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Numerical prediction on the erosion in the hearth of a blast furnace during tapping process
International Communications in Heat and Mass Transfer 36 (2009) 480–490
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Numerical prediction on the erosion in the hearth of a blast furnace during tapping process☆ C.M. Chang a, W.T. Cheng a,⁎, C.E. Huang a, S.W. Du b a b
Department of Chemical Engineering, National Chung Hsing University, Taichung 402, Taiwan, ROC Department of Steel and Aluminum Research and Development China Steel Corporation, 1 Chung Kang Road, Kaohsiung 81233, Taiwan, ROC
a r t i c l e
i n f o
Available online 25 March 2009 Keywords: Mass transfer Carbon Blast furnace hearth Tapping process Thermal convective flow
a b s t r a c t The erosion caused by mass transfer in hearth is the most important factor for determining blast furnace campaign life. To support a helpful insight information of mass transfer for the hearth of the No. 2 blast furnace at CSC (China Steel Corporation), a numerical model including the mass transfer of carbon in thermal convective flow from a blast furnace hearth has been developed during the steady tapping process (based on a uninterrupted tapping process assumption). The three dimensional Navier–Stokes equation combined with the transport equations of energy and species with conjugate heat transfer and physical dissolution source is solved by the finite control volume scheme subjected to the segregated iterate under propriety boundary conditions. The results showed the concentration distribution of carbon expressed in terms of mass flux for analyzing the erosion of carbon brick in the blast furnace hearth with the different conditions including the status of dead-man, production of liquid iron, carbon concentration at the inlet, and porosity distribution in coke zone during tapping process at steady state. The result is useful to mitigate the erosion caused by mass transfer, and prolong the life span of the blast furnace. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction The computational model of the erosion rate at the wall experimental relationships, depending on the velocity at the surface of carbon stick, was improved by Olsson et al. [1]. Further, the process of carbon dissolution is investigated in advance [2]. The results of their researches relate to the carbon source formed by iron flow, including the carbon brick and the coke in deadman. In addition, Preuer et al. [3,4] numerically analyzed the influence of fluid flow during tapping-period, coke free and coke regions to modify the prediction of the erosion rate through the different degree of carbon dissolution in the different sections of the hearth experimentally. This model was developed more completely in 2003 [5]. There were more and more properties considered like as nature convection caused by temperature and concentration, viscosity and diffusivity of carbon in liquid iron flow in a two-dimensional model, and it made the simulative result more close to the reality. Consequently, we established a symmetrical three-dimensional domain of the hearth in the computational fluid mechanics (CFD) model based on the BF.2 of Chinese Steel Co (CSC) and cooperated with the on-line data. As to the research of the analyzing CSC BF.2, we extend the results of the previous study [6], and combined the real hearth model and CFD model to analyze liquid iron flow along the wall and carbon concentration depending on the furnace
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (W.T. Cheng). 0735-1933/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2009.02.006
