Materials Transactions, Vol. 48, No. 2 (2007) pp. 189 to 194 #2007 The Japan Institute of Metals
Development and Verification of Accretion Similarity Conversion Method for Gas Bottom-Blowing Process inside Pyrometallurgical Vessels Yu Pin Huang1 , Weng Sing Hwang1;2; * , Jia Shyan Shiau3 and Shih Hsien Liu3 1
Department of Material Science and Engineering, National Cheng Kung University, Tainan, Taiwan, R. O. China Metal Industries Research and Development Centre, Kaohsiung, Taiwan, R. O. China 3 Steel & Aluminum Research and Development Department, China Steel Corporation, Kaohsiung, Taiwan, R. O. China 2
In this research, a water model with an extra low temperature (177 C) gas blown-in system was established to simulate the phenomena inside pyrometallurgical vessels for investigating effects of gas bottom blowing conditions on the shape and dimensions of solid accretion sitting on the refractory lining near gas tuyeres. In addition, Buckingham Pi theorem was adopted to derive the important dimensionless parameters for correlating conditions of accretion formation in the similar systems. Then, by combining dimensionless parameters with heat transfer equations that describe the heat transfer across the accretion, quantitative relations based on the similarity conversion of the similar systems was established. The method mentioned above is called Accretion Similarity Conversion Method (ASCM). Meanwhile, the experimental work of a wax model was conducted to evaluate the accuracy of ASCM. The results indicate that the size of solid accretion inside the wax model under a specific condition can be reasonably estimated by ASCM. [doi:10.2320/matertrans.48.189] (Received July 10, 2006; Accepted November 27, 2006; Published January 25, 2007) Keywords: accretion size, water model, dimensionless parameters, similarity conversion, ironmaking vessel, steelmaking vessel, gas bottomblowing
1.
Introduction
In ironmaking and steelmaking, the gas bottom-blowing technique has been widely applied to agitate the liquid bath to enhance metallurgical efficiency via the high mixing intensity of liquid bath inside the vessel. In general, the erosion of refractory lining near gas bottom-blowing tuyeres is severer than other area inside the vessel due to back attack of blown gas bubbles. One of countermeasures to alleviate the erosion is to generate an iron accretion sitting on the refractory lining via appropriate bottom-blowing conditions. The covering of the accretion can protect the refractory lining from being eroded by the attack of gas bubbles. Therefore, how to generate accretion with proper size and shape is one of important issues for high performances bottom blowing technology. This was the motivation to initiate this study. Due to extremely high temperature, it is impossible to visualize what is happening inside the pyrometallurgical vessels. Therefore, the water model was adopted used to investigate the effects of gas bottom blowing conditions on the shape and dimensions of solid accretion. Kyllo1) had studied the effects of heat transfer on the change of morphology for three types of solid accretion. He also employed a simplified physical model to investigate the heat transfer phenomena in water model with bottom-blown gas. Huang2) employed a water model using transparent acrylic and a low temperature gas piping system to construct experiments of solid accretion formation. At constant bottom-blown gas flow rate, the characteristic pattern of the blown gas pressure varied with time were found to the specific type of solid accretion. The most important point that whether experimental data of the cold model are accurately applied to the hot model is how to connect the systematic parameters among the two *Corresponding
author, E-mail:
[email protected]
units. For dimensionless groups, much work has been carried out to apply to similarity conversions. Gary3) presented a more theoretical and mathematical study to simulate the cold and hot model of bottom-blown BOF by using the dimensionless groups. Matway4) considered that the dimensionless physical quantity including the force of inertia, gravity and surface tension between gas and liquid phases in the converter to relate the cold model with the hot model. Fukutaka5) used the dimensionless parameters to simulate the fluid field of the blast furnace dropping zone. Grace,6) Mclaughlin,7) Weber8) employed the similarity of dimensionless parameters to confer the float of bubbles. However, there have been no reports with the approach considered not only phase transformation but also heat transfer between liquid and solid phase at the same time. In the study, Buckingham Pi theorem, a dimensional analysis technique, was adopted to derive the important dimensionless parameters for correlating conditions of accretion formation in the similar systems. Then, by combining dimensionless parameters with heat transfer equations that describe the heat transfer across the accretion, quantitative relations based on the similarity conversion between different conditions of the similar systems was established. Hereafter, the method mentioned above is called Accretion Similarity Conversion Method (ASCM). 2.
