3D thermodynamics and parameters analysis of the external combustion hot blast stove

Abstract

The external combustion hot blast stove is widely used in the steelmaking industry due to the advantage of providing a large amount of high-temperature and stable hot blast for blast furnaces. To research the thermal efficiency and stability of external combustion hot blast stoves, the non-equilibrium porous medium model coupled with transient thermal analysis is used to discuss the characteristics of two types of external combustion hot blast stoves during the cyclic operation process. In this paper, a comparison of the numerical data and in situ data during one cycle to ensure the accuracy of the calculation, which of the results showed that the temperature maximum relative error value is within 3%. The numerical results displayed that the velocity and temperature distribution of fluid are mainly affected by pressure, flow rate, cycle time, and geometric structure, where the hot blast temperature is affected by the cycle time but the distribution of velocity and relative pressure are affected by the height of hot blast branch. It can be concluded that the flow field and the structure of type A hot blast stove are more stable than that of type B by comparing the results of two types of hot blast stoves.

Introduction

The structure of hot blast stoves is developed from the internal combustion type to the external combustion type and the top combustion type in these years gradually to supply high-quality hot blast for a blast furnace. Where the external combustion hot blast stove has improved the distribution of fluid by separating the combustion chamber from the regenerator compared to the internal combustion chamber. The advantage of the external combustion hot blast stove can provide a larger flow of stable and high-temperature hot blast for a blast furnace. However, due to the characteristic of the complex structure and the un-uniform distribution of gas, the external combustion hot blast stove is operated with poor stability of the structure during the cyclic process. The operation process of the external combustion hot blast stove is cyclic with two periods as same as other hot blast stoves. ¹ To research the operating characteristics and improve the stability and thermal efficiency, this paper focuses on investigating the temperature, pressure, and velocity distributions of two types of hot blast stoves under different conditions to ensure that the external combustion hot blast stove can be operated stable and effective over extended durations under different parameters.

In recent years, many researchers have been devoted to improving the performance of hot blast stoves in the heat transfer process and the stability of fluid flow under various boundary conditions. To improve the thermal efficiency of hot blast stoves, researchers have conducted innovative studies since the introduction of the hot blast stove. Some researchers found that the thermal efficiency of the hot blast stove can be effectively by optimizing the oxyfuel technology, which can be used to increase the hot blast temperature and decrease the flue gas temperature.^2,3 Based on thermodynamic heat balance and the computational fluid dynamic simulation. Some researchers mainly focused on analyzing the process of transient heat exchange of hot blast stoves by considering heat exchange, turbulence, and combustion conditions to analyze the performance of fluid and the heat transfer mode between fluid and checker brick and control the fluid temperature.^4–7 Subsequently, some research is devoted to solving the unreasonable temperature distribution in the combustion chamber and regenerator by proposing an improved design or designing a reasonable refractory structure, and so on.^8–10 In the meantime, the authors used the thermos-structural coupling model to analyze the performance of a hot blast stove during the operating process in the earlier research, whose content mainly included the distribution and periodic variation rules of temperature, velocity, thermal stress, and deformation.^11,12

Despite the progress made, previous numerical simulations on the performance of hot blast stoves mainly focused on a single hot blast stove. However, the comparative performance analysis between different structures (or types) of hot blast stoves has not been reported at present. This phenomenon in the literature motivated the authors to carry out the present investigation by using a non-equilibrium porous medium model coupled with transient thermal analysis to discuss the characteristics of two types of external combustion hot blast stoves under different conditions. These results are used to analyze the performance of the different types of external combustion hot blast stoves and discuss the impact of the operation cycle and the structure of the hot blast branch on the temperature field, velocity field, and relative pressure field. It provides theoretical support for optimizing the structure of the external combustion hot blast stove.

Physical model

Two common types of hot blast stoves were discussed in this paper, which is illustrated in Figure 1 (type A and type B hot blast stove model). Both of the two types of external combustion hot blast stoves of the structure are mainly composed of five parts: the checker chamber, the combustion chamber, the dome/fire bridge, the hot blast branch, and the cold flue branch. The main difference in the structure of the two types of hot blast stoves is the dome/fire bridge, which is located at the top of the hot blast stove. The top structure of type A is composed of a section of a quarter cone connected with two-quarters spherical of different radii at a certain angle, but type B consists of two hemispheres with different radii and a cylinder as shown in Figure 2.