production, the situation of dead man, the porosity distribution of coke, production of liquid iron and carbon concentration at inlet, for evaluating the erosion rate in the hearth during tapping process at steady state. We expect that it will be useful to mitigate the erosion for the hearth according to these results, when changing the operating factor. 2. Physical system In the present study, the BF 2 of CSC is taken as the physical model, including the solid zone (refractory) and fluid zone (deadman and cokefree zone) [6], displayed in Fig.1 for the numerical simulation of the flow pattern, temperature, and carbon concentration to estimate erosion rate in the hearth of the blast furnace. According to the documents [7,8], the shape of designed deadman is described as a paraboloid. Due to the ratio of the depth (the distance from the taphole to the hearth bottom) and the diameter of hearth larger than 0.2 [9], the situations of the designed deadman are all floating. The other physical properties of the refractory refer to the previous publication [6]. 3. Mathematic formulation 3.1. Conservation equations The effects of nature convection, chemical reaction, and thermal radiation are not considered in this work. In addition, the 3D laminar and impressible hot fluid flow through porous free zone and porous coke as well as energy conservation with conjugated heat transfer between liquid and solid interfaces in a blast furnace during tapping
C.M. Chang et al. / International Communications in Heat and Mass Transfer 36 (2009) 480–490
Nomenclature Asp C Cp Cs DC–Fe Dp g K K0 keff kcoke kiron mc P Su Sc T V → v v0 x y z ε μ ρ
Specific surface area (1/m) Mass fraction of carbon (−) Specific heat (J/kg K) Saturated mass fraction of carbon (−) Diffusivity of carbon into (liquid) iron (m2/s) Diameter of coke (m) Gravity (m/s2) Mass convection coefficient (m/s) Mass convection constant (m/s) Effective thermal conductivity in porous zone (W/m K) Thermal conductivity of coke (W/m K) Thermal conductivity of iron (W/m K) Erosive mass flux from the hearth wall (kg/m2 s) Pressure (N/m2) Source term in momentum in porous zone see Eq. (3) Source term in mass in porous zone see Eq. (8) Temperature (°C) Periphery velocity Superficial velocity (m/s) Reference velocity (m/s) x direction (m) y direction (m) z direction (m) Porosity (−) Viscosity (N/m s2) Density (kg/m3)
481
The conductivity of carbon varies with temperature and porosity in the fluid zone, but the conductivity of iron is constant (=16.5 W/m-k) supposedly. 2
→
j ðρ v C Þ = ρDC−Fe j C + Sc
ð7Þ
In this work, the mass conservation is expressed in Eq. (7).Where, DC-Fe is the diffusivity (=3 × 10− 8 m2/s) in this system. Sc is the mass source term which describe the carbon dissolving behavior in the deadman has shown in Eq. (8), where, K and Asp defined in Eq. (9) are the mass convection coefficient and the specific area. Sc = KρAsp ðCs − C Þ Asp =
ð8Þ
6ð1 − eÞ Dp
ð9Þ
The saturated carbon concentration is expressed in Eq. (10). On the other hand, Sc is zero in the coke-free zone. Cs = 0:01 × ð1:35 + 0:00254 × T Þ
ð10Þ
In addition, the mass convection coefficient is defined as Eq. (11) K = K0 × V
0:7
and V =
→ jvj ½1 v0
ð11Þ
where V is equal to the periphery velocity of the graphite cylinder, K0 (=0.00053) is the mass convection constant, and periphery velocity is related to the velocity and reference velocity [5]. 3.2. Boundary conditions
are applied for examining metal fluid flow and carbon concentration in the hearth. The result in continuity, Navier–Stokes equation, energy and mass conservation at steady state can be written respectively: →
j ðρ v Þ = 0
According to the average production in the BF 2 of CSC on April, May, and July in 2006, the production can be specified as 38, 43 and
ð1Þ 2→
→→
→
j ðρ v v Þ = − jP + μj v + ρ g + Su
ð2Þ
v , μ [5], and → g are the density, pressure, where, ρ (=7200 kg/m3), P, → the superficial velocity, the viscosity and the gravity. In the fluid zone, it was divided into two zones, coke-free zone and deadman. Thus, Su is used to describe the momentum source in porous zone by the Ergun equation [10], 2
Su = − 150μ
ð1− eÞ → 1− e → → v − 1:75ρ j vj v eDp e2 D2p
ð3Þ
In the Eq. (3), ε is the porosity, and Dp (=0.03 m) is the diameter of coke. In this model, there is no porous media in coke-free zone, and Su is certainly zero in coke-free zone. → 2 j ρCp v T = keff j T
ð4Þ
Eq. (4) is the heat conservation in the hearth. In which, keff, T, and Cp are the effective conductivity, temperature, and the heat capacity (850 J/kg K). keff = e × kiron + ð1 − eÞ × kcoke
ð5Þ
The effective conductivity shown as Eq. (5) in porous zone relates to porosity of dead-man in the hearth [11]. 2=3 ð6Þ kcoke = ð0:973 + 0:00634 × T Þ 1 − e
Fig. 1. (a) Geometric dimensions and refractory components of hearth, and (b) the diagram of solid zone and liquid zone in the hearth.
