The blast furnace structure has an important influence on burden movement, flow of coal gas, and utilization of chemical and thermal energy in blast furnace production. Besides, rational furnace structure could also avoid the abnormal erosion of refractory and prolong the service time of blast furnace [1, 2]. Domestic furnace structure has the following development trend characters [3]:

Value of height/diameter diminishes, which means furnace structure becomes from “high and thin” to “low and fat”;

Shaft angle *β* and Bosh angle *α* both diminish and become close to each other. For modern large-scale blast furnaces, the shaft angle normally ranges from 79 ° to 81 °, while for Bosh angle, the range is between74 and 80 °.

Before application of copper cooling stave, the brick in Bosh, belly, and shaft areas used to be thick, and after blow-in of the furnace the lining of the furnace would be eroded into different shapes according to various furnace operations; thus, the operating furnace profile was formed. Rational operating furnace profile could maintain good production indexes and prolong service life of the furnace [4, 5, 6, 7]. Due to this reason, furnace operation could make up improper designing of the traditional thick bricking furnace. However, after application of cooper cooling stave, the structure of “thin bricking furnace” was formed for which only 120–150 mm insert bricks existed at hot surface of cooling stave, so the influence of insert brick erosion on final furnace profile was limited and the designing furnace profile was also the final furnace profile [8]. It could be summarized that after application of cooper cooling stave, the requirement for furnace design becomes stricter. But in fact after application of cooper cooling stave, no practical improvement was presented in furnace designing area.

After investigation of cooper cooling stave damage cases in recent years, many scholars considered irrational furnace structure as an important reason. Scholars holding this standpoint thought that for most of blast furnace they all had overlarge Bosh angle and undersize shaft angle, which would lead to fierce brush of coal gas on hot face of cooling stave and cause fast damage [9].

In order to investigate the influence of furnace structure on lifetime of cooling stave, commercial software Fluent was used in this paper to establish a coal gas distribution model in blast furnace. Coal gas distribution near the surface of cooling stave under conditions of various Bosh angles and shaft angles was calculated to ascertain the influence of furnace structure on coal gas distribution. For coal gas distribution in blast furnace, many scholars have done abundant work and good results were obtained. Based on transfer phenomenon among phases of gas, solid, and fluid, Hatano and Kurita established a coal gas distribution model and also took chemical reaction and heat transfer into account [10]. Austin et al. established a model considering four phases of gas, solid, fluid, and particle, which could accurately calculate the gas and temperature distribution [11, 12], and based on this some scholars further developed five-phase model considering coal gas, solid burden, dust, slag, and hot metal [13]. Through finite-difference method, Zhang et al. [14] established a coal gas distribution model in which parameters of burden diameter, resistance coefficient, stack angle, and burden thickness could be considered and calculation was more suitable to practical furnace.

However, aforementioned models are more focused on transport phenomena of heat and mass between different phases of solid burden and gas, and the influence of furnace structure is less considered. In this study, the influence of furnace structure on coal gas distribution is the main focus, so the interaction among different phases in the furnace is neglected, and shaft angle and Bosh angle are chosen as the main influence factors. Besides, “equivalent Bosh angle” concept is proposed, and a thorough analysis of the influence of different factors on coal gas flow rate near cooling stave surface is finished and the influence of furnace structure on lifetime of cooling stave is summarized.

## Foundation of coal gas distribution model in the blast furnace

## Assumption and simplification of the model

Considering the axial symmetrical property of blast furnace, the following assumptions are made:

The model is two-dimensional steady-state model, and blast furnace is considered as axial symmetrical structure, and half of longitudinal section is selected as the computational area;

Particle size change of ore and coke are considered, and lowering the rate of solid burden is fixed as constant;

Position and shape of cohesive zone are considered, and heat transfer is neglected;

Different layers of coke, ore, and cohesive zone are distinguished according to different sets of porosities.

Coal gas is treated as incompressible Newtonian fluid.

Based on these assumptions, mathematical formulas for the established model through software “Fluent” are as follows.

## Gas distribution model

Gas distribution model consists of equation of continuity, momentum equation, turbulence model equation, turbulence energy dissipation equation, and Ergun equation. Under two-dimensional rectangular coordinate system, the above equations are presented as follows:

(1) Equation of continuity

$\frac{\mathrm{\partial}\rho {u}_{i}}{\mathrm{\partial}{x}_{i}}=0$(1)In the formula, *ρ* is gas density, kg·m^{−3}; *u*_{i} is gas flow speed, m·s^{−1}.

