# A mathematical modelling study of fluid flow and mixing in gas stirred ladles

Cloete, Schalk Willem Petrus (2008-12)

Thesis (MScEng (Process Engineering))--Stellenbosch University, 2008.

Thesis

A full scale, three dimensional, transient, mathematical model was developed to simulate fluid flow and mixing in gas stirred ladles. The volume of fluid (VOF) and discrete phase (DPM) models were used in combination to account for multiphase aspects, and a slightly modified version of the standard - model was employed for turbulence modelling. The model was validated to compare well against published physical modelling results. Model results were interpreted from the fundamental grounds of kinetic energy transport within the ladle. This approach led to the specification of three key measures of mixing efficiency: The rate and efficiency of kinetic energy transfer from the buoyant gas to the bulk steel as well as the total kinetic energy holding capacity of the ladle. These measures describe the quantity of mixing in any specific ladle setup, whereas the traditional measure of mixing time reflects mixing quality, i.e. the degree of kinetic energy distribution through the entire ladle. The model was implemented in designed experiments to assess various operating and design variables pertaining to mixing quantity and quality. Considerable time was invested in finding the correct balance between numerical accuracy and computational time so that the model could be used to generate the required data within the given time frame. Experiments on the operating variables drew an important distinction between factors influencing the shape and the strength of gas induced flow patterns. Flow pattern strengthening variables, such as gas purge rate, significantly affected the quantity of mixing, but had a limited effect on mixing quality. Variables such as mass loading that influence the shape of the flow patterns had much larger potential to influence both the quantity and quality of mixing. Minimization of turbulence losses in the region of the plume eye was identified as the primary outcome of ladle design. It was shown that a taller vessel allowed more distance over which the plume could disperse, thereby reducing velocity gradients and subsequent turbulence generation at the free surface. Multiple tuyere systems yielded similar improvements by dividing the gas flow into several weakened plumes. Surface wave formation was investigated as an added mixing mechanism and demonstrated to be impractical for application in full scale gas stirred ladles. The conditions for resonance between the surface wave and the bubble plume were met only in vessels with a very low aspect ratio. Performance improvements offered by swirl in these ladles could easily be replicated in more practical ways. This study demonstrated the potential of mathematical modelling as a tool for in-depth investigation into fluid flow and mixing in the hostile environment of a full scale gas stirred ladle. Scaled-down cold models are the only alternative and can offer no more than a reasonably reliable predictive framework. The ease of flow data extraction from the numerical model also proved invaluable in facilitating a fundamental understanding of the effects of various important independent variables on ladle hydrodynamics. At this stage of development, however, the model is recommended for use on a comparative basis only. Two important developments are required for complete quantitative agreement: The inclusion of turbulence modulation by the bubbles and the increased turbulence kinetic energy dissipation rate in the vicinity of the free surface. A general strategy was developed to account for these effects and it compared favourably with published cold model results. Further research is required to generalize this approach for application in full scale gas stirred ladles.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/1699

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