Study of Solid Accretion Formation inside Pyrometallurgical Vessels by a Wax Model and Similarity Conversion for Gas Bottom-Blown Process

Transcription

1 Materials Transactions, Vol. 48, No. 9 (07) pp to 200 #07 The Japan Institute of Metals Study of Solid Accretion Formation inside Pyrometallurgical Vessels by a Wax Model and Similarity Conversion for Gas Bottom-Blown Process Yu-Pin Huang 1, Chiung-Chieh Kuo 1, Weng-Sing Hwang 1; *, Jia-Shyan Shiau 2 and Shih-Hsien Liu 2 1 Department of Material Science and Engineering, National Cheng Kung University, Tainan City, Taiwan, R. O. China 2 Steel and Aluminum Research and Development Department, China Steel Corporation, Kaohsiung City, Taiwan, R. O. China In this study, a wax model with an extra low temperature ( 1 C) gas blown-in system was established to simulate the phenomena inside ironmaking and steelmaking vessels and investigate the effects of gas bottom-blown conditions on the shape and dimensions of solid accretion sitting on the refractory lining near gas tuyeres. The experiments were conducted with the gas flow rate set in the range of 30. The results show that increasing gas flow rate or decreasing wax temperature increases the sizes of the wax Not only accretion size but also formation time and growth rate increase with gas flow rate and decreases with wax temperature. The results also show that final height of accretion is directly proportional to its growth rate and square of the formation time. In addition, Accretion Similarity Conversion Method (ASCM) was developed for correlating conditions of the accretion formation in the similar systems. A cone-shaped accretion was assumed to increase the accuracy of ASCM. The results indicate that the accretions sizes inside the wax model under a specific condition can be reasonably estimated by modified ASCM with the observed results of the water model from a previous study. [doi:.23/matertrans.mra077] (Received May 7, 07; Accepted July 3, 07; Published August 22, 07) Keywords: solid accretion, wax model, dimensionless number, similarity conversion, ironmaking, steelmaking, gas bottom-blown process 1. Introduction In pyrometallurgical process, gas bottom-blown technique has been widely applied to agitate the liquid bath inside the vessel to enhance metallurgical efficiency via high mixing intensity. In general, the erosion of refractory lining near gas bottom-blown tuyere is severer than other area inside the vessel due to back attack of blown gas bubbles. One of the countermeasures to alleviate the erosion is to generate an iron accretion sitting on the refractory lining via appropriate bottom-blown conditions. The covering of the accretion can protect the refractory lining from being eroded by the back attack of gas bubbles. Therefore, how to generate accretion with proper size and shape is one important issue for high performance gas bottom- blown process. In fact, the physical system of solid accretion formation via blowing gas through bottom tuyeres into the vessel is complicated. What happens in the system includes heat transfer among three phases, (gas, solid and liquid,) as well as phase change between liquid and solid. Therefore, it is very difficult to estimate the size and shape of accretion with reasonable accuracy by simple mathematical equations. Due to high temperature operation, it is extremely difficult to visualize what is happening inside the pyrometallurgical vessels. Therefore, water model was usually adopted to investigate the effects of gas bottom-blown condition on the shape and dimensions of solid Kyllo 1) had studied the effects of heat transfer on the change of morphology for three types of solid He also employed a simplified physical model to investigate the heat transfer phenomena in water model with bottom-blown gas. Huang 2) employed a water model using transparent acrylic *Corresponding author, wshwang@mail.ncku.edu.tw and a low temperature gas piping system to construct experiments of solid accretion formation. At constant bottom-blown gas flow rate, the pattern of the blown gas pressure with respect to time was found to be a characteristic of the type of solid The most important question whether experimental data of the simplified physical model can be accurately applied to the actual vessel is how to correlate the system parameters among the two units. A number of works has been carried out to apply the similarity conversions by employing dimensionless groups. Gary 3) presented a more theoretical and mathematical study to simulate the cold and hot model of bottom-blown BOF by using dimensionless groups. Matway 4) used the dimensionless physical quantities including the forces of