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48 kg/s at the inlet, therefore, the carbon concentration at the inlet is specified as 0, 2.5, and 3.5 wt.% respectively. The upper surface of the refractory is adiabatic, the temperatures of bottom surface and side wall of the blast furnace are both at 20 °C, the conjugated heat transfer is employed at the interface between metal fluid and refractory brick, and the carbon dissolution from the sidewall and bottom of the refractory are not considered, which means the insulation wall is proposed on the refractory in the hearth. 4. Numerical method The control–volume-based technique is used to convert Eqs. (1), (2), (4), (7) into algebraic equations that can be solved numerically. The discretization of these equations and their solutions were solved by means of the segregated solver which was provided by FLUENT package [12]. A standard pressure interpolation scheme was required to compute the face values of pressure from the cell values. SIMPLE algorithm was
applied in pressure–velocity coupling in the segregated solver to adjust the velocity fields by correcting the pressure field. The first order upwind scheme was chosen to discrete the convection term of every governing equation. As displayed in Fig. 2, the analytical domain included deadman, coke-free zone, and refractory, in which computational mesh number was about 257764. The calculation was considered as convergence when all field flux (velocity, temperature, mass, pressure) and then normalized residuals were reduced to less than 10− 6. Approximately 60,000 iterations were needed for complete convergence. The above-mentioned numerical computations were performed with the package Fluent (Version 6.2), which was used in the previous publication [6]. 5. Result and discussion In order to gain the reasonable simulative result, we validate the present CFD. The measured temperatures from the thermocouples of BF.2 of CSC (April, May and July in 2006) are taken to compare the
Fig. 2. Computational grids in (a) top view; (b) cross section, and (c) stereogram.
C.M. Chang et al. / International Communications in Heat and Mass Transfer 36 (2009) 480–490
483
Fig. 3. Validation of the simulative result: (a) Comparison of the online data (bottom-layer 2 located at 900 mm) and the simulative result and (b) velocity vector with floating deadman.
computational results at bottom-layer2 (900 mm) in the refractory brick for the case of the dead man floating 30 cm from the hearth bottom in the hearth, as demonstrated in Fig. 3a. The result is compared favorably with the operating data of CSC BF.2. Additionally, the flow pattern is shown in Fig. 3b. It can be observed that the iron flow has the same tendency as the result of Huang et al. [6] when the deadman is floating (30 cm). After the calculation, the distribution of concentration and velocity can be obtained. In this model, the diffusivity is 3 × 10− 8 m2/s, and the average mass convection coefficient is about 10− 6 m/s [2]. It means that the mass boundary layer is too thin to be considered. Relatively, the influence of convection is more serious than the influence of diffusion. For reducing grids and calculating time, we assume that all nodes are out of mass boundary layer. The carbon concentration is saturated at the surface of brick and there is a hypothetical mass flux caused by the erosion at the nearest node from the hearth wall. The node value including velocity, carbon concentration, and temperature is used to estimate the erosion rate by Eq. (12). mc = KρðCs − C Þ
ð12Þ
There are three kinds of height to be taken as examples, such as, 10 cm, 30 cm and 50 cm. The influences of floating deadman on velocity, difference between carbon concentration and saturated carbon concentration, and erosion rate are shown in Figs. 4, 5, and 6 respectively. Due to deadman floating lower leading to less free space, it will form a faster flow in the hearth. On the other hand, deadman floating lower will release more carbon source and enhance carbon concentration simultaneously. In addition, the erosion rate of hearth wall can be estimated by corresponding velocity and difference between carbon concentration and saturated carbon concentration. It is found that the heaviest erosion is formed at the bottom center, when the deadman is floating 30 cm and 50 cm, but the most serious parts of erosion cause at the side from the center, when the deadman is floating 10 cm from the hearth bottom. This is because that the liquid iron is pinched and flowed toward the hearth sides. In sum, the different height of deadman will make the heaviest erosion form in different area at the hearth bottom. To analyze the effect of inlet boundary, it is divided into two parts: (1) production of liquid iron, and (2) carbon concentration at the inlet.
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Fig. 4. Velocity of the different height of deadman floating near the hearth bottom: (a) floating 10 cm, (b) floating 30 cm, and (c) floating 50 cm.
Figs. 7 and 8 show the velocity, carbon concentration, and erosion rate on the line near the hearth bottom at the symmetrical face. The fact of having more production causes the effect of flowing faster of iron.
Owing to high velocity, the remaining time of liquid in the deadman decrease and form the lower carbon concentration, inducing heavier erosion at the hearth bottom.
