Dev. Chem. Eng. Mineral Process. 14(3/4), pp. 449-458,2006. Mathematical Modeling of the Vacuum Chamber of RH-KTB Process Zong-Ze Huangl*, Yi-Sheng Chen2 and You-Duo He2 I R & D Center, Baoshan Iron & Steel Co., Ltd., Shanghai 201900, P. R. China Inner Mongolia University of Science & Technology, Baotou 014010, P. R. China ' A mathematical model was developed for the simulation of gas flow, combustion and heat convection in the vacuum chamber of RH-KTB process at Baosteel. Under different conditions, the model was used to predict the influence of the top oxygen blowing lance on the gas flow; chemical reactions and temperature distribution were calculated. The optimum position of the lance is suggested for the RH-KTB process. Introduction In recent years, the quality specifications for steel products have significantly increased. Secondary refining processes now impose additional requirements and the resultant increase in process complexity has hampered efforts to produce high-purity steels in large quantities at low cost. The RH process that was originally developed for the removal of hydrogen from steel is also used for decarburization, deoxidation, inclusions removal, and composition control because it is easy to operate and has the capability for large volume production. The functions of forced decarburization and heating by oxygen blowing were added to facilitate the production of ultra low-carbon steel, and also adding the function of desulfurization by flux refining. With these improvements, the RH process has made rapid progress as a multifunctional secondary refining facility [I-31. There are three kinds of RH facilities at Baosteel, including RH-OB (RH with oxygen blowing), RH-KTB (RH with top oxygen blowing) and RH-MFB (RH with multifunction blowing). The capacity of the RH facility is 300 ton. These facilities have a very important role in the production of clean steel. Based on hndamental studies, many technologies were incorporated into the RH process for production of ultra low carbon steel, pipeline steel, tin-plate steel, electrical steel, etc. These include double slag deoxidation technology for ultra low-carbon steel, flux powder injection for desulhrization, inclusions modification technology by calcium treatment . The RH vacuum chamber has previously been considered as a semi-black box, however, its complex internal processes and reactions need to be understood through * Author for correspondence (zzhuang(@baosteel.com). 449 Zong-Ze Huang, Yi-Sheng Chen and You-Duo He physical simulation experiments and mathematical simulations. For example, water-modeling experiments can model processes such as circulatory flow, decarburization, degassing, etc. [ 5 ] . High-temperature experiments are used to investigate reactions such as desulfurization, decarburization, and inclusions modification in the RH process. Certain process simulations such as post-combustion, heat convection, and gas flow are conducted only by computer-based mathematical modeling for reference to actual operations. Especially in the process of RH-KTB and RH-MFB, the determination of the position of the top lance for different functions is very important for the production of high quality steel at lower cost. In this study, a 3D-mathematical model was developed for the simulation of gas flow, combustion and heat convection in the vacuum chamber of an RH-KTB facility at Baosteel. The optimum position of the lance for carrying out the heating and the insulation of the molten steel are proposed. Mathematical Model The combustible gases of the RH vacuum chamber usually escape from the molten steel in a circulatory motion. The amount of outlet gases follows the normal distribution of irregular patterns, with the up-leg as the symmetry center. Diffising gradually during their ascent, the outlet gasses are uniformly distributed at the end. These gases generally consisted of circulating carrying gas (Ar or N2), decarburized product (CO) and degassing products (H2and N2).The temperature of the outlet gases is nearly the same as that of the molten steel. If oxygen is provided by an oxygen lance at the top of the RH chamber, then the high-speed oxygen jet will move in the direction opposite to the escaping rising gases and bring a strong agitation to the liquid steel in the chamber. Meanwhile, the turbulent diffusing combustion reaction of CO and O2takes place in the chamber where the combustion flame heats the molten steel, and its heating efficiency depends on the lance position of KTB, hence the shape and position of the combustion flame can usually be obtained. The mathematical model was established on the basis of the above description . (4 Basic assumptions (1) It is assumed that the gases belong to the continuous medium when the degree of vacuum is below 133 Pa, i.e. there are enough gases in the small chosen volume. The outlet gases from the molten steel in the vacuum chamber follow the pattern (2) of the normal distribution, taking the up-leg as the symmetrical center axis: (3) (4) 450 Where a,,a,are x-axis and y-axis coordinates of the up-leg; b,,b2 are x-axis and y-axis intensity values of the Gaussian distribution; Q is the circulation flow of the gas; A is cross sectional area of RH vacuum chamber. The combustion of CO in the vacuum chamber is assumed to be turbulent diffision combustion. The trace amounts of H2and N2 in the gases are not taken into consideration. Mathematical Modeling of the Vacuum Chamber of RH-KTB Process (ii) Mathematical model The k - c two-equation turbulent model was used to perform the numerical calculations of the fluid field. The model includes the continuity equation, momentum equations in x, y and z directions, turbulent kinetic energy k equation, and turbulent kinetic dissipation E equation. In the vacuum chamber, the post combustion of CO is turbulent diffusion combustion and the quick reaction model is applied to the simple chemical reaction system in the turbulent diffision combustion. It is presented as follows. Mixture fraction is defined: ...(2) Pulse dissipation of mixture fraction is defined: Where 4 is the conservation value in the system; and subscripts A, F and A4 represent oxygen, CO and the product stream respectively; P v) is the PDF of the mixture fraction. After the mixture fraction and the pulse dissipation were defined, then their control equation (similar to that in the turbulent kinetic energy equation) can also be obtained. After incorporating the energy-T equation and the concentration-Mi equation, the mathematical model is available. The universal equation for all these components is: a(pm)+&(Puo+-(Pm)+~(Pwm) a a at (; -_ a(r am) +ax # a x ij, ...(4) r,-a4) +-a ( r am) +s, ij, az * az The parameters defining each equation are given in Table 1. (iii) Boundary conditions ( I ) Velocity$eld At the molten steel plane on the bottom of the vacuum chamber where u = 0, v then w is the same as given by Equation ( 1 ) . At the top and on the walls of the vacuum chamber, then: %=o, i=1,2,3,j=1,2,3, = 0, i# j % 451 Zong-Ze Huang, Yi-Sheng Chen and You-Duo He (2) Temperaturefield On the molten steel surface in the vacuum chamber, then: q = a x (TI - Tg) At the top of the flow and on the walls, then: q, = o (i=l, 2, 3 ) (3) Concentrationfield On the molten steel surface in the vacuum chamber, then: m, = m,, (i=CO, H2, N2, 0 2 , A d At the top of the flow and on the walls, then: m, = o (i=CO,H2, N2,Oz, Ar) Table 1. Parameters of the general equations. 4 r+ s, 1 0 Turbulent kinetic energy equation k - Turbulent kinetic dissipation equation E Equation Continuity equation X Momentum equation 0 Y Momentum equation Z Momentum equation Mixture fraction Equation Pe G, - P& =k - Pc E i(clGk -C*PE) =s f =/ 0 Energy ecluation Concentration equation m, Pc - r c=< Where subscript i represents CO, CO2 and Ojorespectively: Q k is heat released by combustion: r is the rate of chemical reaction. 452 Mathematical Modeling of the Vacuum Chamber of RH-KTB Process (iv) Numerical solution method to the equations The equations in Table 1 were discretized and transformed into difference equation groups by using a control volume method. The numerical solutions to the variables were obtained by using the SIMPLE calculation method. Calculated Results and Discussion (i) Velocityfield When the flow rate of the carrying gas (Ar) is 1.608 Nm’/min and the degree of vacuum is 10532 Pa, then the velocity field of the gas in RH chamber is generally characterized as follows. The horizontal branch velocity of the gases escaping from the vacuum chamber is low compared with that in the vertical direction. The velocity of the gas along the up-leg is very high, and it is uniformly distributed on all the intersections of the RH chamber with increasing altitude. If an oxygen stream is present, it will give rise to a vigorous agitation zone. The gas flow fields on the cross section of the vacuum chamber are shown in Figure 1 . Figure 1. The velociqjeld in RH chamber for diTerent positions of the top lance; (a) no top lance; (6) I m; (c) 2 m; (4 3 m. 453 Zong-Ze Huang, Yi-Sheng Chen and You-Duo He After comparison of the velocity fields shown in Figure 1 (a) to (d), the influence of different positions of the top lance on the flow field at the bottom of the vacuum chamber is obvious. The oxygen stream has a strong impulsive force that causes a compression zone 3-4 m tall in the environment of the rising gases. Comparing Figure I(b) with (c) and (d), for situation (b) when the position ofthe lance is at Im to the molten steel surface, the high-speed jet descends too quickly to diffuse before reaching the surface of the molten steel in the vacuum chamber. This creates many steel drops and excess oxidization of the molten steel, In Figure I(d), the position of the lance of RH-KTB is 3 m from the molten steel surface, the compressive kinetic energy of the oxygen jet has dissipated without reaching the molten steel surface, and the oxygen stream rises because the gases flow in the reverse direction. Although excess oxidization may