inertia, gravity and surface tension between gas and liquid phases in the converter to relate the cold model with the hot model. Fukutaka ) used dimensionless numbers to simulate the flow field of the blast furnace dropping zone. In a previous research, the authors 6) considered phase transformation and heat transfer between liquid and solid phases at the same time and an Accretion Similarity Conversion Method (ASCM) was proposed. The purpose of this study is to establish a wax model with low temperature gas bottom-blown system to investigate the formation of wax Using the low temperature wax model, the formation of wax accretion can be directly observed and subsequently the mechanism for solid accretion formation can be understood. In addition, a Modified Accretion Similarity Conversion Method (ASCM), which deals with the cone-shaped accretion instead of the cylindrical accretion in the original Accretion Similarity Conversion Method, was developed to correlate the conditions of accretion formation in the similar systems. The experimental results from the wax model were also used to verify the

2 Study of Solid Accretion Formation inside Pyrometallurgical Vessels by a Wax Model and Similarity Conversion 249 accuracy of the modified Accretion Similarity Conversion Method. 2. Theory 2.1 System description When low temperature gas is injected into the molten metal bath through the bottom tuyeres of a pyrometallurgical vessel, it contacts with and 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/steel resulting from sufficiently high heat transfer from liquid metal to blown-in gas near the tips of the tuyeres. In fact, there are many factors to determine whether the accretion can be exist in the system or not. Furthermore, the factors also affect the shape and size of the solid In ironmaking and steelmaking processes, many different types of gas bottom-blown tuyere have been adopted to agitate the liquid bath in the vessels. In this study the single tube 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) Heat transfers from the liquid bath to the solid accretion at the liquid-solid interface; outer surface of the cone, by forced convection mechanism. (2) Heat transfers across the solid accretion, from outer surface to the inner surface, by heat conduction mechanism. (3) Heat transfers from the solid accretion to the gas flowing through the hollow channel at the solid-gas interface by forced convection mechanism. 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 similarity of the accretion formation, Buckingham Pi theorem is 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 are 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 for the phase change of a liquid matter. Here, Stefan number describes the thermal state of the liquid matter to the point of being solidified. Ste ¼ H ð1þ C p T where H is latent heat, C p 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 Pe ¼ C pvl ð2þ k m where C p is specific heat of bottom-blown gas, is density of gas, V is gas velocity, L is characteristic length and k m is thermal conductivity of solid 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 Nu ¼ hl ð3þ k m where L is characteristic length, k m is thermal conductivity of accretion and h is convection heat transfer coefficient. Reynolds Number in eq. (4) represents the ratio of 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 gas density, V is gas velocity, is gas viscosity and L is characteristic length (diameter). Prandtl Number in eq. () 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 C p ðþ k f where is viscosity of fluid, C p is specific heat of liquid. k f is thermal conductivity of fluid. 2.3 Similarity conversion To consider phase transformation and heat transfer between liquid and solid phases at the same time, an Accretion Similarity Conversion Method (ASCM) was proposed by the. authors in a previous research. 6) In developing ASCM, some assumptions are made to simplify the real system as follows: (1) The accretion is in cone shape with a hollow and cylindrical channel for gas flow. (2) Heat transfer between the accretion and the bottom wall of the vessel is negligible. (3) Conductive heat transfer is uni-directional across the (4) Liquid flows in parallel with the outer surface of the () Temperatures of gas, liquid and solid at the upper tip of the accretion are equal. (6) Temperature gradient of the flowing gas along the channel axis inside the accretion is linear. The procedures in ASCM for correlating the conditions of a water model and a wax model including three main steps are shown in Fig. 1. (1) Thermal Conversion: At first, the Stefan Number is used to deal with the issue of thermal similarity between water model and wax model. As the superheat of water in the water

