ON MATHEMATICAL-MODELS AND NUMERICAL-SOLUTIONS OF GAS STIRRED LADLE SYSTEMS

Mathematical models describing bulk liquid motion and turbulence pheno mena in axisymmetric gas bubble driven systems have been rigorously an alyzed. Some ambiguities in previous work have been pointed out and th rough detailed considerations of the relevant fundamentals, a new equa tion has been proposed for estimating plume rise velocity in such syst ems. It is shown that the proposed simplified equation provides estima tes that agree reasonably well with experimental measurements as well as results derived from a more detailed differential model (e.g., turb ulent Navier-Stokes equation). Energy transfer considerations in such systems further illustrate that the turbulence phenomena typically dis sipate only a minor fraction (approximately 20-30%) of the energy inpu t rate. Such observations appear to indicate that slip rather than no- slip between bubbles and the surrounding liquid provides a more realis tic description of the actual physical phenomenon. Finally, it is show n that the k-epsilon model together with the assumption of bubble slip page can describe the bulk phase hydrodynamics fairly realistically. D espite good agreement between measured and predicted flows, significan t differences between predicted and experimental values of various tur bulence parameters have been noted.