where \(H_{l}/4\) is the filling level for unaerated conditions of each compartment and is equal to 0.625 T. A possible effect of surface aeration is minimized as it is subtracted, except of the bottom impeller where this influence can be assumed to be negligible under aerated conditions (Chapman, Nienow, & Middleton, 1980).
Power consumption was determined by measurement of the torque \(M\)applying a strain gauge with telemetry technique (Trachsler Electronics GmbH, Switzerland) mounted above the top impeller. Thus, \(M\) and the resulting represents the total power consumption of all immersed impellers. The torque measurements were conducted in parallel to the gas hold-up measurements leading to the respective power input \(P\) of compartment 1-4, 1-3, 1-2 and the bottom compartment. Similar to the gas hold-up determination, each impeller stages’ power draw was calculated applying, \(P_{n}-P_{(n-1)}\). Below a Fr number of 0.352 the low torsion yielded in high measuring uncertainty of the strain gauge signal and measurements were therefore not considered in this study.

CFD Simulations

CFD Simulations were conducted applying the Euler-Lagrange approach of the two-phase flow as described in Witz et al. (2016) and Eibl, Rustige, Witz, and Khinast (2020). The Lattice Boltzmann method (LBM) was used for simulation of the liquid flow field and the bubble movement was captured via a Lagrangian approach by solving the Newton’s equation of motion with the forces fluid stresses, gravity, drag, lift and added mass forces acting on the bubbles.
The modified half-way bounce back method (Ladd, 1994) was applied for the static boundaries in the LBM, like the reactor walls. The moving boundaries, e.g. the Rushton stirrers, were represented by a wet node boundary approach by Lallemand and Luo (2003). The top surface of the simulation domain was modelled as a free surface using a free slip boundary condition.
Bubbles with similar properties were grouped together, forming parcels to reduce the memory consumption and hence enabling the simulation of the large number of bubbles inside the reactor. Turbulent eddies in a size range similar to the bubble diameter were assumed to be the main cause for bubble breakup. The daughter bubble size distribution was determined using the model of Luo and Svendsen (1996). The fluid field and the bubbles are two-way coupled, i.e. the fluid experiences feedback forces generated by the bubbles. The displacement of the fluid by the bubbles was not considered.
All dimensions of the simulated reactor are similar to the pilot scale reactor to allow a direct comparison (Figure 1). Two test cases were simulated, the first with an aeration rate Q of 6 m3/h and a superficial gas velocity ug of 0.011 m/s at an impeller speed of 440 min-1 (Fr = 0.87, Fl = 0.06). The second test case was simulated with 4 m3/h aeration and a ug of 0.007 m/s at 280 min-1 (Fr = 0.35, Fl = 0.06) impeller speed. The gas hold-up was calculated by