In contrast, under MOFC mode, the NOx mass fraction increases from 5.65 × 10⁻⁷ to 9.04 × 10⁻⁵ over the same oxygen concentration range, corresponding to a 160-fold increase. Through comparison, the NOx emissions under MOFC mode are 1–2 orders of magnitude lower than that under OEC mode. This is primarily because OEC typically results in higher flame temperatures. Combustion is more intense and concentrated under OEC mode and heat released cannot be effectively diluted by flue gas. This causes flame temperatures to rise sharply and nitrogen–oxygen reaction rates to accelerate. The expansion of high-temperature zones and local overheating intensify the thermal NOx formation.

Figure 10 shows the average O₂ mass fraction at the outlet under OEC and MOFC modes. At O₂% = 31~91%, the outlet O₂ mass fraction fluctuates between 0.00639 and 0.01 under OEC mode. Particularly at O₂% = 51~81%, O₂ emissions are at a high level. Because in this range, OEC tends to form localized high-temperature flames, where oxygen reacts with nitrogen at elevated temperatures, leading to increased thermal NOx formation. Additionally, unreacted oxygen in the high-temperature zones is directly discharged without being fully consumed. OEC requires high fuel–oxygen mixing uniformity. When the mixing is uneven, oxygen surplus occurs locally. This further increases unreacted O₂ emissions. At O₂% = 31~81%, O₂ emissions under MOFC mode stay low. O₂ emissions increase sharply with rising oxygen concentrations above 81%. This indicates that excessive oxygen destroys the MILD state, and MOFC mode begins to change into OEC mode.

Figure 11 shows the CO₂ distribution inside the furnace under MOFC mode at different oxygen concentrations. As oxygen concentration increases from 31% to 91%, the average mass fraction of CO₂ inside the furnace rises from 0.292 to 0.47, nearly doubling. The combustion reaction rate is enhanced by the higher oxygen concentration, leading to a significant accumulation of CO₂ in the furnace. Near the burner, the CO₂ mass fraction exhibits a radial gradient, increasing from the center outward, with the burner as the focal point. As the oxygen concentration increases from 31% to 91%, this radial gradient becomes more pronounced. At O₂% = 31~51%, the CO₂ diffusion zone is relatively narrow and the gradient is mild, which is consistent with the characteristics of MILD combustion, including high dilution and low flame front intensity. In contrast, at O₂% = 61~91%, the high-concentration CO₂ region expands, and the gradient zone becomes narrower, indicating that the oxygen concentration has exceeded the dilution limit. This suggests a transition of the flame from a “volume-dominated” to a “front-dominated” structure. At O₂% = 81%, a distinct concentration of the CO₂ gradient is observed, indicating that the MOFC mode is gradually transitioning toward the OEC mode.

3.2.3. Slab Heating Characteristics

Figure 12 shows the average surface temperature of the slab under OEC and MOFC modes. As shown in Figure 12a,b, average lower surface temperature of the slab decreases significantly across each zone with increasing oxygen concentration. The increase in oxygen concentration greatly reduces flue gas generation, leading to lower flue gas velocity and turbulence intensity. Convective heat transfer between flue gas and the slab becomes weaker. This indirectly slows the lower surface temperature rise rate. Figure 12c,d show slab temperature uniformity per zone at O₂% = 31%. Both modes show the upper/lower surface and center temperature rise rapidly and then stabilize. MOFC mode gives better temperature uniformity than OEC. Strong flue gas recirculation under MOFC mode distributes hot gas more evenly. This enhances convective heat transfer between flue gas and the slab.

3.2.4. Thermal Efficiency and Energy Saving Rate of Furnace

(1) Thermal efficiency

Thermal efficiency is core for evaluating furnace energy utilization. Common calculation methods are the direct and indirect balance methods. Direct balance calculates efficiency as useful heat divided by total input heat. Its process is relatively simple. However, it requires high accuracy measurement. Indirect balance calculates all heat losses. Useful heat is total heat minus losses. Efficiency is then calculated. Indirect balance reflects actual operation more comprehensively. It is especially suitable for complex conditions. Therefore, the indirect balance method was used in this paper. This accurately assesses furnace energy utilization efficiency.