C.M. Chang et al. / International Communications in Heat and Mass Transfer 36 (2009) 480–490
485
Fig. 5. Difference between carbon concentration and saturated carbon concentration at the hearth bottom: (a) floating 10 cm, (b) floating 30 cm, and (c) floating 50 cm. (The carbon concentration is 2.5% at inlet, and the production is 43 kg/s.)
For analyzing the influence of the porosity distributions in the deadman, we designed three kinds of given deadman floating 30 cm from the hearth bottom, namely: Case.1: there is a cylindrical zone with
0.1 in porosity and 2.5 m in radius (other zones are 0.35 in porosity) at the center of deadman; Case.2: the porosity is all 0.35 in dead man; and Case.3: there is a cylindrical zone with 0.35 in porosity and 2.5 m in
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C.M. Chang et al. / International Communications in Heat and Mass Transfer 36 (2009) 480–490
Fig. 6. Erosion rate of the different height of deadman floating: (a) floating 10 cm, (b) floating 30 cm, and (c) floating 50 cm. (The carbon concentration is 2.5% at inlet, and the production is 43 kg/s.)
C.M. Chang et al. / International Communications in Heat and Mass Transfer 36 (2009) 480–490
487
Fig. 7. The effect of production of liquid iron on (a) velocity, (b) carbon concentration, and (c) erosion rate on the line at the symmetrical face. (The carbon concentration was 2.5% at inlet, and the height of deadman floating was 30 cm.)
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Fig. 8. The effect of different carbon concentration at inlet on (a) velocity, (b) carbon concentration, and (c) erosion rate on the line at the symmetrical face. (The production is 43 kg/ s, and the height of deadman floating is 30 cm.)
C.M. Chang et al. / International Communications in Heat and Mass Transfer 36 (2009) 480–490
489
Fig. 9. Erosion rate of the different porosity distribution in deadman: (a) Case.1, (b) Case.2, and (c) Case.3. (The production; the carbon concentration at inlet, and the height of deadman floating are 43 kg/s, 2.5%, and 30 cm respectively.)
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C.M. Chang et al. / International Communications in Heat and Mass Transfer 36 (2009) 480–490
radius (other zones are 0.7 in porosity) at the center of dead man. In Fig. 9, it is shown that the case.1 results in heavier erosion than the Case.2. This is because that when the proportion of the surrounding flowing increased in deadman and decrease the remaining time in the deadman due to the dense zone at center causing the lower carbon concentration near the bottom. Furthermore, in Case.3, the result expresses that the lack of coke will cause the larger porosity and serious erosion. This suggests that the uniform porosity in deadman is not only decreasing the erosion rate but also lessening the erosive area. 6. Conclusion According to our simulative results, the following conclusions can be made as listed below: (1) The higher deadman causes the quicker flow but lower the carbon concentration, meaning that there is a most suitable height of deadman which make the minimization of the erosion rate. (2) Increasing the production let the fluid flow quickly and shorten the remaining time of liquid in the deadman. (3) Higher carbon concentration at inlet is helpful to the protection of hearth wall, but it must improve the quality and amount of coke relatively. (4) A uniform porosity distribution in deadman is useful to lower the erosion rate. It is helpful that the above information is useful to protect the hearth during tapping process with different operational conditions of the blast furnace. Acknowledgements The authors would like to gratefully acknowledge the financial support and the plant operational data provided from China Steel Corporation, Taiwan.
