Mathematical modeling of mixing phenomena in a gas stirred liquid bath |
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Authors: | G G Krishna Murthy A Ghosh S P Mehrotra |
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Affiliation: | (1) Department of Materials Science and Engineering, Massachusetts Institute of Technology, 02139 Cambridge, MA;(2) Department of Metallurgical Engineering, Indian Institute of Technology, 208016 Kanpur, India |
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Abstract: | A macroscopic, steady state energy balance model has been formulated to describe mixing phenom-ena in a liquid bath stirred
by injecting gas through a straight nozzle fitted axially at the bottom of the vessel. This, along with experimental data
on a water model previously reported, was employed to make predictions. Input energy terms considered in the model consist
of buoyancy energy and empirically determined fraction of gas kinetic energy. Dissipation of energy was attributed to liquid
circulation and bubble slip. The two-phase plume was assumed to be a truncated cone whose dimen-sions depended upon operating
conditions. Numerical solution of model equations gave liquid velocity and gas hold-up inside the plume as well as liquid
circulation rate and liquid velocity in the region outside the plume. Influence of process variables, e.g., gas flow rate,
bath height, and nozzle diameter, have been predicted. Validity of the model has been established by comparing some pre-dicted
entrainment ratios with those experimentally measured by other investigators. Empirical cor-relations to predict circulation
time and circulation number have been proposed. Circulation number was found to vary between 2 and 12 in contrast to the existing
assumption in the literature of a con-stant value of 3. Usefulness of these correlations in predicting mixing time for industrial
vessels has been demonstrated.
Formerly a Graduate Student in the De-partment of Metallurgical Engineering at the Indian Institute of Technol-ogy, Kanpur |
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