Figure 1.

The 3D physical model: (a) type A and (b) type B.

Figure 2.

The dome structure of the external combustion hot blast stove: (a) type A and (b) type B.

Figure 2 shows that the fire bridge of type A as an integral component is more continuous than type B. Moreover, the down thickness of the fire bridge (t_A-down) is designed thicker than the up (t_A-up). The top structure of type B can be divided into three sections: checker-dome, connecting pipe, and combustion-dome. It is noticed that, for the checker-dome, connecting pipe, and combustion-dome, the center points of the inner and outer diameters are all located at different points and the down thickness of the connecting pipe (t_B-down) is designed thinner than the up (t_B-up), which is different with the type A. On the other hand, the operating parameters of the two types of hot blast stoves are different too, for instance, the cyclic time and the average temperature of inlet et al. as shown in Table 1.

Table 1.

The parameters of the two types of the external combustion hot blast stove.

Operating condition	Type A	Type B
Cyclic time (min)
On-gas period	55	100
On-blast period	32	114
The average temperature of inlet (°C)
Flue gas	1446	1468
Blast	223	225
The maximum temperature of outlet (°C)
Flue gas	292	295
Blast	1221	1232
The volume of the fluid zone (m3)	1294	1256
The volume of the porous (m3)	889	805
The area of the porous (m2)	60,829	55,085

Due to the complex structure of the external combustion hot blast stove, the calculation region is divided into the gas flow region, heat exchange region, and the solid region as shown in Figure 3, where, the solid region is composed of a variety of insulating bricks, and the thickness and the materials vary with the position. The heat exchange region can be divided into fluid and solid regions by using a non-equilibrium porous medium model, which is located in the checker chamber and composed of kinds of checker brick. The in situ data are obtained at the top of the checker brick, the cold flue gas outlet, and the hot blast outlet corresponding to point 1, point 2, and point 3, respectively. Moreover, the location of the hot blast branch has been changed to the height (±Δh) to analyze the influence of the structure of the hot blast branch on the flow field of the hot blast stove.

Figure 3.

The calculation zones of the external combustion hot blast stove (Type A).

Mathematical model

In this study, the cyclic operation process of the two types of external combustion hot blast stove is simulated with transient thermal analysis by building a 3D physical model to calculate the temperature, velocity, and relative pressure distribution by considering various complex phenomena, for instance, the turbulent of the fluid, heat radiation, heat conduction, and heat transfer between the gas and checker bricks, and so on. Where, the non-equilibrium porous medium model was used to simplify the complex structure of the checker brick, and the operating process with an on-gas period and on-blast period was regarded as a quasi-steady state process. Moreover, a user-defined coupled equation written in C language was incorporated in ANSYS2024R1. The flowchart of the calculation process is plotted in Figure 4.

Figure 4.

The flowchart of the calculation process.

Governing equations

The operating process of the external combustion hot blast stove is a transient process with periodic cycles, which is regarded as a quasi-steady state process. For the thermal fluid analysis of the gas flow region, the governing equations can be described as follows,^13–15

Continuity equation:

$$\frac{\partial \rho }{\partial t}+\frac{\partial \rho {\overline{u}}_i}{\partial x_i}=0$$

(1)

Momentum equation:

$$\frac{\partial \rho {\overline{u}}_i}{\partial t}+\frac{\partial \rho {\overline{u}}_i{\overline{u}}_j}{\partial x_j}=-\frac{\partial \overline{p}}{\partial x_i}+\rho g_i+\frac{\partial }{\partial x_j}[{\mu }_{\mathrm{eff}}(\frac{\partial {\overline{u}}_i}{\partial x_j}+\frac{\partial {\overline{u}}_j}{\partial x_i})-\rho {\overline{u}\prime }_i{\overline{u}\prime }_j]$$

(2)

