A new theoretical analysis and corresponding mathematical modeling of the widely used type of one dimensional flow models and related characteristic flow parameters such as reversion point of flow

Reynolds shear stress

reversion flow position

and so on

were presented to detail the buoyancy - driven two - phase turbulence flow structures in bubble columns. Different relations between the said flow parameters and design parameters were obtained and compared with other mathematical modeling results. Based on the above analysis

a scale - up rule of such reactors was derived from hydrodynamic similarity

that is

with the local maximum Reynolds shear as the characteristic force scale

that is estimated by a theoretical relation provided in the present work

two bubble columns with different scales would have the same or approximate flow patterns and velocity distributions when the two columns have the same or approximate maximum Reynolds shear values. The said rule is verified through a comparison of the prediction results with experimental data available in literature

and good agreements were obtained.