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