Theory
2.1 System description When low temperature gas is injected into the liquid bath through the bottom tuyeres of a pyrometallurgical vessel, agitates the high temperature liquid during ascending in the bath. The basic mechanism of the accretion formation inside steelmaking and ironmaking vessels includes the phase change from liquid metal to solid iron resulting from sufficiently high heat transfer from liquid metal to blown-in
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gas near the tip of tuyeres. In fact, there are many variables to determine whether the accretion can exist in the system. Furthermore, the variables also affect the shape and size of the solid accretion. In ironmaking and steelmaking, many different types of the bottom blowing tuyere have been adopted to agitate the liquid bath in vessels. In this study the single tube type tuyere was selected because of its popularity. In general, the geometric shape of the solid accretion looks like a hollow cone. The dimensional lengths of the hollow cone are determined by the complicated heat transfer conditions of the system. Basically, the heat transfer of the system includes three different mechanisms explained below: (1) Forced heat transfer from the liquid bath to the solid accretion at the liquid-solid interface, outer surface of the cone. (2) Heat conduct across the solid accretion, from outer surface to the inner surface. (3) Forced heat convection from the solid accretion to the gas flowing through the hollow channel at the solid-gas interface. Ideally, when the system reaches a state of heat equilibrium, the dimensions of the accretion will be kept at constant. 2.2 Dimensionless groups On the thermal and dynamic similitude of the accretion formation, Buckingham Pi theorem was applied to derive a set of dimensionless groups that can be used to correlate the conditions between any two similar systems. Among these groups, Stefan number, Nusselt number, Peclet number, Reynolds number and Prandtl number were selected as important dimensionless numbers of the system for the similarity conversion. The formula and physical meaning of the dimensionless numbers are explained as follows: Stefan number in eq. (1) represents the ratio of the latent heat to the superheat heat for the phase change of a liquid matter. Here, Stefan number describes the heat state of the liquid matter to the point of being solidified. Ste ¼
Hm Cp T
ð1Þ
Where Hm is latent heat, Cp is specific heat of liquid and T is superheat of liquid. Modified Peclet number in eq. (2) describes heat capacity change of the flowing gas via the conductive heat transfer across the solid wall of the channel inside the solid accretion. Cp VL Pe ¼ km
ð2Þ
Where Cp is specific heat of bottom-blown gas, is density of gas, V is gas velocity, L is characteristic length and km is thermal conductivity of solid accretion. Nusselt number in eq. (3) represents the ratio of convective heat transfer to conductive heat transfer at a solid–liquid or solid–gas interface. Here, Nu number indicates the ability difference between convective heat transfer and conductive heat transfer at the outer and inner surface of the solid accretion.
T1 T1/s
q
hout Ts/g hin
rout
Tg rin
L
Fig. 1 Simply accretion.
Nu ¼
hL km
ð3Þ
Where L is characteristic length, km is thermal conductivity of accretion and h is convection heat transfer coefficient. Reynolds number in eq. (4) represents the ratio of the inertial force to viscous force of the fluid. Here, Re number indicates the turbulence intensity of the liquid metal or the bottom blown gas. Re ¼
VL
ð4Þ
Where is the gas density, V is gas velocity, is gas viscosity and L is characteristic length (diameter). Prandtl number in eq. (5) represents the ratio of the of the momentum diffusivity of the fluid to the thermal diffusivity of the solid accretion at the solid–fluid interface. Pr ¼
Cp kf
ð5Þ
Where is viscosity of fluid, Cp is specific heat of liquid. kf is thermal conductivity of fluid. 2.3
Heat transfer equations for a cylinder-shaped accretion In ASCM, heat transfer equations, eq. (6)–(9), of a cylinder-shaped accretion were applied to correlate the variables in the system, illustrated in Fig. 1. In the similarity conversion, these equations are required for the estimation of the height and diameter of the accretion in a pryometallurgical vessel based on experimental results of the water model. qout ¼ Aout hout ðTl Tl=s Þ Tl=s Ts=g qmid ¼ rout ln rin 2km L qin ¼ Ain hin ðTs=g Tg Þ 3 2 Tl=s Tg km rin hin hout ¼ rout 7 Tl Tl=s 6 4 5 rb km þ rin hin ln rin
ð6Þ ð7Þ
ð8Þ ð9Þ
Where Tl , Tl=s , Ts=g and Tg are temperature of liquid bath, temperature at the interface of liquid and solid, temperature at the interface of solid and gas, temperature of gas, respectively. km is the conductivity of accretion. hin and
Development and Verification of Accretion Similarity Conversion Method for Gas Bottom-Blowing Process
Water temperature at ice formation in cold model, (Tl)cold
Identical Stefan Number
Gas velocity in cold model, Vcold
Identical Modified Peclet Number
Accretion in cold model (radius, height), (rb)cold, Lcold
Reynolds, Prandtle and Nusselt Number Dimensionless heat transfer equations
Liquid tempereture when solid accretion formation in hot model, (Tl)hot
Air pump
Gas velocity in hot model, Vhot
Accretion in hot model (radius,height), (rb)hot and Lhot
Fig. 2 Major Procedures in Accretion Similarity Conversion Method (ASCM).
