Several mixing Time correlations applicable to central injection of gas into a cylindrical vessel have been critically reviewed and analyzed. Assuming flow phenomena in typical gas agitated systems are dominated by the inertial and gravitationalforces, a dimensional analysis has been carried out to establish the functional relationship between the operating parameters (the liquid depth, L, the radius of the vessel, R and the gas flow rate, Q) and the mixing time (τ{sub}m). The results of thedimensional analysis in conjunction with published experimental data indicate that, for axisymmetric bubble stirred ladles, the appropriate form of correlation for mixing time is: τ{sub}m 2{sup left}g/R =C{sub}o (L/R){sup}-2.0(Q{sup}2/gR{sup}5){sup}-033To determine a unique, reasonably accurate, value for the pre-exponent C{sub}o, a large number of experimental data from a set of six different investigations was applied. Due care was taken to ensure that the chosen experimental data conform to practical ladle metallurgy steelmaking situations (e.g., Reynolds number in the order of 10{sup}5, specific potential energy input rate in the order of 0.01 W/kg, L/D≈1.0, etc.). Regression analysis of the data thus derived leads to a value of C{sub}o equal to4.1×10{sup}3, valid essentially for a degree of bulk mixing up to 95 percent The present work thus reconfirms that mixing time and the operating variables under ladle metallurgy steelmaking conditions can be effectively correlated via: τ{sub}m (95bulk) = 25.4 Q{sup}-0.33 L{sup}-1 R{sup}2.33, in which Q is the ambient volumetric flow rate of gas within the ladle (m{sup}3 /s, referenced to the mean temperature and pressure), L is the depth of liquid (m) and R is the mean radius of the ladle (m).Finally mixing in geometrically and dynamically similar Systems has been considered and an explicit relationship between the mixing times in model and full scale system derived in terms of the geometrical scale factor, λ.
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