Energy equation:

$$\begin{array}{c}\multicolumn{1}{c}{\frac{\partial \left(\rho c_p\overline{T}\right)}{\partial t}+\frac{\partial }{\partial x_j}\left(\rho c_p{\overline{u}}_j\overline{T}\right)={\overline{u}}_j\frac{\partial \overline{p}}{\partial x_j}+\overline{u}{\prime }_j\frac{\partial \overline{p}\prime }{\partial x_j}}\\ +\frac{\partial }{\partial x_j}(k\frac{\partial \overline{T}}{\partial x_j}-\rho c_p{\overline{u}\prime }_j\overline{T}\prime )-\nabla ·{\overrightarrow{q}}_r\hfill \end{array}$$

(3)

The standard κ-ε turbulence model is based on model transport equations for the turbulence kinetic energy (κ) and its dissipation rate (ε).

The transport equation for κ and ε are:

$$\frac{\partial \rho \kappa }{\partial t}+\frac{\partial }{\partial x_i}\left(\rho {\overline{u}}_i\kappa \right)=-\frac{\partial }{\partial x_i}(\frac{{\mu }_{\mathrm{eff}}}{{\sigma }_{\kappa }}·\frac{\partial \kappa }{\partial x_i})+\rho (P_r-\epsilon )$$

(4)

$$\frac{\partial \rho \epsilon }{\partial t}+\frac{\partial }{\partial x_i}\left(\rho {\overline{u}}_i\epsilon \right)=-\frac{\partial }{\partial x_i}(\frac{{\mu }_{\mathrm{eff}}}{{\sigma }_{\epsilon }}·\frac{\partial \epsilon }{\partial x_i})+\rho \frac{\epsilon }{\kappa }[c_1{P}_r-c_2\epsilon ]$$

(5)

Where, $P_r=\frac{{\mu }_t}{\rho }[2{\left(\frac{\partial u_i}{\partial x_i}\right)}^2-\frac{2}{3}{(\nabla u_i)}^2]$ , ${\mu }_{\mathrm{eff}}=\mu +{\mu }_t,{\mu }_t=\rho c_{\mu }\frac{{\kappa }^2}{\epsilon }$ , $P_r$ is the turbulent kinetic energy production rate, ${\mu }_{\mathrm{eff}}$ is the efficient turbulence viscosity, ${\mu }_l$ and ${\mu }_t$ are the laminar viscosity and turbulence viscosity, respectively, ${\sigma }_{\kappa }$ and ${\sigma }_{\epsilon }$ are the Prandtl number for turbulent kinetic energy and turbulent energy dissipation, respectively. In this study, the κ-ε model parameters with standard values were used: ${\sigma }_{\kappa }$  = 1.0, ${\sigma }_{\epsilon }$  = 1.3, C₁ = 1.44, C₂ = 1.92, C_µ = 0.09.

The radiation heat transfer between the high-temperature fluid and the internal surfaces/checker bricks of the hot blast stove is very important in the heat exchanging process, which can be written as follows, ¹³

$$\begin{array}{c}\multicolumn{1}{c}{(\overrightarrow{s}·\nabla )I_r(\overrightarrow{r},\overrightarrow{s})=-{\epsilon }_e{I}_r(\overrightarrow{r},\overrightarrow{s})+{\sigma }_a{I}_{r,b}\left(\overrightarrow{r}\right)}\\ +\frac{{\sigma }_s}{4\pi }{\int }_0^{4\pi }{I}_r(\overrightarrow{r},\overrightarrow{s})\mathrm{\Phi }(\overrightarrow{s},\overrightarrow{s}\prime )d\mathrm{\Omega }\prime \hfill \end{array}$$

(6)

where ${\epsilon }_e={\sigma }_a+{\sigma }_s$ , ${\sigma }_a$ is absorptivity, ${\sigma }_s$ is scattering coefficient, $\overrightarrow{r}$ is the position vector, $\overrightarrow{s}$ is direction vector, $\overrightarrow{s}\prime$ is scattering direction vector, $I_{r,b}$ is blackbody radiation intensity, $\mathrm{\Phi }$ is scattering phase function, $\mathrm{\Omega }\prime$ is the solid angle.