References [1] R.G. Olsson, V. Koump, T.F. Perzak, Rate of dissolution of carbon in molten Fe–C alloys, Transactions of the Metallurgical Society of AIME 236 (1966) 426–429. [2] H.W. Gudenau, J.P. Mulanza, D.G.R. Sharma, Carburization of hot metal by industrial and special cokes, Steel Research 61 (1990) 97–104. [3] A. Preuer, J. Winter, H. Hiebler, Computation of the iron flow in the hearth of a blast Furnace, Steel Research 63 (1992) 139–146. [4] A. Preuer, J. Winter, H. Hiebler, Computation of the erosion in the hearth of a blast furnace, Steel Research 63 (1992) 147–151. [5] J.R. Post, T. Peeters, Y. Yang, M.A. Reuter, Hot metal flow in the blast furnace hearth: thermal and carbon dissolution effects on buoyancy flow and refractory wear, Third International Conference on CFD in the Minerals and Process Industries, CSIRO, Melbourne, Australia, 2003, pp. 433–440. [6] C.E. Huang, S.W. Du, W.T. Chang, Numerical investigation on hot metal flow in blast furnace hearth through CFD, ISIJ Internaional 48 (2008) 1182–1187. [7] K. Shibata, Y. Kimura, M. Shimizu, S.-i. Inaba, Dynamics of dead-man coke and hot metal flow in a blast furnace hearth, ISIJ International 30 (1990) 208–215. [8] K.H. Peters, H.W. Gudenau, G. Still, Hot metal flow in a blast furnace hearth — model tests, Steel Research 56 (1985) 547–552. [9] W. Kowalski, State of the Art for Prolonging Blast Furnace Campaigns, La Revue Metallurrgie-CIT, 2000, pp. 493–505. [10] S. Ergun, Fluid flow through packed columns, Chemical Engineering Progress 48 (1952) 89–94. [11] A. Kasai, T. Murayama, Y. Ono, Measurement of effective thermal conductivity of coke, ISIJ International 33 (1993) 697–702. [12] FLUENT 6.2 Flow Solver User Guide, (2005).
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Numerical prediction on the erosion in the hearth of a blast furnace during tapping process☆ C.M. Chang a, W.T. Cheng a,⁎, C.E. Huang a, S.W. Du b a b
Department of Chemical Engineering, National Chung Hsing University, Taichung 402, Taiwan, ROC Department of Steel and Aluminum Research and Development China Steel Corporation, 1 Chung Kang Road, Kaohsiung 81233, Taiwan, ROC
a r t i c l e
i n f o
Available online 25 March 2009 Keywords: Mass transfer Carbon Blast furnace hearth Tapping process Thermal convective flow
a b s t r a c t The erosion caused by mass transfer in hearth is the most important factor for determining blast furnace campaign life. To support a helpful insight information of mass transfer for the hearth of the No. 2 blast furnace at CSC (China Steel Corporation), a numerical model including the mass transfer of carbon in thermal convective flow from a blast furnace hearth has been developed during the steady tapping process (based on a uninterrupted tapping process assumption). The three dimensional Navier–Stokes equation combined with the transport equations of energy and species with conjugate heat transfer and physical dissolution source is solved by the finite control volume scheme subjected to the segregated iterate under propriety boundary conditions. The results showed the concentration distribution of carbon expressed in terms of mass flux for analyzing the erosion of carbon brick in the blast furnace hearth with the different conditions including the status of dead-man, production of liquid iron, carbon concentration at the inlet, and porosity distribution in coke zone during tapping process at steady state. The result is useful to mitigate the erosion caused by mass transfer, and prolong the life span of the blast furnace. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction The computational model of the erosion rate at the wall experimental relationships, depending on the velocity at the surface of carbon stick, was improved by Olsson et al. [1]. Further, the process of carbon dissolution is investigated in advance [2]. The results of their researches relate to the carbon source formed by iron flow, including the carbon brick and the coke in deadman. In addition, Preuer et al. [3,4] numerically analyzed the influence of fluid flow during tapping-period, coke free and coke regions to modify the prediction of the erosion rate through the different degree of carbon dissolution in the different sections of the hearth experimentally. This model was developed more completely in 2003 [5]. There were more and more properties considered like as nature convection caused by temperature and concentration, viscosity and diffusivity of carbon in liquid iron flow in a two-dimensional model, and it made the simulative result more close to the reality. Consequently, we established a symmetrical three-dimensional domain of the hearth in the computational fluid mechanics (CFD) model based on the BF.2 of Chinese Steel Co (CSC) and cooperated with the on-line data. As to the research of the analyzing CSC BF.2, we extend the results of the previous study [6], and combined the real hearth model and CFD model to analyze liquid iron flow along the wall and carbon concentration depending on the furnace