3 2496 Y.-P. Huang, C.-C. Kuo, W.-S. Hwang, J.-S. Shiau and S.-H. Liu (1) Thermal Conversion Water temperature at ice formation in water model, (Tl)water (2) Gas Flow Rate Conversion Gas velocity in water model, Vwater Identical Stefan Number Identical Modified Peclet Number Wax temperature when wax accretion formation in water model, (Tl)wax Gas velocity in wax model, Vwax (3) Accretion Dimensions Conversion Accretion in water model (radius, height), (rb)water, Lwater Reynolds, Prandtle and Nusselt Number Dimensionless Heat transfer equations Accretion in wax model (radius, height), (rb)wax, Lwax Fig. 1 Major procedures in Accretion Similarity Conversion Method (ASCM). 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 (ðsteþ water ¼ðSteÞ wax ). As the latent heat and specific heat of liquid of water and wax are known, liquid temperature when wax accretion formation in the wax model can be obtained by conversion from superheat of water. (2) Gas Flow Rate Conversion: 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 behaviors from gas to the liquid phase of two units are similar, their Modified Peclet Numbers are the same (ðpeþ water ¼ðPeÞ wax ). As the specific heat of bottom-blown gas, characteristic length and thermal conductivity of solid accretion are known; the gas velocity in wax model can be calculated from gas flow rate of water model. (3) Accretion Dimensions Conversion: The last part is the accretion dimensions conversion which is the most complex part 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 numbers which include Nusselt number, Reynolds number and Prandtl number were used to calculate the heat transfer coefficients inside the accretion of water and hot models. Then, by combining dimensionless numbers with the heat transfer equation that describes the heat transfer across the accretion, the heat transfer coefficients outside the accretion can be obtained. Eventually, the height and radius of accretion can be obtained. 3. Experimental Apparatus A wax model with its cold gas supply system, illustrated in Fig. 2, was established to investigate the conditions of the accretion formed in the vessel. In order to observe the Fig. 2 Variables Range in experiments Schematic illustration of the wax model with its gas supply system. Table 1 Gas Temperature ( C) Experimental conditions. Gas Flow rate Wax Temperature ( C) , 0, 70, 90 67, 77, 87 phenomena of the solid accretion formation, the wax vessel is made of stainless steel with a transparent and circular glass plates. A gas blowing tuyere of mm in inner radius was installed at the center of the vessel bottom. Cold compressed air was used as the bottom blown gas. The air temperature was controlled at 1 1 C by flowing air through the pipe immersed in the liquid nitrogen bath. A wax with melting point of 47.2 C was selected to simulate the molten iron. The bulk temperature of the wax inside the vessel was controlled at constant during the experiment by a heating apparatus. The variables studied in the experiments are flow rate of bottom-blown air, and superheat of wax. 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. 4. Modified ASCM for the Cone-shaped Accretion Since all the accretions formed in the water and wax models are in cone shape, a cone-shaped accretion is considered in the modified ASCM as illustrated in Fig. 3 instead of the cylinder-shaped accretion considered in ASCM. Therefore, the conductive heat transfer condition across the cone accretion from outer surface to inner surface must be modified. Figure 4 shows a cross-section of the solid In the figure, L is the height of the accretion and l is any height between 0 and L. The temperature gradient of the flowing gas along the channel axis inside the accretion is assumed to be linear. The solid temperature at the solid/gas interface can be calculated as follows. T sjg ¼ T e þðt l=s T e Þ r b r out ð6þ r b r in

