ISIJ International, Vol. 46 (2006), No. 11, pp. 1731–1733

Fluid mixing assumes an important role in various processing industries, in which the chemical efficiencies of typical processing operations carried out are intrinsically related to their hydrodynamic performance. In order to achieve high product qualities in steelmaking, submerged gas injection in ladles has now become a widely accepted industrial practice in almost every steelmaking shop. The gas injected from the bottom of the ladles rises through the liquid steel and induces a spontaneous mixing, promotes chemical reactions, thereby helping the system to achieve a compositional and thermal homogeneity. In addition, the gas injection also aids inclusion agglomeration and floatout. Primarily because of such significant technological implications, serious attention has been paid over the last few decades to study the fluid flow and mixing phenomena in gas stirred ladle systems. Szekely et al. were the first to model the flows in gasstirred ladles by solution of the turbulent Navier–Stokes equations in conjunction with the k–w turbulent model. Hsiao et al. investigated fluid flow phenomena in the water model and industrial argon-stirred ladles. Their work indicated the importance of buoyancy force of upward rising gas bubbles to generate a recirculatory flow field in the gas-stirred ladle. Zhu et al. carried out water-model experiments and mathematical modeling studies of fluid flow and mixing phenomena in argon-stirred ladles with multi-tuyere arrangements. The experimental work of Nakanishi et al., for the first time, proposed a functional relationship (tm e ) between the mixing time (tm) and specific energy input rates (e), for a wide range of metal processing operations. Since then, many empirical relationships similar to this type have been reported. In all these, influence of different operating variables (e.g., gas flow rates, vessel geometries, nozzle configurations) on mixing were studied and expressed by a suitable correlation. Two most common hydrodynamic models used to characterise the gas-liquid two-phase regions, as commonly employed in these studies, have been the quasi-single phase approach and a combined Lagrangian–Eulerian calculation procedure. Of these, in terms of computational complexities, the quasi-single phase procedure is the simplest and has been widely used for numerical modeling purpose. In this method, the gas-liquid mixture in the upwelling plume is considered to rise like a homogeneous fluid and the gas volume fraction in the two-phase plume region is calculated by applying the principle of volume continuity. It may be mentioned here that although this method has been quite effective in capturing the relevant flow physics in a gas-stirred system, the important consideration of bubble slippage phenomena in developing the numerical models have largely been ignored. However, earlier studies indicated that in gas-stirred ladle systems, slippage between rising bubbles and the surrounding fluid can dissipate a significant part of the input energy. Therefore, the calculated value of gas volume fraction corresponding to zero or no bubble slippage tend to be overestimated, thereby producing an erroneous velocity field. On the other hand, incorporation of the bubble slippage phenomena in a mathematical model can provide a more realistic description of the gasstirred system and adequately simulate the bulk phase hydrodynamics. Such an improved numerical model can then be utilized to predict the mixing phenomena in a more accurate manner, which in turn, can have important applications and far-ranging consequences in the industry. Although some preliminary studies with similar objective have been reported recently, a systematic study addressing this extremely significant issue is yet to be found in the literature. The present work is an attempt to study the mixing process and investigate the effects of bubble slip phenomena in predicting the mixing time through a mathematical modeling procedure. This is accomplished by three-dimensional numerical simulation of fluid flow in the ladle via a modified version of the previously reported computational fluid dynamics (CFD) model pertinent to this process. The hydrodynamic description of the gas-liquid two phase region is suitably modified to take into account the slippage between rising gas bubbles and the surrounding liquid. Particular attention is paid to model the transient mixing phenomena and critically analyze the capability of the present model to predict the mixing time in an accurate manner. This is accomplished by comparing the numerical simulation predictions with results from an ongoing experimental study at Tata Steel, India. Parametric studies are also undertaken to examine the effects of gas flow rate and bottom nozzle positioning on the mixing time. The combined model, therefore, throws a significant insight on the effect of bubble slippage considerations on the numerical prediction of mixing time in a gas stirred ladle and is expected to provide an effective quantification of flow characteristics and mixing behaviour, thereby facilitating the subsequent optimization of the overall process.