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (W.T. Cheng). 0735-1933/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2009.02.006
production, the situation of dead man, the porosity distribution of coke, production of liquid iron and carbon concentration at inlet, for evaluating the erosion rate in the hearth during tapping process at steady state. We expect that it will be useful to mitigate the erosion for the hearth according to these results, when changing the operating factor. 2. Physical system In the present study, the BF 2 of CSC is taken as the physical model, including the solid zone (refractory) and fluid zone (deadman and cokefree zone) [6], displayed in Fig.1 for the numerical simulation of the flow pattern, temperature, and carbon concentration to estimate erosion rate in the hearth of the blast furnace. According to the documents [7,8], the shape of designed deadman is described as a paraboloid. Due to the ratio of the depth (the distance from the taphole to the hearth bottom) and the diameter of hearth larger than 0.2 [9], the situations of the designed deadman are all floating. The other physical properties of the refractory refer to the previous publication [6]. 3. Mathematic formulation 3.1. Conservation equations The effects of nature convection, chemical reaction, and thermal radiation are not considered in this work. In addition, the 3D laminar and impressible hot fluid flow through porous free zone and porous coke as well as energy conservation with conjugated heat transfer between liquid and solid interfaces in a blast furnace during tapping
C.M. Chang et al. / International Communications in Heat and Mass Transfer 36 (2009) 480–490
Nomenclature Asp C Cp Cs DC–Fe Dp g K K0 keff kcoke kiron mc P Su Sc T V → v v0 x y z ε μ ρ
Specific surface area (1/m) Mass fraction of carbon (−) Specific heat (J/kg K) Saturated mass fraction of carbon (−) Diffusivity of carbon into (liquid) iron (m2/s) Diameter of coke (m) Gravity (m/s2) Mass convection coefficient (m/s) Mass convection constant (m/s) Effective thermal conductivity in porous zone (W/m K) Thermal conductivity of coke (W/m K) Thermal conductivity of iron (W/m K) Erosive mass flux from the hearth wall (kg/m2 s) Pressure (N/m2) Source term in momentum in porous zone see Eq. (3) Source term in mass in porous zone see Eq. (8) Temperature (°C) Periphery velocity Superficial velocity (m/s) Reference velocity (m/s) x direction (m) y direction (m) z direction (m) Porosity (−) Viscosity (N/m s2) Density (kg/m3)
481
The conductivity of carbon varies with temperature and porosity in the fluid zone, but the conductivity of iron is constant (=16.5 W/m-k) supposedly. 2
→
j ðρ v C Þ = ρDC−Fe j C + Sc
ð7Þ
In this work, the mass conservation is expressed in Eq. (7).Where, DC-Fe is the diffusivity (=3 × 10− 8 m2/s) in this system. Sc is the mass source term which describe the carbon dissolving behavior in the deadman has shown in Eq. (8), where, K and Asp defined in Eq. (9) are the mass convection coefficient and the specific area. Sc = KρAsp ðCs − C Þ Asp =
ð8Þ
6ð1 − eÞ Dp
ð9Þ
The saturated carbon concentration is expressed in Eq. (10). On the other hand, Sc is zero in the coke-free zone. Cs = 0:01 × ð1:35 + 0:00254 × T Þ
ð10Þ
In addition, the mass convection coefficient is defined as Eq. (11) K = K0 × V
0:7
and V =
→ jvj ½1 v0
ð11Þ
where V is equal to the periphery velocity of the graphite cylinder, K0 (=0.00053) is the mass convection constant, and periphery velocity is related to the velocity and reference velocity [5]. 3.2. Boundary conditions
are applied for examining metal fluid flow and carbon concentration in the hearth. The result in continuity, Navier–Stokes equation, energy and mass conservation at steady state can be written respectively: →
j ðρ v Þ = 0
According to the average production in the BF 2 of CSC on April, May, and July in 2006, the production can be specified as 38, 43 and
ð1Þ 2→
→→
→
j ðρ v v Þ = − jP + μj v + ρ g + Su
ð2Þ
v , μ [5], and → g are the density, pressure, where, ρ (=7200 kg/m3), P, → the superficial velocity, the viscosity and the gravity. In the fluid zone, it was divided into two zones, coke-free zone and deadman. Thus, Su is used to describe the momentum source in porous zone by the Ergun equation [10], 2
Su = − 150μ
ð1− eÞ → 1− e → → v − 1:75ρ j vj v eDp e2 D2p
ð3Þ
In the Eq. (3), ε is the porosity, and Dp (=0.03 m) is the diameter of coke. In this model, there is no porous media in coke-free zone, and Su is certainly zero in coke-free zone. → 2 j ρCp v T = keff j T
ð4Þ
Eq. (4) is the heat conservation in the hearth. In which, keff, T, and Cp are the effective conductivity, temperature, and the heat capacity (850 J/kg K). keff = e × kiron + ð1 − eÞ × kcoke
ð5Þ
The effective conductivity shown as Eq. (5) in porous zone relates to porosity of dead-man in the hearth [11]. 2=3 ð6Þ kcoke = ð0:973 + 0:00634 × T Þ 1 − e
Fig. 1. (a) Geometric dimensions and refractory components of hearth, and (b) the diagram of solid zone and liquid zone in the hearth.