4 Study of Solid Accretion Formation inside Pyrometallurgical Vessels by a Wax Model and Similarity Conversion 2497 accretion accretion Fig. 3 Cone-shaped Fig. 6 The shape of the wax accretion formed in the case of blown air and 67 C wax temperature. Fig. Fig. 4 Cross-section of An A3 A2 A1 Division of the cone-shaped accretion into cylinders. r b þ r in q min ¼ klðt l=s T e Þ ð9þ r b r in In modified ASCM, heat transfer equations, eq. (9)(12), of a cone-shaped accretion were applied to correlate the variables in the system. 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 wax model. q out ¼ A out h out ðt l T l=s Þ ðþ q in ¼ A in h in ðt sjg T g Þ 2 3 ð11þ h out ¼ T l=s T g k MU r in h in!! T l T g r b r in 2r b k MU þ r in h in r b þ r in ð12þ where T l and T g are of liquid bath and gas temperatures. k m is the conductivity of h in and h out are inner and outer convection heat transfer coefficient. where r in is the inner radius of the accretion which is equal to the radius of tuyere, r out is the outer radius of the accretion which is varied with l, r b is the outer radius of accretion base, T l=s is the liquid/solid interface temperature which is equal to the melting point of liquid, T sjg is the solid temperature at the solid/gas interface, and T e is the solid temperature at the base of solid/gas interface. The conductive heat transfer equation in Cylindrical Coordinate System is shown as follows. dq A Since it is much more complicated to calculate the heat flux across the cone-shaped accretion, the cone is divided into many hollow cylinders as illustrated in Fig.. The heat flux across one of the hollow cylinder accretion can be expressed as follows. ðt l=s T e Þ r out r in r b r in q n ¼ 2r out L k ð8þ r out r in As the heat flux is integrated from l ¼ 0 to l ¼ L (r out ¼ r b to r out ¼ r in ), the total heat flux across the accretion can be obtained. ð7þ. Results and Discussion.1 Dimensions of wax accretions In wax model experiments, it was observed that wax accretions were in the shape of thin-long cone with a hollow channel for gas flowing through. The left part of Fig. 6 is the wax accretion formed in the case of 30 NL/min blown air and 67 C wax temperature. And the right part is the schematic shape of the Different from the previous study in water model, 6) the appearance of wax accretion was thinner and longer so that it looked like a cylinder. However, it was still a cone in shape. The lower thermal conductivity of wax results in higher heat transfer from the bottom-blown gas than the heat transfer across the wax The final dimensions of the accretion which were measured when the experimental condition reached a steady state are shown in Table 2. It is found that increasing gas flow rate or decreasing wax temperature increases the final size of the wax Figure 7 shows linear relationship between wax height and wax temperature under different gas flow rate. Figure 8 shows relationship between wax diameters and wax temperature. Generally, the diameters of wax accretions are proportional to gas flow rate and inversely proportional to the wax temperature.

5 2498 Y.-P. Huang, C.-C. Kuo, W.-S. Hwang, J.-S. Shiau and S.-H. Liu Table 2 Dimensions of wax accretions. Gas flow rate Wax temperature /Superheat ( C) height radius height radius height radius height radius 97/0 no no no no / / / (unit: cm, no: means no accretion formed) 30 Height, H / cm 2 0 Nl/min Formation Time, t / min 0 Nl/min Temperature, T / o C Temperature, T / O C Fig. 7 Relationship between wax height and wax temperature under different gas flow rate. Fig. 9 Relationship between formation time and the wax temperature under different gas flow rate Diameter, D / cm Nl/min Height, H / cm 2 30 NL/min 0 NL/min 70 NL/min 90 NL/min Temperature, T / o C 0 0 Time, t / min Fig. 8 Relationship between wax diameters and wax temperature under different gas flow rate. Fig. Relationship between wax height and growth time under different gas flow rate..2 Growth rate of wax accretion The phenomena of accretion formation were recorded by a video camera. Therefore, the kinetics of accretion growth can be obtained. In this paper, the formation time is the duration from the wax accretion just formed until it reached a steady state. Figure 9 shows the relationship between the formation time and the wax temperature under different gas flow rate. In the figure, the formation time increases with gas flow rate and decreases with wax temperature. Because wax accretion size also increases with gas flow rate and decreases with wax temperature, the formation time increases with final accretion size. In another word, if the final accretion size is bigger, it needs more time to grow. The accretion heights growing with time under different gas flow rate are shown in Fig.. It shows that the height of wax accretion is linear with time, and the average growth rate of height can be calculated. Figure 11 shows the relationship between height growth rate and the wax temperature under different gas flow rate. It shows the growth rate increases with gas flow rate and decreases with wax temperature, so the accretion growth rate is proportional to the final accretion size as well. Therefore, accretion growth rate and the formation time are both proportional to the final accretion size. Figure 12 shows the relation between accretion s final height and its growth rate in height. It also shows that the accretion growth rate is directly proportional to its final size. Figure 13 shows the relation between formation time s square and final height of It also shows the direct proportional relationship between formation time s square