not take place at this time, it is very difficult to heat the molten steel surface by means of the combustion of CO because the oxidizing zone is away from the surface region of the molten steel under this condition. If the position of the top lance is at 2 m to the molten steel surface, then it is relatively easy to heat the molten steel by combustion of CO, and the molten steel can also avoid becoming excessively oxidized by the oxygen stream. Temperaturefield When O2 is blown in by the top lance of RH-KTB, at first the low temperature center (ii) is formed around the top lance, then the temperature rises gradually toward the peripheral section and reaches the highest value in the combustion and diffusion zone of CO and 02,and then the gas temperature continuously declines approaching the furthest peripheral region. The post combustion region in the vacuum chamber is a high-speed flame in turbulent motion and with diffusion to create an irregular curve-like interface. Figure 2 displays three temperature fields corresponding to the three flow fields having the same position of the top lance. Comparing the results of the three temperature fields shows that there is no obvious change in temperature near the molten steel surface after lowing the position of the lance from 2 m to 1 m. This is because when the lance position is too low there is insufficient time for the oxygen jet to filly contact the up-rising CO and, hence, generate the required combustion. In this case, post combustion takes place mostly in the upper part of the vacuum chamber. Comparing the temperature field of the lance position at 2 m with that at 3 m, then the lower is the position of the lance, the higher is the temperature next to the surface of the liquid steel. Therefore, the preferred position of the top lance is at 2 m for heating the molten steel by means of post combustion. (iii) Concentrationfleld In the vacuum chamber of RH-KTB process, the gases mainly consisted of CO, C 0 2 and O2 whose distributions are characterized as follows. The CO is concentrated mostly on the molten steel surface, especially on the area round the up-leg, and disappearing quickly with an increase in distance away from the surface. The concentration of C 0 2 increases with the increase of height, and there is a comparatively low concentration region near the head of the oxygen lance. The 02 is 454 Mathematical Modeling of the Vacuum Chamber of RH-KTB Process distributed in an asymmetrical curve-like zone with the head as its center, and the oxygen concentration reducing from the center to the peripheral region. The distributions of the gases CO, COz and O2at the three lance positions (at 1 m, 2 m and 3 m) are shown in Figure 3 and Figure 4, corresponding to the velocity fields at the same positions o f the top lance in Figure 1. Analysis of the results presented in Figures 1 to 4 indicates that when the lance position is at 1 m, the oxidized zone extends to the liquid steel surface and causes direct oxidization of the liquid steel by the oxygen stream. Therefore, more deoxidizer was consumed and more deoxidized products were produced. For the lance at 3 m, the oxidized zone is far away from the molten steel surface and there is failure in the heating and insulation of the liquid steel. For the lance at 2 m, the peripheral part of the oxidized zone lies on the liquid steel surface, which can protects the liquid steel from excess oxidization and also means that there is good heating of the molten steel from post combustion. 8.1 - 3.1 2. I 1.1 0.1 2.3 1.6 0.8 0 2.3 1.6 0.8 0 2 . 3 1.6 0.8 0 X Figure 2. Temperature field in the RH vacuum chamber for diflerent positions of the top lance; (a) I m; (b) 2 m; (c) 3 m. 455 Zong-Ze Huang, Yi-Sheng Chen and You-Duo He L. L ~ r I I I' 1.1 0.1 L 2.3 1.6 . -..."l 0.8 0 x Figure 3. Concentrationsfields of CO (a-c) and CO2 (d-fl in RH vacuum chamber: (a) and (d) I m position of top lance; (b) and (e) 2 m position of top lance; (c) and fl 3 m position of top lance. I . 456 Mathematical Modeling of the Vacuum Chamber of RH-KTB Process a -, (b) ~ . .. ................ ic) .. __ 2. 1 1.1 0. 1 2.3 1.6 0.8 0 2.3 1.6 0.8 0 2.3 1.6 0.8 0 X Figure 4. O2 concentration field in RH vacuum chamber: (a) I m position of lance; (b) 2 m position of oxygen lance; (c) 3 m position of oxygen lance. Conclusions 1. An oxygen jet in post combustion can create vigorous agitation of the fluid field at the bottom of the vacuum chamber of the RH-KTB process, and the agitation contributes significantly to the uniform distribution of gases at the cross-sections of the vacuum chamber. 2. The optimum position of the top lance of the RH-KTB to ensure heating and insulation of the molten steel is at an altitude of 2m in the vacuum chamber. References 1. Kuwabara, T., Harada, S., Furusaki, T., et al. 1986. The development of RH-Injection technology. Proceedings of the 6VhSfeelmakingConference, ISSIAIME, 293-297. 2. Kazuro, S., and Julian, S. 1983. 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