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48 kg/s at the inlet, therefore, the carbon concentration at the inlet is specified as 0, 2.5, and 3.5 wt.% respectively. The upper surface of the refractory is adiabatic, the temperatures of bottom surface and side wall of the blast furnace are both at 20 °C, the conjugated heat transfer is employed at the interface between metal fluid and refractory brick, and the carbon dissolution from the sidewall and bottom of the refractory are not considered, which means the insulation wall is proposed on the refractory in the hearth. 4. Numerical method The control–volume-based technique is used to convert Eqs. (1), (2), (4), (7) into algebraic equations that can be solved numerically. The discretization of these equations and their solutions were solved by means of the segregated solver which was provided by FLUENT package [12]. A standard pressure interpolation scheme was required to compute the face values of pressure from the cell values. SIMPLE algorithm was
applied in pressure–velocity coupling in the segregated solver to adjust the velocity fields by correcting the pressure field. The first order upwind scheme was chosen to discrete the convection term of every governing equation. As displayed in Fig. 2, the analytical domain included deadman, coke-free zone, and refractory, in which computational mesh number was about 257764. The calculation was considered as convergence when all field flux (velocity, temperature, mass, pressure) and then normalized residuals were reduced to less than 10− 6. Approximately 60,000 iterations were needed for complete convergence. The above-mentioned numerical computations were performed with the package Fluent (Version 6.2), which was used in the previous publication [6]. 5. Result and discussion In order to gain the reasonable simulative result, we validate the present CFD. The measured temperatures from the thermocouples of BF.2 of CSC (April, May and July in 2006) are taken to compare the
Fig. 2. Computational grids in (a) top view; (b) cross section, and (c) stereogram.
C.M. Chang et al. / International Communications in Heat and Mass Transfer 36 (2009) 480–490
483
Fig. 3. Validation of the simulative result: (a) Comparison of the online data (bottom-layer 2 located at 900 mm) and the simulative result and (b) velocity vector with floating deadman.
computational results at bottom-layer2 (900 mm) in the refractory brick for the case of the dead man floating 30 cm from the hearth bottom in the hearth, as demonstrated in Fig. 3a. The result is compared favorably with the operating data of CSC BF.2. Additionally, the flow pattern is shown in Fig. 3b. It can be observed that the iron flow has the same tendency as the result of Huang et al. [6] when the deadman is floating (30 cm). After the calculation, the distribution of concentration and velocity can be obtained. In this model, the diffusivity is 3 × 10− 8 m2/s, and the average mass convection coefficient is about 10− 6 m/s [2]. It means that the mass boundary layer is too thin to be considered. Relatively, the influence of convection is more serious than the influence of diffusion. For reducing grids and calculating time, we assume that all nodes are out of mass boundary layer. The carbon concentration is saturated at the surface of brick and there is a hypothetical mass flux caused by the erosion at the nearest node from the hearth wall. The node value including velocity, carbon concentration, and temperature is used to estimate the erosion rate by Eq. (12). mc = KρðCs − C Þ
ð12Þ
There are three kinds of height to be taken as examples, such as, 10 cm, 30 cm and 50 cm. The influences of floating deadman on velocity, difference between carbon concentration and saturated carbon concentration, and erosion rate are shown in Figs. 4, 5, and 6 respectively. Due to deadman floating lower leading to less free space, it will form a faster flow in the hearth. On the other hand, deadman floating lower will release more carbon source and enhance carbon concentration simultaneously. In addition, the erosion rate of hearth wall can be estimated by corresponding velocity and difference between carbon concentration and saturated carbon concentration. It is found that the heaviest erosion is formed at the bottom center, when the deadman is floating 30 cm and 50 cm, but the most serious parts of erosion cause at the side from the center, when the deadman is floating 10 cm from the hearth bottom. This is because that the liquid iron is pinched and flowed toward the hearth sides. In sum, the different height of deadman will make the heaviest erosion form in different area at the hearth bottom. To analyze the effect of inlet boundary, it is divided into two parts: (1) production of liquid iron, and (2) carbon concentration at the inlet.