Indirect balance thermal efficiency calculation is as follows [41]:

$$\eta =100\%-q_1^{\prime }-q_2^{\prime }-q_3^{\prime }$$

(6)

where $q_1^{\prime }$ is percentage of exhaust heat loss; $q_2^{\prime }$ is percentage of incomplete combustion loss; and $q_3^{\prime }$ is percentage of surface heat loss, taken as 3%.

$$q_1^{\prime }={\displaystyle \frac{(8.3\times {10}^{-3}+0.031\alpha )(t_g+1.35\times {10}^{-4}{t}_g^2)+(5.65+4.7\times {10}^{-3}{t}_g)w-1.1}{1+3.4\times {10}^{-4}(t_a-15.6)+0.0657w}}$$

(7)

where $\alpha$ is excess air coefficient, $t_g$ is exhaust temperature, $w$ is atomizing steam consumption, taken as 0, and $t_a$ is external air temperature. Without air preheating, $t_a$ = 15.6 °C.

$$q_2^{\prime }={\displaystyle \frac{(4.043\alpha -0.252)\times {10}^{-4}CO}{1+3.4\times {10}^{-4}(t_a-15.6)+0.0657w}}$$

(8)

where $CO$ is carbon monoxide content in flue gas.

Figure 13 shows the furnace thermal efficiency under OEC and MOFC modes. As oxygen concentration increases, the thermal efficiency rises from 55.12% to 57.99% under OEC mode, representing a 2.87% increase. The increase in thermal efficiency mainly comes from continuously reduced sensible heat loss. Chemical incomplete combustion loss remains very low. The increasing oxygen concentration enhances combustion efficiency, thereby improving the overall energy utilization of the furnace. Thermal efficiency increased by 1.37% when oxygen concentration rose from 31% to 51%. However, the rate of increase slows significantly between 51% and 91%, with only a 1.50% improvement. This indicates that excessive oxygen supply yields diminishing returns in terms of thermal efficiency. Under MOFC mode, the thermal efficiency increases from 58.6% at O₂% = 31% to 60.98% at O₂% = 91%. At the same oxygen concentration, the thermal efficiency under MOFC mode is consistently higher than that under OEC mode, with a 3–4% average difference. This demonstrates that MOFC achieves better energy utilization and improves furnace thermal efficiency more effectively compared to OEC.

(2) Energy saving rate

Energy saving rate reflects improvement in energy utilization efficiency. Studying its impact on furnace efficiency aims to reveal key energy loss points. The furnace energy balance equation is as follows:

$$M_f\cdot h+M_f\cdot \alpha \cdot L\cdot c_a\cdot T_a=Q_e+Q+M_f\cdot (1+\alpha \cdot L)\cdot c_{fg}\cdot T_{fg}$$

(9)

where $L$ is theoretical gas requirement, $L=m_{O_2}/x_{m_{O_2}}$; $M_f$ is fuel flow rate (kg/s); $h$ is fuel calorific value (J/kg); $\alpha$ is excess air coefficient; $c_a$ is air specific heat (J/(kg·°C)); $T_a$ is air temperature; $Q_e$ is the environmental heat loss, set as 0; $Q$ is the required heat flux; $c_{fg}$ is the flue gas-specific heat (J/(kg·°C)); $T_{fg}$ is the flue gas temperature (°C); $m_{o_2}$ is the theoretical oxygen requirement (kg/kg); $x_{m_{O_2}}$ is oxidizer oxygen mass fraction, $x_{m_{O_2}}=(32\times x_{O_2})/(32\times x_{O_2}+28\times (1-x_{O_2}))$; and $x_{O_2}$ is the oxygen mole fraction in oxidizer.

