A computational fluid dynamics prediction of fluid flow in a 50 L HyPerforma Single-Use Bioreactor

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Introduction A computational fluid dynamics (CFD) study was conducted by the Zürich University of Applied Sciences (ZHAW) on a 50 L Thermo Scientific™ HyPerforma™ Single-Use Bioreactor (S.U.B.) to analyze fluid flow and concentration distributions occurring in the system. CFD is a numerical simulation methodology that solves fluid dynamics equations iteratively on a large number of discrete control volumes, which fill and closely represent the shape of the internal fluid space of a system being studied.

The liquid working volume of the S.U.B. in this study was 50 L. The impeller of the bioreactor consists of 3 blades, each at an angle of 45°, which rotate in a counterclockwise (from a top-down view) direction in a downward-pumping mode. The agitation shaft is angled as the vessel does not utilize sidewall baffles.

Results from the mixing experiments in the S.U.B. were correlated with CFD results to validate the simulation.

ResultsThe CFD process requires the geometry to be subdivided into a computational grid, otherwise known as a mesh. The mesh comprises a large number of elements, each of which acts as a “control volume” for numerical fluid flow calculations. The simulation of transient-mode, single-phase stirrer rotation was implemented by using a sliding mesh tip velocity (uTip) of 0.91 m/s (Figure 1).

The movement of the downward-pumping impeller using a single-phase stirrer rotation at uTip of 1.04 m/s created an axial fluid flow pattern with generation of two primary vortices and one eddy. The right vortex constituted 75% of the volume and determined the bulk fluid flow pattern (Figure 2).

Figure 1. Fluid flow and velocity in 50 L S.U.B.

Figure 2. Simulation of steady-state fluid flow with a single-phase stirrer rotation at uTip of 1.04 m/s.

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Ko

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leng

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λ [µ

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50 L S.U.B. eddy length scale simulationThe eddy length scale, λ, is evaluated as described by Kolmogorov in the equation below:

λ = v3

s( )0.25

where λ estimates the size of the smallest turbulent eddy based on kinematic viscosity, v, and kinetic energy dissipation, s. This value must be 0.5–0.6 times larger than the diameter of the cells commonly used for large-scale cell culture in the S.U.B., in order to avoid shear damage. Thus, no damage was expected for Chinese hamster ovary (CHO) cells, as λ ranges from 12 to 20 µm in the main reactor volume.

Comparison of 50 L S.U.B. mixing times at various tip speeds The mixing time in the 50 L S.U.B. was the time it took for the fluid to reach 95% homogeneity. This was determined by introducing a tracer into the tank and monitoring its concentration through the process of mixing until it

Table 1. Comparison of simulated steady-state mixing times in 50 L S.U.B. to experimental data.

Mixing time t95% (s)

Filling volume V (L)

Tip speed uTip (m/s)

Power input (W/m3)

Average CFDAverage from experiments

50

0.18 1.20 82 78

0.31 1.00 42 60

0.62 5.59 28 26

0.74 9.98 22 33

1.04 29.74 14 ND*

* ND = Not determined

reached a fixed value. The concentration of the tracer was estimated with CFD and then compared to the data from experimental mixing at various tip speeds. The time to reach 95% of steady-state values (t95%) was found to be within 5 to 30% of CFD predictions (Table 1).

ConclusionsThe CFD simulation studies successfully predicted the fluid mixing patterns in the 50 L S.U.B. and allowed for the comparison of results to the experimental mixing conditions.

The angled impeller system used in the S.U.B. is capable of robust mixing, and the asymmetrical vortices generated remove the need for baffling. The size of eddies from this mixing are sufficiently large to avoid shear damage to CHO cells at the impeller speeds used in this simulation model. Based on the mixing time comparison of model predictions to experimental results, the CFD simulations appear to give a reasonable estimation of the physics of mixing in the vessel.

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