hout are inner and outer convection heat transfer coefficient. rin and rout are inner and outer radius of accretion, and rb is the outer radius of accretion base. 3.
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Similarity Conversion
In developing ASCM, some assumptions were made to simplify the real system. Assumptions are as follows: (1) The accretion is in cone shape with a hollow and cylindrical channel for gas flow. (2) Heat transfer rate at the interface of the accretion and the bottom wall of the vessel is zero. (3) Conductive heat transfer is uni-directional across the accretion. (4) Liquid flows in parallel with the outer surface of the accretion. (5) Temperature of gas, liquid and solid at the upper tip of the accretion is equal. (6) Temperature gradient of the flowing gas along the channel axis inside the accretion is linear. The major procedures in ASCM for correlating the conditions of a cold model and a hot model are shown in Fig. 2. At first, the Stefan Number is used to deal with the issue of thermal similarity between water model and hot model. As the superheat of water in the water model is known, it is necessary to determine the appropriate superheat of liquid phase in the hot model to exhibit similar behaviors in the formation of solid accretion by using Stefan Number as eq. (1). If the heat states of the liquid matter to the point of being solidified between two units are similar, their Stefan Numbers are set to be identical and liquid temperature when solid accretion can be formed in the hot model. After the thermal conversion, the appropriate gas flow rate to be employed in similar units, which can induce similar heat transfer between the flowing gas and the solid wall of the channel inside the accretion, then requires a careful consideration. In this study, a Modified Peclet number shown in eq. (2) was introduced to assure the similarity between the two systems. If the heat transfer behavior from gas to the liquid phase of two units are similar, their Modified Peclet Numbers are the same and gas velocity in hot model can be
Dehydration device
Thermocouple
Flow rate control module
Recorder
Flow meter
Heat exchanger
P Pressure transducer
Fig. 3 Schematic illustration of the water model with its gas supply system.
calculated from gas flow rate of water model. The last part is the accretion dimensions conversion which is the most complex in ASCM. It was considered not only the difference between convective heat transfer and conductive heat transfer at the outer and inner surface of the solid accretion but the turbulence intensity, momentum and thermal diffusivity of liquid metal and the bottom blown gas. Dimensionless parameters which include Nusselt number, Reynolds number and Prandtl number were used to calculate the heat transfer coefficients inner the accretion of water and hot models. The inner heat transfer coefficients describe the heat transfer from the solid accretion to the gas bubble. Then, by combining dimensionless parameters with heat transfer equations shown as eq. (9) that describes the heat transfer across the accretion, the heat transfer coefficients outer the accretion can be obtained. The outer heat transfer coefficients describe the heat transfer from the liquid bath to the solid accretion. When the inner and outer heat transfer coefficients in the hot model were calculated, the height and radius of accretion can be obtained by using dimensionless heat transfer equations (eq. (9)). 4.
Experimental Apparatus and Work
A water model with its cold gas supply system, illustrated in Fig. 3, was established to investigate the conditions of the accretion formation in the vessel. In order to observe the phenomena of the solid accretion formation, the water vessel is made of transparent acrylic plates. A gas blowing tuyere of 3.125 mm inner radius was installed at the center of the vessel bottom. Cold compressed air was used as the bottom blown gas. The temperature of the blown air was controlled at 177 1 C by flowing air through the pipe immersed in liquid nitrogen bath. The bulk temperature of the water inside the vessel was controlled at constant during the experiment by flowing hot water into the vessel. Different from the previous research2) of water model, the bottom material simulated as refractory on the bottom of the vessels was changed from copper to acrylic.