For the heat exchange region of the external combustion hot blast stove, the calculation zone is composed of different kinds of checker bricks, whose detailed properties are tabulated in Table 2. To accurately calculate the thermal-hydraulic of the heat exchange region, the heat transfer performance between the gas and the checker brick is analyzed by using the non-equilibrium porous medium model in this paper. The non-equilibrium porous medium model shows that the checker brick is symmetry in six faces and the length is much greater than the cross-sectional area, therefore, one of the holes from the checker brick is taken to calculate the temperature and the pressure distribution, which is quoted as Reference 8. The porosity and the surface area density are can be written as below,^7,8

$$\gamma =\frac{P^2}{l^2}·N$$

(7)

$$\beta =\frac{4\sqrt{3}}{3}·\frac{P}{l^2}·N$$

(8)

Where, $\gamma$ is the porosity of the porous medium model, P is the one side length of the checker brick hole, l is the outside length of the checker brick, N is the number of holes per checker brick, $\beta$ is the surface area density.

Table 2.

The properties of the checker brick.

Material	Density (kg/m3)	Thermal conductivity (w/m-k)				Specific heat capacity (J/kg-K)
		Temperature (K)				Temperature (K)
		473	973	1373	1573	400	600	800	1000	1200	1400	1600	1800
Porous 1	2250	1.65	1.65	1.95	1.95	908	1079	1205	1171	1204	1234	1263	1290
Porous 2	2280	1.65	1.65	1.95	1.95	912	1081	1202	1177	1210	1240	1267	1293
Porous 3	2320	1.80	1.80	2.10	2.10	920	1084	1194	1186	1219	1248	1274	1298
Porous 4	2540	1.65	1.65	1.95	1.95	926	1087	1188	1194	1227	1256	1280	1302

The pressure drop in the checker brick along the flow direction is approximately calculated according to the equation developed in pipe flow phenomena, which can be expressed as, ¹⁶

$$\frac{\mathrm{\Delta }p}{L}=f\frac{\rho u_m^2}{2D}$$

(9)

Where, D is the diameter of the checker brick hole, L is the length of the checker brick, and f is the friction factor can be calculated as,

$$f=\{\begin{array}{c}\frac{16}{{\mathrm{Re}}_D}({\mathrm{Re}}_D<2300)\hfill \\ {(0.790\ln {\mathrm{Re}}_D-1.64)}^{-2}(3000\le {\mathrm{Re}}_D<5\times {10}^6)\hfill \end{array}$$

(10)

Different from other fluid models, the porous media model can calculate the flow peculiarity of the porous area by introducing a flow resistance term. Thus, the non-equilibrium porous medium model equation can be expressed as follows,

Continuity equation:

$$\frac{\partial \gamma {\rho }_f}{\partial t}+\frac{\partial {\rho }_f{\overline{u}}_i}{\partial x_i}=0$$

(11)

Momentum equation of the fluid:

$$\begin{array}{c}\multicolumn{1}{c}{\frac{\partial {\rho }_f\gamma {\overline{u}}_i}{\partial t}+\frac{\partial {\rho }_f{\overline{u}}_i{\overline{u}}_j}{\partial x_j}=-\frac{\partial \overline{p}}{\partial x_i}+\frac{\partial }{\partial x_j}[{\mu }_{\mathrm{eff}}(\frac{\partial {\overline{u}}_i}{\partial x_j}+\frac{\partial {\overline{u}}_j}{\partial x_i})-\rho {\overline{u}\prime }_i{\overline{u}\prime }_j]}\\ \frac{\mu }{\alpha }{\overline{u}}_i-C\frac{1}{2}\rho \left|{\overline{u}}_i\right|{\overline{u}}_i\hfill \end{array}$$

(12)