(2) Momentum equation

$\frac{\mathrm{\partial}(\rho {u}_{i}{u}_{j})}{\mathrm{\partial}{x}_{j}}=-\frac{\mathrm{\partial}P}{\mathrm{\partial}{x}_{i}}+\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{j}}\left[{\mu}_{\mathrm{e}\mathrm{f}\mathrm{f}}\left(\frac{\mathrm{\partial}{u}_{i}}{\mathrm{\partial}{x}_{j}}+\frac{\mathrm{\partial}{u}_{j}}{\mathrm{\partial}{x}_{i}}\right)\right]$(2)In the formula, *u*_{i} and *u*_{j} are speed of gas along directions of *i* and *j*, respectively, m·s^{−1}; *x*_{i} and *x*_{j} are coordinate figure of directions *i* and *j*; *ρ* is density, kg·m^{−3}; *P* is pressure, Pa; μeff is effective coefficient of viscosity, Pa·s, which is ascertained by turbulence model.

(3) *k*–*ε* turbulence model

$\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{i}}\left[\rho {u}_{i}k-\frac{{\mu}_{\mathrm{e}\mathrm{f}\mathrm{f}}}{{\sigma}_{k}}\cdot \frac{\mathrm{\partial}k}{\mathrm{\partial}{x}_{i}}\right]={G}_{k}-\rho \epsilon $(3)In the formula: *k* is turbulent kinetic energy, m^{2}·s^{−2}; *G*_{k} is item derived from turbulent energy; *ε* is dissipation ratio of turbulent energy, m^{2}·s^{−3}.

(4) Turbulent energy dissipation equation

$\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{i}}\left[\rho {u}_{i}\epsilon -\frac{{\mu}_{\mathrm{e}\mathrm{f}\mathrm{f}}}{{\sigma}_{k}}\cdot \frac{\mathrm{\partial}\epsilon}{\mathrm{\partial}{x}_{i}}\right]=({C}_{1}\epsilon {G}_{k}-{C}_{2}\rho {\epsilon}^{2})/k$(4)In the formula：

${G}_{k}={\mu}_{\mathrm{t}}\cdot \frac{\mathrm{\partial}{u}_{j}}{\mathrm{\partial}{x}_{i}}\left[\frac{\mathrm{\partial}{u}_{i}}{\mathrm{\partial}{x}_{j}}+\frac{\mathrm{\partial}{u}_{j}}{\mathrm{\partial}{x}_{i}}\right]$(5)${\mu}_{\mathrm{e}\mathrm{f}\mathrm{f}}={\mu}_{\mathrm{l}}+{\mu}_{\mathrm{t}}$(6)${\mu}_{\mathrm{t}}=\rho {C}_{\mu}\frac{{k}^{2}}{\epsilon}$(7)It the formula: *μ*_{t} is turbulence viscosity coefficient, Pa·s; *μ*_{l} is laminar flow viscosity coefficient, Pa·s; *C*_{1}, *C*_{2}, *C*_{μ}, σ_{k}, σ_{t} are empirical constants, which are ascertained through recommended values of Launder and Spalding [15], as shown in .

Table 1: Empirical constant of the kinematics dissipate equation.

(5) Ergun equation

$\frac{\mathrm{\Delta}P}{H}=150\frac{{(1-\epsilon )}^{2}}{{\epsilon}^{3}}\frac{\mu}{{(\varphi {d}_{\mathrm{p}})}^{2}}{\mu}_{\mathrm{A}}+1.75\frac{1-\epsilon}{{\epsilon}^{3}}\frac{\rho}{\varphi {d}_{\mathrm{p}}}{{\mu}_{\mathrm{A}}}^{2}$(8)In the formula: *μ*_{A} is gas flow rate through packed bed calculated according to cross-sectional area, m·s^{−1}; *d*_{p} is particle diameter, m; *μ* is fluid viscosity, Pa·s; *ϕ* is shape factor of particles.

## Physical model of gas distribution

Based on the above formulas, according to structure parameters of a domestic 1,780 m^{3} blast furnace (shown in ), gas distribution model for practical blast furnace is established, as shown in Figure 1.

Figure 1: Gas flow distribution model of the blast furnace.

Table 2: Structure parameters of the model.

Influence of raceway and deadman on gas distribution is considered, and the size of them is ascertained by the following formula:

${L}_{\mathrm{R}}=0.118\times {10}^{-3}{E}_{\mathrm{b}}+0.77,\phantom{\rule{thinmathspace}{0ex}}\frac{{L}_{\mathrm{R}}}{{H}_{\mathrm{R}}}={K}_{\mathrm{R}}$(9)For *E*_{b}:

