Mathematical Investigation of Fluid Flow, Mass Transfer, and Slag-steel Interfacial Behavior in Gas-stirred Ladles

Mathematical Investigation of Fluid Flow, Mass Transfer, and Slag-steel Interfacial Behavior in Gasstirred Ladles QING CAO and LAURENTIU NASTAC In this study, the Euler-Euler and Euler-Lagrange modeling approaches were applied to simulate the multiphase flow in the water model and gas-stirred ladle systems. Detailed comparisons of the computational and experimental results were performed to establish which approach is more accurate for predicting the gas-liquid multiphase flow phenomena. It was demonstrated that the Euler-Lagrange approach is more accurate than the Euler-Euler approach. The Euler-Lagrange approach was applied to study the effects of the free surface setup, injected bubble size, gas flow rate, and slag layer thickness on the slag-steel interaction and mass transfer behavior. Detailed discussions on the flat/non-flat free surface assumption were provided. Significant inaccuracies in the prediction of the surface fluid flow characteristics were found when the flat free surface was assumed. The variations in the main controlling parameters (bubble size, gas flow rate, and slag layer thickness) and their potential impact on the multiphase fluid flow and mass transfer characteristics (turbulent intensity, mass transfer rate, slag-steel interfacial area, flow patterns, etc.,) in gas-stirred ladles were quantitatively determined to ensure the proper increase in the ladle refining efficiency. It was revealed that by injecting finer bubbles as well as by properly increasing the gas flow rate and the slag layer thickness, the ladle refining efficiency can be enhanced significantly. https://doi.org/10.1007/s11663-018-1206-y Ó The Minerals, Metals & Materials Society and ASM International 2018 I. INTRODUCTION DURING ladle refining, argon stirring is commonly used to transport species to and away from the slag-steel interface, to homogenize the temperature and the composition of the molten alloy and to promote the slag-steel interaction, thus creating a large slag-steel interface to promote chemical reactions. Both the slag-steel interfacial area (A) and the mass transfer coefficient within the steel (km) are the main limiting factors for the desulfurization reaction kinetics in argon-stirred ladles.[1,2] The desulfurization rate is proportional to the product of A and km, known as the volumetric mass transfer coefficient (Akm).[3] The accurate prediction of the fluid flow and the slag-steel interaction characteristics in the ladle metallurgical furnace (LMF) is the foundation to study the desulfurization kinetics. Since the temperature of the melt in LMF is typically above 1800 K, it is almost impossible to measure the QING CAO and LAURENTIU NASTAC are with the Department of Metallurgical and Materials Engineering, The University of Alabama, Box 870202, Tuscaloosa, AL, 35487. Contact e-mail: Manuscript submitted September 24, 2017. Article published online February 26, 2018. 1388—VOLUME 49B, JUNE 2018 actual interfacial area and the turbulent flow in gas-stirred ladles during plant operations. Over the past decades, the fluid flow phenomena in the gas-stirred ladle system were extensively investigated by using water model experiments and numerical simulations.[4–6] Computational fluid dynamics (CFD) modeling is considered as the most effective way to predict the turbulent flow and the slag-steel interface in gas-stirred ladles. The multiphase models[7–9] are widely used to predict the gas-liquid multiphase flow in a gas-stirred ladle, and they can be separated into the Euler-Lagrange approach and the Euler-Euler approach depending on how the gas phase is treated.[5,10] The Lagrangian discrete phase model (DPM) in ANSYS Fluent is based on the Euler-Lagrange approach. In the Euler-Lagrange approach, the fluid phase is treated as a continuum by solving the Navier-Stokes equations. The mass and momentum conservation equations are solved only for liquid phase in an Eulerian frame of reference. The discrete phase is treated as individual particles or bubbles, and their trajectories are described by integrating the force balance on the particle under a Lagrangian frame of reference.[11,12] The interphase forces are taken into account through the momentum source term.[5,13,14] The Euler-Lagrange approach is also economical on computational resources.[15,16] The volume of fluid (VOF) METALLURGICAL AND MATERIALS TRANSACTIONS B model is based on the Euler-Euler approach. In this approach, different phases are treated mathematically as non-interpenetrating continua and the equations of conservation of mass and momentum are solved separately for each phase. The interfaces between phases are tracked exactly.[17] VOF model has been widely used to study the fluid flow in gas-stirred ladle systems.[18–20] Petri Sulasalmia et al.[21] developed a multiphase VOF model to simulate slag entrainment and to track the interface between the slag and the steel based on water model experiments. Later, Liu et al.[22] and Li et al.[23] used the multiphase VOF method to simulate the transient three-dimensional and three-phase flow in LMF as well as the behavior of the slag layer. The fluctuant slag surface was simulated as well. Their simulation results showed that the injection flow rate of the argon gas has an effect on the spout height.[8,24] It was found in the experiments that the gas injected into the liquid is dispersed as discrete bubbles.[5] Thus, many researches proposed to employ the Lagrangian DPM in describing the bubble plumes in gas-stirred ladles. Cloete et al.[17] developed a mathematical model by using the Lagrangian DPM to simulate the injected argon bubbles and the Eulerian multiphase VOF model for tracking the interface of the slag/steel phases. One major limitation of their work is that the unsteady fluctuation of the slag layer was not taken into account because of the assumption of the flat liquid surface. Then, Li et al.[25] developed a DPM-VOF coupled model to consider the dynamic free surfaces among liquid steel/slag/air phases. One of the most crucial challenges of modeling multiphase fluid flow in LMF is the interaction between the injected gas and the continuous liquid, as well as the slag layer fluctuation. Although both Euler-Euler and Euler-Lagrange approaches have been applied in simulating gas-stirred ladle system, which model has better accuracy is still unclear. The effects of the gas stirring rate, injected bubble size, and other operating parameters on the turbulent flow and mass transfer in LMF is not thoroughly clarified. A significant amount of research has to be performed to further understand the complex phenomena that occur in gas-stirred ladles. In this study, the Euler-Euler and Euler-Lagrange approaches have been applied to simulate the multiphase flow in water model and gas-stirred ladle systems. The prediction accuracy of these two approaches has been investigated and compared. The effects of the gas stirring rate, injected bubble size, and slag layer thickness on the slag-steel interaction, s (...truncated)