Energy equation of the fluid:

$$\begin{array}{c}\frac{\partial \left(\gamma {\rho }_f{c}_{p,f}{\overline{T}}_f\right)}{\partial t}+\frac{\partial }{\partial x_j}\left({\rho }_f{c}_{p,f}{\overline{u}}_j{\overline{T}}_f\right)\hfill \\ ={\overline{u}}_j\frac{\partial \overline{p}}{\partial x_j}+{\overline{u}\prime }_j\frac{\partial \overline{p}\prime }{\partial x_j}+\frac{\partial }{\partial x_j}(\gamma k_f\frac{\partial {\overline{T}}_f}{\partial x_j}-{\rho }_f{c}_{p,f}{\overline{u}\prime }_j{\overline{T}\prime }_f)+h_c\beta (T_s-T_f)\hfill \end{array}$$

(13)

Energy equation of the solid:

$$\frac{\partial (1-\gamma ){\rho }_s{c}_{p,s}{\overline{T}}_s}{\partial t}=\frac{\partial }{\partial x_j}·\left((1-\gamma )k_s\frac{\partial {\overline{T}}_s}{\partial x_j}\right)+h_c\beta (T_f-T_s)$$

(14)

Where, $1/\alpha$ is the viscous inertial resistance factor, and C is the inertial resistance factor.

The relationship between the viscous inertial resistance factor $1/\alpha$ , the inertial resistance factor C, and the pressure drop per unit $\mathrm{\Delta }p/l$ can be expressed as follows, ¹³

$$\mathrm{\Delta }p/l=\frac{1}{2}\rho ·\mathrm{C}·u^2+\frac{\mu }{\alpha }·u$$

(15)

For the solid region of the hot blast stove, the governing equation (energy equation) can be expressed as follows,

$$\frac{\partial }{\partial x}\left(k\left(T\right)\frac{\partial T}{\partial x}\right)+\frac{\partial }{\partial y}\left(k\left(T\right)\frac{\partial T}{\partial y}\right)+\frac{\partial }{\partial z}\left(k\left(T\right)\frac{\partial T}{\partial z}\right)=\rho ·C_p\left(T\right)\frac{\partial T}{\partial t}$$

(16)

Where, $T_s$ is the surface temperature of the solid, $T_f$ is the surface temperature of the fluid, $h_c$ is the heat transfer coefficient between the solid and the fluid.

Materials property

Flue gas

The components of the high-temperature flue gas (BFG, Blast Furnace Gas) in the on-gas period are CO₂, H₂O, N₂, and O₂, and corresponding with mole fractions are 30.7%, 1.8%, 67.2%, and 0.3%, respectively. In this study, the flue gas of each species has been regarded as an ideal gas and the thermophysical properties are calculated with the pressure, temperature, velocity, and composition of the flue gas.^14,15,17,18

Insulating brick

To simplify the 3D physical model of the hot blast stove in the transient thermal calculation, the insulating brick of the solid part with the same thickness is treated as an equivalent material along the radial direction, which represents the thermophysical properties of the insulating brick at each part vary only along the axial direction but not vary along the radial direction. The thermophysical properties of the equivalent materials with different positions based on the structure of the two types of hot blast stoves be calculated, respectively.^11,12

Computational methods and conditions

Computational domain and mesh generation

In this paper, governing equations are solved by the commercial software ANSYS, and the finite difference numerical method for the pressure-linked equation is used to simulate the temperature and the velocity field analysis. The first-order implicit method was used to maintain the numerical stability with the time step of 20 s to calculate the transient process. The computational grids for the symmetry three-dimensional model due to the symmetry structure of the hot blast stove, which are 698,908 and 1,001,625 cells for type A and type B of the 3D thermal-dynamics analysis, respectively, were typically adopted in the computational domain.

In this paper, the hexahedron mesh is used in the solid part (checker brick and insulting brick) and the tetrahedral mesh is used in the fluid part, which is shown in Figure 5. To ensure the accuracy and validity of the numerical results, a careful check of the grid independence of the numerical solutions of the symmetry model grid systems was tested in this study, which comprised 511,965, 698,908, and 895,832 cells for type A, 771,493, 1,001,625, and 1,102,604 cells for type B of the temperature and the velocity field analysis, respectively. The result of the temperature solutions shows that the relative errors under the same conditions with three types of grids were less than 1%. The discretized system was solved iteratively until it satisfied the following residual convergence criterion.

$$max\left(\frac{|T_{i,j}^n-T_{i,j}^{n-1}|}{T_{i,j}^n}\right)\le {10}^{-6}$$

(17)

Where, $T_{i,j}^{n-1}$ is the previous temperature value, $T_{i,j}^n$ at the same time level.

