The three-dimensional velocity field is numerically calculated for bubble columns using an Euler-Euler approach with an additional transport equation for the interfacial area. The spacial bubble number density is obtained by solving the population balance equation numerically. In order to reduce the numerical effort or to avoid restrictive assumptions for bubble break-up and coalescene processes a partial solution of the population balance is derived. It is valid asymptotically as the bubble swarm moves away from the distributor. The approximate solution leads to a transport equation for the mean bubble volume, which is solved in dependence of the bubble break-up and coalescence processes. Both phenomena are considered. For the numerical calculations the interfacial area transport equation is coupled with the balance equations for mass and momentum transport. The calculations are performed for instationary, three-dimensional flows in cylindrical bubble columns with diameters up to 0.29 m and 4.425 m of height.
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