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Fig. 4. Velocity of the different height of deadman floating near the hearth bottom: (a) floating 10 cm, (b) floating 30 cm, and (c) floating 50 cm.
Figs. 7 and 8 show the velocity, carbon concentration, and erosion rate on the line near the hearth bottom at the symmetrical face. The fact of having more production causes the effect of flowing faster of iron.
Owing to high velocity, the remaining time of liquid in the deadman decrease and form the lower carbon concentration, inducing heavier erosion at the hearth bottom.
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Fig. 5. Difference between carbon concentration and saturated carbon concentration at the hearth bottom: (a) floating 10 cm, (b) floating 30 cm, and (c) floating 50 cm. (The carbon concentration is 2.5% at inlet, and the production is 43 kg/s.)
For analyzing the influence of the porosity distributions in the deadman, we designed three kinds of given deadman floating 30 cm from the hearth bottom, namely: Case.1: there is a cylindrical zone with
0.1 in porosity and 2.5 m in radius (other zones are 0.35 in porosity) at the center of deadman; Case.2: the porosity is all 0.35 in dead man; and Case.3: there is a cylindrical zone with 0.35 in porosity and 2.5 m in
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Fig. 6. Erosion rate of the different height of deadman floating: (a) floating 10 cm, (b) floating 30 cm, and (c) floating 50 cm. (The carbon concentration is 2.5% at inlet, and the production is 43 kg/s.)
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Fig. 7. The effect of production of liquid iron on (a) velocity, (b) carbon concentration, and (c) erosion rate on the line at the symmetrical face. (The carbon concentration was 2.5% at inlet, and the height of deadman floating was 30 cm.)
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Fig. 8. The effect of different carbon concentration at inlet on (a) velocity, (b) carbon concentration, and (c) erosion rate on the line at the symmetrical face. (The production is 43 kg/ s, and the height of deadman floating is 30 cm.)
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Fig. 9. Erosion rate of the different porosity distribution in deadman: (a) Case.1, (b) Case.2, and (c) Case.3. (The production; the carbon concentration at inlet, and the height of deadman floating are 43 kg/s, 2.5%, and 30 cm respectively.)
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radius (other zones are 0.7 in porosity) at the center of dead man. In Fig. 9, it is shown that the case.1 results in heavier erosion than the Case.2. This is because that when the proportion of the surrounding flowing increased in deadman and decrease the remaining time in the deadman due to the dense zone at center causing the lower carbon concentration near the bottom. Furthermore, in Case.3, the result expresses that the lack of coke will cause the larger porosity and serious erosion. This suggests that the uniform porosity in deadman is not only decreasing the erosion rate but also lessening the erosive area. 6. Conclusion According to our simulative results, the following conclusions can be made as listed below: (1) The higher deadman causes the quicker flow but lower the carbon concentration, meaning that there is a most suitable height of deadman which make the minimization of the erosion rate. (2) Increasing the production let the fluid flow quickly and shorten the remaining time of liquid in the deadman. (3) Higher carbon concentration at inlet is helpful to the protection of hearth wall, but it must improve the quality and amount of coke relatively. (4) A uniform porosity distribution in deadman is useful to lower the erosion rate. It is helpful that the above information is useful to protect the hearth during tapping process with different operational conditions of the blast furnace. Acknowledgements The authors would like to gratefully acknowledge the financial support and the plant operational data provided from China Steel Corporation, Taiwan.
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