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In the water model, the variables studied in the experiments were flow rate of bottom-blown air, and superheat of water. The range of variables is listed in Table 1. The phenomena of the accretion formation were recorded by a video camera. And, the dimensions of the accretion were measured when the experimental condition reached a steady state. In order to evaluate the accuracy of ASCM, a wax model was established. Wax model and its cold gas supply system were similar to water model system. A wax with melting point 47.2 C was selected to simulate as molten iron. A gas blowing tuyere of 5.0 mm inner radius was installed at the center of the vessel bottom. Cold compressed air was used as the bottom blown gas. The temperature of the blown air was controlled at 50 1 C by flowing air through the pipe immersed in liquid nitrogen bath. The bulk temperature of the wax inside the vessel was controlled at constant during the experiment by a heating apparatus around the vessel.
Table 2 Gas flow rate (NL/min) Superheat ( C)
Results and Discussion
5.1 Results of water model In water model experiments, it was observed that ice accretions were in the shape of cone with a hollow channel for gas flowing through. The left part of Fig. 4 is the ice accretion formed in the case of 60 NL/min blown air and 9 C water temperature. And the right part is the schematic shape of the accretion. Almost all the ice accretions are cone in shape. The dimensions of ice accretions formed in the experiments are shown in Table 2. It is found that increasing the gas flow rate or decreasing the water temperature increases the size of the ice accretion. Figure 5 shows linear relationship between the ice radius and the water temperature under different gas flow rate. Figure 6 shows relationship between the ice height and the water temperature. Generally, the height of ice accretions is proportional to the gas flow rate and inversely proportional to the water temperature.
Variables Range in experiments
Experimental conditions of the water model.
Temperature of gas ( C) 177 1
Gas flow rate (NL/min) 50, 60, 70, 80, 90
Water temperature ( C)
50 R
H
R
70 H
R
80 H
R
90 H
R
H
1.64 5.20 1.68 6.00 1.72 6.80 1.85 7.50 2.00 8.50 1.38 5.40 1.41 9.30 1.56 6.30 1.70 8.40 1.78 8.00
9
1.16 4.40 1.31 5.70 1.46 4.20 1.50 5.70 1.53 9.50
12
0.99 4.00 1.25 4.20 1.36 4.00 1.40 5.20 1.45 5.30
15
0.84 1.80 1.07 2.60 1.12 3.60 1.20 4.00 1.25 4.80
18
0.63 1.50 0.83 2.30 0.87 1.80 1.03 3.60 1.09 2.70
21
0.60 1.50 0.62 1.70 0.66 2.60 0.76 2.00 0.92 3.40
24
X
X
0.56 2.00 0.61 2.50 0.63 2.10 0.80 2.30
27 30
X X
X X
0.41 1.20 0.47 1.40 0.53 1.30 0.55 1.60 X X X X X X 0.51 0.90
2.5
50 NL/min 60 NL/min 70 NL/min 80 NL/min 90 NL/min
2.0
1.5
1.0
0.5
0.0 0
5
10
15
20
25
30
Temperature, T/ °C
Fig. 5
Relationship between the ice radius and the water temperature.
Fig. 4 The shape of the ice accretion.
accretion
accretion
26.2 mm
24, 27, 30
60
5 7
5, 7, 9, 12, 15, 18, 21,
57.0 mm
Table 1
Dimensions of ice accretions.
(R: radius; H: height; Unit: cm)
Radius, r/cm
5.
In water model experiments, it was found that the radius of the gas channel inside the solid accretion is approximately equal to the inner radius of the bottom blowing tuyere. Based on the relationship between the ice radius and the water temperature, the highest water temperature for ice accretion formation under different gas flow rate can be obtained, shown in Fig. 7. In the figure, ice accretion would be generated and stably existing if the condition is fallen in the region below the curve.
Development and Verification of Accretion Similarity Conversion Method for Gas Bottom-Blowing Process Table 4 Dimensions of wax accretions.