Fuel demand from the equation is as follows:

$$M_f={\displaystyle \frac{Q}{h+\alpha \cdot \frac{m_{O_2}}{x_{m_{O_2}}}\cdot c_a\cdot T_a-(1+\alpha \cdot \frac{m_{O_2}}{x_{m_{O_2}}})\cdot c_{fg}\cdot T_{fg}}}$$

(10)

Energy saving rate is defined as follows:

$$ESR=1-{\displaystyle \frac{M_f}{M_f^0}}$$

(11)

where: $M_f^0$ is fuel required for air combustion (kg/s); and $M_f$ is fuel required at oxygen-enriched condition (kg/s).

$$ESR=1-{\displaystyle \frac{h+\alpha \cdot \frac{m_{O_2}}{x_{m_{O_2}}^0}\cdot c_a\cdot T_a-(1+\alpha \cdot \frac{m_{O_2}}{x_{m_{O_2}}^0})\cdot c_{fg}\cdot T_{fg}}{h+\alpha \cdot \frac{m_{O_2}}{x_{m_{O_2}}}\cdot c_a\cdot T_a-(1+\alpha \cdot \frac{m_{O_2}}{x_{m_{O_2}}})\cdot c_{fg}\cdot T_{fg}}}$$

(12)

where $x_{m_{O_2}}\approx 0.23$.

Figure 14 shows the furnace energy saving rate under OEC and MOFC modes. Energy saving rate increases with rising oxygen concentration under both modes. Under OEC mode, the energy saving rate rises from 27.1% to 45.26%, while under MOFC mode, it increases from 32.28% to 47.04%. At O₂% = 31~51%, both modes exhibit significant improvements in energy saving performance. At O₂% = 51%, the growth rate begins to slow down. This indicates that increasing oxygen concentration at lower levels notably enhances combustion efficiency. However, as the oxygen concentration continues to rise, the combustion efficiency tends to reach a saturation point, beyond which further increases in oxygen concentration yield only marginal improvements in energy efficiency.

3.3. Effect of Fuel Composition

3.3.1. Temperature and Velocity Distribution

Figure 15 shows temperature distribution near the burners for different fuels at O₂ = 51%. As shown in Figure 15a,b, it shows no clear flame for NG and MG under MOFC mode. Especially for NG, there is almost no visible flame. Average furnace temperature is 1512 K for NG and 1520 K for MG. The difference between the two is small. However, it gives more uniform temperature distribution for NG. This is because 1 mole NG consumes more oxygen than 1 mole MG, resulting in more flue gas being generated for NG. Fuel and oxidant are diluted more sufficiently by the recycled flue gas. It is more easy for NG to form a MILD combustion state. Figure 15c,d, show clear flames for MG and COG under OEC mode. The flame is short and bright under the COG condition, with a peak temperature reaching up to 2448 K. However, this high temperature does not raise overall furnace temperature. Instead, it causes obvious uneven temperature distribution in soaking zone, which will reduce the heating quality of the slab. This phenomenon can be attributed to the main components of COG—hydrogen and methane. Hydrogen burns rapidly, producing a short, high-temperature flame with limited heat transfer capability, which hinders the formation of a uniform temperature field within the furnace. Additionally, the water vapor and carbon dioxide generated during methane combustion absorb part of the heat, further exacerbating the non-uniformity of the temperature distribution.

Figure 16 shows the velocity distribution near burners for different fuels at O₂% = 51%. As shown in Figure 16a,b, the max velocity for MG under MOFC mode is 378.9 m/s, while the max velocity for NG is 438.6 m/s. Velocity distributions are similar for both. Notably, flue gas entrainment and recycling are stronger for NG that that for MG. This is most obvious in the preheating zone. As shown in Figure 16c,d, max velocity is 8.7 m/s (MG) and 5.5 m/s (COG) under OEC mode. Velocity distributions are similar. Entrainment range in the soaking zone is larger for MG. Near the burners in third heating zone, it shows a small recirculation zone for COG. This is the main reason for the local high temperature zone formation.

