A Mathematical Model for Prediction of Carbon Concentration During RH Refining Process
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he Ruhrstahl–Heraeus (RH) degasser is mainly used for the production of the ultralow-carbon (ULC) steel. Due to the limitations of high-temperature, multiphase system, and vacuum conditions, many mathematical modeling studies have been performed to simulate the decarburization process in the RH degasser.[1–8] The predicted results are well validated by the experimental measurements. However, in these investigations, several important problems are still unsolved. First, the free surface in the vacuum chamber is often assumed to be flat, and the top gas phase and slag phase above the liquid are ignored. The decarburization reaction at the free surface is typically considered to occur on the cross section of the vacuum chamber.[1,4,9] Due to the metal splashes and the escape of gas bubbles, the free surface of the molten steel in the vacuum chamber frequently waves.[3] Second, the recirculation rate is generally estimated by some empirical equations.[3,10] These equations have limitations because many important variables such as vacuum pressure, snorkel immersion depth, the number of nozzles, its diameter, etc., have been neglected. In addition, the expansion of gas bubbles in
HAITAO LING is with the School of Metallurgical Engineering, Anhui University of Technology, Ma’anshan 243002, Anhui, China. Contact e-mail: [email protected] LIFENG ZHANG is with the School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083, China. Manuscript submitted March 6, 2018. METALLURGICAL AND MATERIALS TRANSACTIONS B
the molten steel caused by the temperature change and static pressure drop is seldom considered. Li et al.[11] and Chen et al.[12] reported that the bubble volume near the steel surface in the vacuum chamber could expand to be eight to ten times of its initial value at the nozzle exit. The above problems further influence the decarburization process. In the current study, the above-mentioned problems could be solved, and a decarburization model was developed to predict the evolution of the carbon content in the RH degasser. For the gas–liquid multiphase flow, a coupled model reported in a previous work[13] was employed to simulate the fluid flow and the motion of gas bubbles in the RH degasser. The coupled model included the volume of fraction (VOF) method and the discrete particle model (DPM). Thus, the fluctuation of the free surface and motion of gas bubbles can be simultaneously simulated and tracked. According to the ideal gas law, the expansion of gas bubbles in the up-leg snorkel is also considered. Furthermore, the decarburization reaction is expressed by[14] ½C þ ½O ¼ COðgÞ
½1a
DGh ¼ 22364 39:63T;
½1b
where DGh is the standard Gibbs free energy (J/mol), and T is the temperature (K). The decarburization reaction accompanied by the flow of the molten steel occurs continuously. The transport equations of the carbon and oxygen contents in the molten steel are as follows: ! @ ðql ½Pct CÞ þ r ql ul ½Pct C @t ½2a l ¼ r eff r½Pct C þ SC Sc ! @ ðql
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