${E}_{\mathrm{b}}=\frac{1}{2}{\rho}_{\mathrm{b}}\frac{{V}_{\mathrm{b}}}{gn}[\frac{4{V}_{\mathrm{b}}}{\pi n{({d}_{\mathrm{b}})}^{2}}\times \frac{{T}_{\mathrm{b}}{P}_{0}}{273{P}_{\mathrm{b}}}{]}^{2}$(10)In the formula, *L*_{R} is the depth of raceway, m; *H*_{R} is the height of raceway, m; *K*_{R} is the raceway shape coefficient and is dimensionless, which lies between 0.6 and 1.17 according to different furnace volumes; *E*_{b} is the blast kinetic energy, kg·m·s^{−1}; *V*_{b} is the blast volume, m^{3}·s^{−1}; *N* is the tuyere number; *G* is the acceleration of gravity, m^{2}·s^{−1}; *d*_{b} is the diameter of tuyere, m; *T*_{b} is the blast temperature, K; *P*_{b} is the blast pressure, Pa; *P*_{0} is the atmosphere pressure, Pa.

## Boundary conditions

Wall surface: boundary condition for wall touching gas part is set as non-slipping;

Inlet: inlet of the model is tuyere and is set as velocity boundary condition, which is calculated from conversion of blast volume;

Outlet: outlet of the model is the up edge of furnace throat and is set as the pressure boundary condition, which is equal to top pressure;

Surface of liquid metal and slag: the bottom of the model is slag–metal surface and is set as constant, $\frac{\mathrm{\partial}u}{\mathrm{\partial}y}=0$;

Axial symmetry boundary: along the axis of symmetry the radial velocity is 0, $\frac{\mathrm{\partial}u}{\mathrm{\partial}x}=0$.

## Calculation parameters and modeling scheme

Parameters of the practical blast furnace are used for calculation, which are shown in .

Table 3: Parameters for calculation.

Influence of furnace structure on gas distribution is the focus of the study, especially for gas flow in edge area. So Bosh angle and shaft angle are chosen as variable parameters. For practical blast furnace in which furnace structure is unchangeable, the measure of prolonging tuyere could be adopted, for which the included angle between horizontal line and line between tuyere front and belly bottom wall side could be changed. In this study, the angle is defined as “equivalent Bosh angle” and is also set as a variable parameter.

According to the design parameters and practical data, variation standard of the variables is ascertained and shown in . For specific calculation considering one factor, the values of other variables are set as their characteristic value.

Table 4: Influence factors and their value level.

## Results and discussion

## Method for analysis

As shown in Figure 2, in order to analyze the gas distribution under different conditions, along 10 mm near the wall surface from bottom of Bosh to the lower area of shaft, some points are chosen and the gas velocity of these points is used as the surface velocity of gas. The chosen points are scattered along the red line in Figure 2.

Figure 2: Schematic diagram of the sampling points of the gas flow velocity.

## Influence of Bosh angle on lifetime of cooling stave

For Bosh angle changing from 74 ° to 79 ° (shaft angle 78 °, equivalent Bosh angle 76 °), distribution of surface gas velocity is shown in Figure 3. The 1st to 10th points are located at Bosh area, the 11th to 20th points are located at belly area, and 21st to 30th points are located at lower area of shaft. It could be found that from Bosh area to the bottom of cohesive zone, gas flow rate decreases quickly. At cohesive zone, due to rectification effect of cohesive zone, most of gas goes through coke lawyer and near-wall surface gas flow has a low rate. After cohesive zone, coal gas is redistributed and gas flow rate near-wall surface increases gradually. At belly area due to constant of diameter, change of gas flow rate is limited. At shaft area due to diminishing of diameter, gas flow rate increases gradually. At the same time, from Figure 3, it could be summarized that changing of Bosh angle has a significant influence on the gas flow rate for region lower than cohesive zone at Bosh area, and for region higher than cohesive zone the influence is limited. Before rectification of cohesive zone, with increase of Bosh angle gas flow rate, near-wall surface increases gradually.

Figure 3: The velocities of the gas flow on the surface of the cooling stave under different conditions of variational Bosh angles.

In order to accurately analyze flow rate change at Bosh region, 30 equidistance points alone Bosh wall surface were selected. Surface flow rate under various conditions are shown in Figure 4. At Bosh region, for different Bosh angles, gas flow rates are different, and smaller the Bosh angle, the lower the gas flow rate (Figure4(a)). At the bottom area of Bosh, the influence of Bosh angle on the surface flow rate is limited, and with distance away from the Bosh bottom, the influence of the Bosh angle increases, when further to the bottom of cohesive zone, the difference of gas flow rate diminishes gradually. Take No. 8 point at Bosh area for example, when Bosh angle changes from 74 ° to 79 °, the gas flow rate increases by 78 % from 0.97 m·s^{−1} to 1.73 m·s^{−1}.

Figure 4: The gas flow velocities at the Bosh area before “rectifying effect” under the conditions of different Bosh angles.