3.3.2. Emission Analysis

Figure 17 shows the NO_x production for different fuels at O₂% = 51%. The NO_x concentration is below 47 mg/m³ for MG under MOFC mode. It increases gently along the furnace length, which is due to the uniform temperature distribution. The temperature in the soaking zone is higher than other zones, which slightly strengthens the thermal NO_x formation. For NG under MOFC mode, the high calorific value of methane causes a NOx peak (533.45 mg/m³). The peak value appeals to the front part of the soaking zone, after the peak position, and the flue gas recirculation reduces NO_x to 507.75 mg/m³. For COG under OEC mode, the flame temperature is uneven, and the local high temperature leads to NOx surges to 1919.7 mg/m³ at 41 m furnace length. This is much higher than NG and MG.

3.3.3. Thermal Efficiency and Energy Saving Rate Analysis

Thermal efficiency, energy saving rate, and ${\mathrm{q}}_1^{\prime }$ for different fuels are shown in Figure 18. Thermal efficiency for NG is 62.68% and about 2.8% higher than MG. Under OEC mode, although the exhaust gas heat loss for MG is high (36.82%), thermal efficiency is still 59.88% as the flue gas dilution reduces the local high-temperature loss. The exhaust gas heat loss for COG is high (38.71%), which is due to elevated high-temperature loss from the poor flue gas dilution and mixing. So, the thermal efficiency for COG is only 58.29%, but this is still higher than that for MG under OEC mode.

The energy saving rate for MG is the highest (52.14%). This is because its combustion products contain a high content of H₂O and CO₂. The proportion of CO₂ in the exhaust gas of MG reaches 39.6%, which is the highest among the three fuels, along with a 16.9% content of H₂O. The radiation heat transfer to the steel slab is elevated by the high H₂O and CO₂ concentration. Although the flue gas temperature of NG is the lowest, its average specific heat capacity is higher than that of MG, which leads to an increase in sensible heat loss per unit of flue gas. At the same time, the relatively insufficient concentration of CO₂ weakens the radiation advantage. The H₂O content in the exhaust gas of COG is the highest, but the CO₂ concentration is the lowest, and the exhaust temperature rises to 1175.9 K. This causes dual heat loss in exhaust gas and radiation efficiency. Although it achieves the highest thermal efficiency for NG under MOFC due to its high calorific value and uniform combustion, its energy saving rate is lower than MG. This occurs because energy saving rate measures improvement relative to the air combustion baseline. NG’s baseline efficiency is higher than MG, thus exhibiting a smaller relative gain despite superior absolute performance.

4. Conclusions

In this study, the flow, heat transfer properties, and thermal efficiency of a steel reheating furnace were studied with numerical simulations. The effects of different oxygen concentrations and fuels were analyzed under OEC and MOFC modes. The main findings are as follows:

(1) The temperature uniformity of the furnace is improved with the elevated oxygen concentration. The most uniform temperature distribution appeals at O₂% = 31% under MOFC mode.

(2) MOFC mode drastically reduces NO_x compared to OEC. NO_x emission under MOFC mode is 1–2 orders of magnitude lower than that under OEC mode.

(3) The increasing oxygen concentration improves the thermal efficiency and energy saving rate of the furnace. At O₂% = 91%, the thermal efficiency under MOFC reaches 60.98% and the energy saving rate reaches 47.04%.

(4) There is a uniform gas flow distribution and almost no visible flame exists under MOFC mode for NG. The thermal efficiency in this condition is the highest (62.68%).

(5) Considering the heating characteristics of the slabs, MOFC technology combined with MG or NG is recommended. Efficient, low-emission operation is achievable at O₂% = 51~71%.