6 Study of Solid Accretion Formation inside Pyrometallurgical Vessels by a Wax Model and Similarity Conversion Table 3 Dimensions of ice accretions. Growth Rate, R / cm - min Nl/min Gas flow rate Superheat ( C) radius height radius height (unit: cm) Temperature, T / o C Fig. 11 Relationship between accretion growth rate and wax temperature under different gas flow rate. Water temperature ( C) Table 4 Thermal conversion of ASCM. Superheat of water ( C) Superheat of molten wax ( C) Wax temperature ( C) Fig. 12 Growth Rate in Height, R / cm - min -1 Final Height of Accretion, H / cm Final Height of Accretion, H / cm Relation between accretion s final height and its growth velocity Formation Time's Square, t 2 / min 2 Fig. 13 Relation between the formation time s square and final height of and final height of It can be reasoned that the accretion which has bigger size not only grows longer but also faster..3 Verification of accretion similarity conversion method Table 3 shows the ice accretion sizes of water model in a previous research. 6) There are three steps, including thermal conversion, conversion of gas flow rate and dimensions conversion, in ASCM. The first two steps of ASCM were Gas flow rate in water model Table conducted before the wax model experiment. Corresponding superheat and gas flow rate in the wax model could then be calculated from the conditions of the water model. The first step was the thermal conversion. 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. Table 4 shows the results of thermal conversion, the wax temperatures could then be calculated from the water temperatures. The second step was the conversion of gas flow rate. If the heat transfer behaviors from gas to liquid phase of the two units are similar, their Modified Peclet Numbers should be the same. The gas velocity in the wax model could then be calculated from the gas flow rate of the water model. Table shows the results of the gas flow rate conversion. The sizes of wax accretion were obtained from the wax model experiments. The dimensions of the accretions measured in the wax model experiments and estimated from the water model results by ASCM are listed in Table 6. From the comparison, the accuracy of the modified ASCM is reasonably acceptable. It is then believed that modified ASCM method would be applicable to estimate the size of the accretion in the steelmaking and ironmaking vessels. 6. Conclusions Gas flow rate conversion of ASCM. Gas velocity in water model (m/s) Gas flow rate in Gas velocity in wax model wax model (m/s) A low temperature wax model was constructed in this study using a low temperature gas piping system. The effects of operating conditions; mainly gas flow rate and superheat of wax temperature, on the conditions of the wax accretion were investigated. The following conclusions are made. (1) Shapes of all wax accretions are thin and long cones. (2) Wax accretion size, formation time and growth rate all

7 200 Y.-P. Huang, C.-C. Kuo, W.-S. Hwang, J.-S. Shiau and S.-H. Liu Table 6 Measured and estimated dimensions of the accretions. Measured in experiments Estimated by modified ASCM Gas flow rate Superheat ( C) height radius height radius height radius height radius (unit: cm) increase with gas flow rate and decrease with wax temperature. (3) Wax accretion grows linearly with time. (4) Final height of accretion is directly proportional to its growth rate as well as formation time s square. () A modified Accretion Similarity Conversion Method (ASCM) has been developed and modified from cylindershaped to cone-shaped accretion to estimate the dimensions of the It has been proven to be reasonably accurate for the conversion of water model experiment and wax experiment. Acknowledgements This work has been supported by the National Science Council in Taiwan (NSC E ), for which the authors are grateful. REFERENCES 1) A. K. Kyllo and G. G. Richards: The Howard Worner International Symposium on Injection in Pyrometallurgy. (The Minerals, Metals and Materials Society, 1996), ) Y. P. Huang, C. M. Fan, Y. L. Chen, W. S. Hwang, I. G. Chen and S. H. Liu: Ironmaking and Steelmaking 30 (03) ) A. K. Gary and K. D. Peaslee: ISS Transaction 2 (1998) ) R. J. Matway, H. Henein and R. J. Fruehan: ISS Transaction 13 (1992) ) T. Fukutake and V. Rajakumar: Transactions ISIJ 22 (1982) ) Y. P. Huang, W. S. Hwang, J. S. Shiau and S. H. Liu: Mater. Trans. 48 (07)