Figure 5.

Computational grid system: (a) type A and (b) type B.

Initial and boundary conditions

To ensure the accuracy of the calculation, two different initial temperatures are designed for all parts of the physical model until the same quasi-steady state temperature distribution through many cycles in this study, which is treated as the initial temperature conditions in the simulation process. In addition, the temperature changes of the hot blast stove are all continuous in two-stage periods. The operating parameters of two types of hot blast stoves are shown in Table 1.

Boundary conditions

The inlet conditions in two-stage periods of type A and type B hot blast stoves are listed in Table 3, which is imported in the form of UDF (User Define Function) by C language in this paper. A no-slip boundary condition is applied inside of the insulting brick surfaces, and the heat exchange between the insulting brick and gas is considered by assuming that the insulting brick surface temperature is equal to the gas:

$$k_f\left(\frac{\partial T_f}{\partial n}\right)=k_s\left(\frac{\partial T_s}{\partial n}\right),T_f=T_s$$

(18)

Table 3.

Inlet conditions.

Period	Inlet pressure P (Pa)	Mass flow rate Q (kg/s)	Inlet temperature Tin (K)
On-gas
Type A	5884	64.4	1655.2–1.464t
Type B	5884	64.76	1620.15
On-blast
Type A	431,493	99.1+0.2086t	496
Type B	431,493	54+0.0129t	498

The heat transfer between the steel surface and the environment is mainly natural convective, which is calculated by using the equation as follows:

$$q″=-k{\frac{\partial T}{\partial n}|}_{\mathrm{surface}}=h(T_s-T_{\infty })$$

(19)

where h is the convective heat transfer coefficient for the surface of the solid, $T_{\infty }$ is the environment temperature of 30°C.

Result and discussion

The confirmatory calculations of the pressure drop versus velocity distribution and the temperature versus height distribution have been finished in author’s previous work in Reference 11 to examine the validity result of the non-equilibrium porous medium model. Moreover, as same as type B in Reference 12, the temperatures in the thermal simulation under the quasi-steady state of type A are compared with the corresponding in situ data at three points to examine the validity of the simulation results, which is shown in the physical model: points 1 (dome), 2 (flue gas outlet), and 3 (hot blast outlet).

Figure 6(a) and (b) illustrate a comparison of the numerical data and the in situ data of one cycle for type A under the quasi-steady state with point 1, point 2, and point 3, respectively, which two sets of data are mutually consistent overall. Figure 6(a) shows that the temperature of the checker brick at point 1 is increased at first and then gradually leveled off with time until enters the on-blast period, due to the heat being transferred from flue gas to the checker brick in the on-gas period. After entering the on-blast period, the temperature of the checker brick at point 1 is decreased continuously due to the heat being transferred from the checker brick to the hot blast in the on-gas period. The temperature ranges of point 1 are 1234°C–1337°C and 1233°C–1320°C corresponding with the in situ data and numerical data during one cycle, respectively. The maximum temperature difference is 33°C, which happens at the start of the cycle and the maximum error is 2.6%. Figure 6(b) displays that, as the time passage, the temperature distribution of the flue gas at point 2 is monotonically increasing with the temperature of checker brick increasing in the on-gas period, while temperature distribution of the hot blast at point 3 is monotonically decreasing with the temperature of checker brick decreasing in the on-blast period. The temperature ranges of point 2 are 238°C–292°C and 240°C–285°C corresponding with the in situ data and numerical data in the on-gas period, respectively. The maximum relative error is 2.6%, which happens at the end of the on-gas period. In addition, the temperature ranges of point 3 are 1171°C–1242°C and 1153°C–1240°C corresponding with the in situ data and numerical data in the on-blast period, respectively, and the maximum relative error is 3.0%. The result explains that both the temperature of the flue gas and hot blast were changed with the temperature of the checker brick and the time. The temperature of the checker brick is impacted by its thermophysical properties and the characteristics of the fluid flow in the hot blast stove.