The above analysis shows that Bosh angle has a significant influence on the wall surface gas flow rate, and too big Bosh angle could lead to surface flow rate become over high and make brushing effect strengthened, which would make adhering slag layer on copper cooling stave become unstable and even lead to damage of cooling stave.

## Influence of shaft angle on lifetime of cooling stave

Changes of gas distribution for shaft angle changing from 76 ° to 80 ° are shown in Figure 5. It could be concluded that, for Bosh and belly area, changes of shaft angle has limited influence on gas flow, but for shaft area, the influence is significant.

Figure 5: The velocities of the gas flow on the surface of the cooling stave under different conditions of variational shaft angles.

In order to investigate influence of shaft angle on gas flow, from the bottom to the middle of the shaft, 30 points were selected and the flow rates on these points are shown in Figure 6. It could be found that the smaller the shaft angle, the higher the surface flow rate for lower area of shaft. With distance away from the bottom of shaft, influence of shaft angle on gas flow rate becomes more and more obvious. Take the 30th point, for example, when shaft angle is changed from 76 ° to 80 °, the flow rate at this point is changed from 19.42 m·s^{−1} to 15.27 m·s^{−1}, lowered by 21 %. So too small shaft angle could lead to high surface flow rate at shaft region and cause brushing effect of gas, which is bad for longevity of cooling stave.

Figure 6: The gas flow velocities at the shaft area after “rectifying effect” under the conditions of different shaft angles.

## Influence of equivalent shaft angle on lifetime of cooling stave

For Bosh angle 76 ° and shaft angle 78 °, when equivalent Bosh angle is increased from 74 ° to 78 ° change of surface gas low rate for regions of Bosh, belly, and lower area of shaft are shown in Figure 7. It could be concluded that equivalent Bosh angle has a significant influence on gas flow at Bosh region, but for region above cohesive zone the influence is limited. In order to investigate the influence of equivalent shaft angle on gas flow in Bosh region, 30 points were selected and the surface flow rate of these points is shown in Figure 8.

Figure 7: The velocities of the gas flow on the surface of the cooling stave under different conditions of variational equivalent Bosh angle.

Figure 8: The gas flow velocities at the Bosh area before “rectifying effect” under the conditions of different equivalent Bosh angels.

From Figure 8, it could be concluded that the bigger is equivalent Bosh angle is, the higher surface flow rate at belly region is, which is bad for longevity of cooling stave. At the same time, the closer to bottom of Bosh, the greater the influence is. Take the break point of hearth and Bosh for example (Point 1), when equivalent Bosh angle is changed from 74 ° to 79 °, surface flow rate at this point is increased by 5 times from 1.74 m·s^{−1} to 10.73 m·s^{−1} . So it could be concluded that it equivalent Bosh angle is too big, the brushing effect at Bosh region is significant, and this is in accordance with the domestic practical situation of cooper cooing stave damage. From this aspect, through method of lengthening tuyere to lower equivalent Bosh angle could obviously decrease brushing effect at Bosh region and stabilize adhering slag layer, which is good for longevity of cooper cooling stave.

## Conclusions

Bosh angle has an obvious influence on the surface gas flow rate at Bosh region, and a large Bosh angle could give a surface flow rate at Bosh region and strengthen brushing effect, which is bad for stability of adhering slag layer and could cause damage of cooling stave.

Lowering of shaft angle could lead to increase of surface flow rate at the shaft region and strengthen brushing effect, which is bad for longevity of cooper cooling stave.

Influence of equivalent Bosh angle on lifetime of cooper cooling stave is the most obvious and increase of equivalent Bosh angle could lead to a sharp increase of the surface flow rate. If equivalent Bosh angle is too big, the brushing effect of coal gas on cooling stave (especially for lower area) would become serious.

Lengthening tuyere to lower equivalent Bosh angle could obviously decrease the brushing effect of coal gas at Bosh region and stabilize adhering slag lawyer which is good for longevity of cooper cooling stave.

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## About the article

**Received**: 2017-03-22

**Accepted**: 2017-07-23

**Published Online**: 2018-06-19

**Published in Print**: 2019-02-25

This paper had been aided by the following foundations: (1) Natural Science Foundation of China: Study on induced cracking mechanism of BF copper cooling stave and constructing technology of hydrogen permeation suppression coating (51604103); (2) Natural Science Foundation of Hubei Province: Research on the cracking mechanism of BF cooling stave caused by hydrogen and the key technology of hydrogen permeation suppression (2016CFB293); (3) The Doctoral Research Start-up Foundation of Hubei University of Automotive Technology (BK201607).

**Citation Information: **High Temperature Materials and Processes, Volume 38, Issue 2019, Pages 1–7, ISSN (Online) 2191-0324, ISSN (Print) 0334-6455, DOI: https://doi.org/10.1515/htmp-2017-0040.

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