Characterization of the Aeration and Hydrodynamics in Vertical-Wheel™ Bioreactors

Abstract

In this work, the oxygen transport and hydrodynamic flow of the PBS Vertical-Wheel MINI^™ 0.1 bioreactor were characterized using experimental data and computational fluid dynamics simulations. Data acquired from spectroscopy-based oxygenation measurements was compared with data obtained from 3D simulations with a rigid-lid approximation and LES-WALE turbulence modeling, using the open-source software OpenFOAM-8. The mass transfer coefficients were determined for a range of stirring speeds between 10 and 100 rpm and for working volumes between 60 and 100 mL. Additionally, boundary condition, mesh refinement, and temperature variation studies were performed. Lastly, cell size, energy dissipation rate, and shear stress fields were calculated to determine optimal hydrodynamic conditions for culture. The experimental results demonstrate that the kL can be predicted using Sh=1.68Re0.551Sc13G1.18, with a mean absolute error of 2.08%. Using the simulations and a correction factor of 0.473, the expression can be correlated to provide equally valid results. To directly obtain them from simulations, a partial slip boundary condition can be tuned, ensuring better near-surface velocity profiles or, alternatively, by deeply refining the mesh. Temperature variation studies support the use of this correlation for temperatures up to 37 °C by using a Schmidt exponent of 1/3. Finally, the flow was characterized as transitional with diverse mixing mechanisms that ensure homogeneity and suspension quality, and the results obtained are in agreement with previous studies that employed RANS models. Overall, this work provides new data regarding oxygen mass transfer and hydrodynamics in the Vertical-Wheel bioreactor, as well as new insights for air-water mass transfer modeling in systems with low interface deformation, and a computational model that can be used for further studies.

Keywords: Kolmogorov; LES; OpenFOAM; Sherwood; WALE; energy dissipation rate; homogeneity; human induced pluripotent stem cell; mass transfer; mesh refinement; optimization; oxygenation; partial slip; rigid-lid; shear stress; stirred suspension bioreactor; vertical-wheel.

Figure 1

(a) Picture of the bioreactor in its base unit. (b) Virtual representation of the bioreactor.

Figure 2

Representation of the experiment set-up (equipment not drawn to scale).

Figure 3

Oxygen–water diffusion coefficients and linear fitting computed from various sources [27,29,30,31,32,33,34,35,36].

Figure 4

Experimental $k_L$ values and experimental correlation predictions against agitation rate. Lines refer to average experimental conditions, while crosses refer to the conditions measured for each respective trial.

Figure 5

Instantaneous $k_L$ over time for the 100 mL and 20 to 95.5 rpm with slip boundary condition cases.

Figure 6

(a) Simulation–based $k_L$ and simulation-based correlation against agitation rate. (b) Comparison between the experimental–based results and the corrected simulation–based correlation, against agitation rate.

Figure 7

$k_L$ values calculated from the experimental–based correlation versus $k_L$ values obtained from simulations with a slip coefficient of 12.5%, against agitation rate.

Figure 8

(a) y⁺ surface values and (b) resolved kinetic energy ratio profiles.

Figure 9

Instantaneous velocity magnitude and SGS eddy viscosity fields, and mesh grid in the central xy-plane for the 100 mL/30 rpm case with (a) a slip coefficient of 12.5% and with the coarser mesh, and (b) a slip coefficient of 5% and with the finer mesh. (c) Comparison between the instantaneous $k_L$ of both cases.

Figure 10

Comparison of the instantaneous surface velocity magnitude field for the slip with coarse mesh (right), partial slip 12.5% with coarse mesh (left), and partial slip 5.00% with fine mesh cases (middle).

Figure 11

(a) Instantaneous velocity magnitude (top frame) and near-surface oxygen concentration fields (bottom frame; amplification) in the central xy-plane over 7.50 s of operation. The red frame highlights the amplification performed for the oxygen concentration field. (b) Instantaneous $k_L$ over time of the refined mesh 100 mL/30 rpm case with a slip coefficient of 5.00%.

Figure 12

Instantaneous field of velocity magnitude in the central xy-plane for agitations rates between 40 and 95.5 rpm at 60 s.

Figure 13

3D and 2D stream tracers of the instantaneous velocity magnitude field for an agitation rate of 30 rpm across different planes.

Figure 14

Instantaneous velocity magnitude and directional component fields in the central xy-plane at 7.0 s.

Figure 15

(a) Oxygen concentration fields in the central xy-plane for the 100 mL/60 rpm case over 60 s of operation (with a time interval of 10 s). (b) Local concentration plots and regressions for all 100 mL cases. (c) Average bulk concentration plots and regressions for all 100 mL cases.

Figure 16

(a) Kolmogorov length scale distributions. (b) EDR distributions. (c) Kolmogorov length scale, (d) EDR, and (e) shear stress fields for the 100 mL/30 rpm refined mesh case at 7.5 s.