Figure 6.

The comparative curves of numerical and in situ data during one cycle at quasi-steady state: (a) point 1 and (b) point 2 and point 3.

Figure 7(a) and (b) display the velocity distribution of the flue gas and blast during one cycle in the checker chamber for type A and type B of the hot blast stove, respectively. It can be seen that, during the on-gas period, the velocity of the flue gas decreases along the direction fluid flow but increases as the height of the checker brick and time passage increases, which of the velocity range are 5–14.9 m/s and 4.5–15.7 m/s for type A and type B, respectively. However, during the on-blast period, the velocity range of the blast under the high-pressure condition (the relative pressure is about 431,493 Pa) for type A and type B are only 0.5–4.7 m/s and 0.5–2.7 m/s, respectively, which are lower than the velocity of the flue gas during the on-gas period. The velocity of the hot blast increases along the direction of fluid flow in the checker chamber and increases as the height of the checker brick increases as well, but is almost not affected by time. It can be noticed that the change of flue gas velocity for type B hot blast stove is higher than type A in the on-gas period, and the velocity range of the blast for type A is larger than type B, which is due to the cycle time of type B longer than type A but the flowrate of the blast for type A larger than type B. Therefore, the velocity distribution of the flue gas and blast are directly affected by temperature, pressure, flow rate of the fluid, cycle time, and so on.

Figure 7.

The velocity distribution of the checker chamber during one cycle: (a) type A and (b) type B.

Figures 8 and 9 express the velocity distribution of the flue gas and the blast for type A and type B hot blast stoves during one cycle, respectively. It can be found that the two types of hot blast stoves of the fluid flow pattern are complex and similar during one cycle, which expresses that the high-temperature flue gas flows from the combustion chamber to the checker chamber through the fire bridge and then passes the cold flue branch exhaust to the chimney in the on-gas period, and the flow direction is opposite to the cold blast flows in the on-blast period. Moreover, the velocity of the flue gas and blast not only change as the cross-sectional area of the fluid channel varied but also changed along the direction of fluid flow in the checker chamber in the on-gas period and on-blast period, respectively. Due to the influence of the structural characteristics of the fire bridge, the vortex flow is generated in the middle and bottom of the fire bridge during the on-gas period (0–55 min), but the obvious turbulence flow is formed in the combustion chamber during the on-blast period (55–87 min) for type A hot blast stove from Figure 8. It can be found that, from the position L1 to L5 of type A hot blast stove, the fluid field of the flue gas gradually becomes stable and the velocity of the flue gas increases slowly during the on-gas period but the blast velocity has barely changed during the on-blast period. However, the vortex flows are generated in the total dome during the on-gas period (0–100 min) and the combustion dome during the on-blast period (100–214 min) for type B hot blast stove from Figure 9. It also can be discovered that the distribution of the flue gas flow field is irregular and complicated for type B of the hot blast stove, and the velocity of the flue gas increases during the on-gas period from position L1 to L5. During the on-blast period, the fluid field of the flue gas gradually becomes stable and the change of blast velocity is not obvious from the position L1 to L5 of type B of the hot blast stove, which is similar to type A of the hot blast stove. It can be concluded that the flow field of type A hot blast stove is more stable than that of type B.

Figure 8.

The velocity distribution of the type A: (a) on gas period and (b) on blast period.

Figure 9.

The velocity distribution of the type B: (a) on gas period and (b) on blast period.

Figures 10 and 11 present the effect of the prolonged cycle time on the cold flue gas outlet (point 2) and hot blast outlet (point 3) temperatures with different cases for type A. Figure 10 shows the comparative curves of the cold flue gas outlet and hot blast outlet temperature when the on-gas period operating time from 55 min prolonged to 60 min. It can be seen that, as the on-gas period operating time increases, both the cold flue gas outlet and hot blast outlet temperature increases obviously, and the temperature range increases from 243°C–285°C and 1241°C–1153°C to 257°C–298°C and 1248°C–1167°C, respectively. Figure 11 shows the comparative curves of the cold flue gas outlet and hot blast outlet temperature when the on-blast period operating time from 32 min prolonged to 37 min. It can observed that both the cold flue gas outlet and hot blast outlet temperature decrease as the on-blast period operating time increases, and the trend is opposite compared with the on-gas period operating time increased, and the maximum of the decreasing temperature are 8°C and 33°C, respectively. In general, the hot blast temperature can be increased as the on-gas period operating time increases and the cold flue gas temperature can be decreased as the on-blast period operating time increases.

