A mathematical modelling study of fluid flow and mixing in gas stirred ladles
Date
2008-12
Authors
Cloete, Schalk Willem Petrus
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : Stellenbosch University
Abstract
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.
Description
Thesis (MScEng (Process Engineering))--Stellenbosch University, 2008.
Keywords
Gas stirred ladles, Fluid flow, Turbulence modelling, Dissertations -- Process engineering, Theses -- Process engineering