12
Gas flow rate (NL/min)
10
50 NL/min 60 NL/min 70 NL/min 80 NL/min 90 NL/min
8
Height, h / cm
193
Superheat ( C)
6
4
2
0 0
5
10
15
20
25
30
Temperature, T/ °C
16 R
19 H
R
22 H
R
25 H
R
28 H
R
H
8
0.63 4.59 0.63 5.53 0.64 6.57 0.66 7.79 0.68 9.12
11 15
0.58 4.14 0.59 4.97 0.61 6.22 0.64 7.44 0.65 8.58 0.54 3.66 0.57 4.74 0.60 5.96 0.60 6.90 0.61 7.86
20
0.51 3.23 0.56 4.57 0.58 5.68 0.58 6.58 0.59 7.56
25
0.47 2.76 0.52 4.04 0.53 4.92 0.55 5.92 0.56 6.85
30
0.42 1.98 0.47 3.22 0.48 3.97 0.51 5.23 0.52 6.17
35
0.41 1.81 0.41 2.25 0.43 2.88 0.45 3.90 0.49 5.31
40
X
X
0.40 1.88 0.41 2.59 0.42 3.10 0.46 4.61
45
X
X
0.35 0.83 0.37 1.55 0.39 2.33 0.40 2.80
50
X
X
X
X
X
X
X
X
0.38 2.41
(R: radius; H: height; Unit: cm) Fig. 6
Relationship between the ice height and the water temperature.
5.2 Similarity conversion results of wax model The experimental conditions of wax model, in Table 3, were estimated from experimental data of water model by ASCM and were appropriate between water and wax model. The dimensions of wax accretion, showed in Table 4, were calculated by ASCM. Just as the trend of water model results shows, the dimensions of wax accretions are proportional to the gas flow rate and inversely proportional to the wax temperature. Nevertheless, almost all the wax radii were much smaller than wax height, and the values of wax radii are fallen into a narrow range from 0.35 cm to 0.68 cm. These results showed that the shapes of wax accretions might be thin and long and the experimental conditions affected the wax radius slightly.
40
Water Temperature, T/ °C
35 30 25 20
stable zone for ice accretion 15 10 5 0 50
60
70
80
90
5.3
-1
Gas Flow Rate, F/ NL-min
Fig. 7 The operational regime for ice accretion formation in the water model.
Experimental conditions of wax model by ASCM.
Variables Range in wax model
Temperature of gas ( C)
Gas flow rate (NL/min)
50 1
16, 19, 22, 25, 28
Superheat of wax ( C) 8, 11, 15, 20, 25, 30, 35, 40, 45, 50
Wax temperature 90°C
60.0 mm
Wax temperature 80°C
11.4 mm Fig. 8
30.0 mm
Table 3
Experimental results of wax model and similarity conversion In order to evaluate the accuracy of ASCM, a wax model was established and two experiments were carried out. Figure 8 shows the appearance of the wax accretion formed in the case of 80 C and 90 C wax temperature, respectively, under 30 NL/min blown gas. Because the lower thermal conductivity of wax results in the heat transfer from the bottom-blown gas easier than the heat transfer across the wax accretion, the wax accretions, thin and long cylinder in shape, were observed. This shape was coincident with the estimation of ASCM.
10.0 mm
The appearance of the wax accretion formed in the cases of 80 C and 90 C wax temperature, when gas flow rate is 30 NL/min.
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Table 5 Measured and estimated dimensions of the accretions in the wax model. Estimated by ASCM (28 Nl/min) Superheat
Radius
Measured in experiments (30 Nl/min)
Height
Superheat
radius
Height
( C)
(cm)
(cm)
( C)
(cm)
(cm)
30.0 40.0
0.52 0.46
6.17 4.61
32.8 42.8
0.57 0.50
6.00 3.00
The dimensions of the accretions measured in the wax model experiments and estimated by ASCM are listed in Table 5. From the viewpoint of process practice, difference between the measured and the estimated dimensions is reasonably acceptable. Therefore, it is believed that ASCM method would be applicable to estimate the size of the accretion in the steelmaking and ironmaking vessel. 6.
Conclusions
Accretion Similarity Conversion Method (ASCM) has been developed to estimate the dimensions of the accretion generated via the bottom gas blown into the pyrometallurgical vessels. And the method was examined by a series of experiments in the water model and the wax model. Based on
the experimental data in the water model, the accuracy of the estimated dimensions of the wax accretion by ASCM is acceptable. Acknowledgements This work has been supported by the National Science Council in Taiwan (NSC92-2216-E-006-041), for which the authors are grateful.
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