Figure 10.

The comparison temperature of the point 2 and 3 with different on-gas period time: (a) point 2 and (b) point 3.

Figure 11.

The comparison temperature of the point 2 and 3 with different on-blast period time: (a) point 2 and (b) point 3.

Figure 12 displays the velocity distribution of the hot blast stove during the on-blast period with different heights of the hot blast branch for type A. As mentioned in the previous section, in the on-blast period, the cold blast becomes the hot blast by absorbing heat from the checker brick in the checker chamber, and then flows to the hot blast branch through the fire bridge and the combustion chamber. Figure 12(a) to (c) represent the velocity distribution of the original model, the height of the hot blast branch with lower 5 m, and the height of the hot blast branch with higher 5 m, respectively. It can be noticed that the height of the hot blast branch mainly affects the velocity distribution of the hot blast in the combustion chamber. The velocity distribution is more stable than the original model with the height descending but less stable than the original model with the height rising, moreover, the unstable velocity distribution will lead to the non-uniformity temperature of the hot blast outlet. It means that the impact and pressure of the hot blast on the inner wall of the combustion chamber and the temperature of the hot blast outlet will be affected by the height of the hot blast branch.

Figure 12.

The velocity distribution with different hot blast stove position: (a) original model, (b) down 5 meters model, and (c) up 5 meters model.

Figure 13 shows the relative pressure distribution of the hot blast stove during the on-blast period with different heights of the hot blast branch during the on-blast period for type A, which corresponds with the velocity distribution in Figure 12. It can be found that the relative pressure is decreased as the fluid flow direction, and the negative pressure appears at the corner of the hot blast branch. By comparing Figures 12(a) to (c), it can be observed that the pressure distribution is affected by the height of the hot blast branch and velocity distribution, which is manifested that the relative pressure of the fluid increases as the height of the hot blast branch increases in the total hot blast stove but decreases as the stability of the flow field increases.

Figure 13.

The pressure distribution with different hot blast stove position: (a) original model, (b) down 5 meters model, and (c) up 5 meters model.

Conclusions

The non-equilibrium porous medium model coupled with transient thermal analysis is used to discuss the characteristics of two types of external combustion hot blast stoves during the cyclic operation process. In this paper, a comparison of the numerical data and the in situ data during one cycle to ensure the accuracy of the temperature calculation. Based on the validity of the model, the structure and flow field of two types of hot blast stoves are compared and analyzed by using fluid dynamics software. Meanwhile, the different operation times and the different heights of the hot blast branch are discussed to study the thermal-dynamics characteristics of type A of the hot blast stove. It makes up the gap of the present research and provides theoretical support for optimizing the structure of the external combustion hot blast stove. Based on the above results, the conclusion can be summarized as follows:

• (1) The main difference in the structure of two types of hot blast stoves is the dome/fire bridge, which is located at the top of the hot blast stove. The type A structure of fire bridge as an integral component is more continuous than type B.

• (2) Under the quasi-steady state, a comparison of the numerical data and in situ data during one cycle to ensure the accuracy of the calculation, which of the results showed that the temperature maximum relative error value is within 3%.

• (3) The velocity of the flue gas and blast increases along the direction of fluid flow in the checker chamber and increases as the height of the checker brick increases as well, but almost not affected by time.

• (4) The vortex flow was generated in the fire bridge during the on-gas period and the obviously turbulence flow was formed in the combustion chamber during the on-blast period. The flow field of type A hot blast stove is more stable than that of type B.

• (5) The hot blast temperature can be increased as the on-gas period operating time increases and the cold flue gas temperature can be decreased as the on-blast period operating time increases.

• (6) The height of the hot blast branch affected the velocity and relative pressure distribution in the combustion chamber.