only possible for r/R between 0.50 and 0.82 due to the pronounced curve of the
vessel surface. The differences between CFD and PIV can be accounted for by
measurement uncertainties based on optical phenomena (light refraction and distortion) and the restricted measurement accuracy directly at the edges of the impeller
bar (pixel resolution of the camera chip). Thus, direct comparison to the fluid
velocities in direct proximity to the impeller is difficult. All three velocity components in the SP300 were well captured by the PIV measurements. The greatest
differences (7.9–15%) were found for u
! between r/R 0.70 and 0.85. Hence, it can
be concluded that the single-phase CFD model provides reliable fluid flow predictions in both spinner flask types.
3.2.3 Results from Multi-phase Modelling
Oxygen Mass Transfer
Oxygen represents a critical parameter in the cultivation of human cells because it is
essential for mitochondrial respiration and oxidative phosphorylation. Hence, the
determination of the oxygen mass transfer (OTR) represents an important aspect.
However, many of the small-scale bioreactor systems frequently used for the
expansion of hMSCs are not equipped with oxygen sensors, which makes it impossible to experimentally determine the oxygen transfer. In such cases, multi-phase
CFD simulations can be used to estimate the oxygen mass transfer coefficient (k L a),
which is shown in the following representative for the SP100.
The multi-phase VOF approach, which takes the headspace into account, was
used for the prediction of the k L a in the spinner flasks. Figure 8 (a) shows the
stationary fluid flow pattern (N ¼ 49 rpm) obtained from the multi-phase VOF
model, without significant differences to that derived from the single-phase simulations (see Sect. 3.2.2). This conformity between the single and multi-phase simulations was due to the fact that the transport equations for mass and momentum were
corrected only at the phase boundary where both the liquid and the gaseous phase
were within the control volume. Since only low impeller speeds ( 120 rpm) were
used in the SP100, marginal changes in the fluid surface with relative low interactions between the liquid and gaseous phases occurred. As a result, the multi-phase
VOF model also provided reliable predictions for the fluid flow as well as the fluid
surface.
The calculation of the k L a value by means of CFD is usually performed in
surface-aerated systems using Higbie’s penetration model. In this approach, the
mass transport is modelled by surface renewal, whereby a characteristic contact
time between fluid elements and the phase boundary is calculated (see Eq. (3)).
Numerical Methods for the Design and Description of In Vitro Expansion. . .
207
vessel surface. The differences between CFD and PIV can be accounted for by
measurement uncertainties based on optical phenomena (light refraction and distortion) and the restricted measurement accuracy directly at the edges of the impeller
bar (pixel resolution of the camera chip). Thus, direct comparison to the fluid
velocities in direct proximity to the impeller is difficult. All three velocity components in the SP300 were well captured by the PIV measurements. The greatest
differences (7.9–15%) were found for u
! between r/R 0.70 and 0.85. Hence, it can
be concluded that the single-phase CFD model provides reliable fluid flow predictions in both spinner flask types.
3.2.3 Results from Multi-phase Modelling
Oxygen Mass Transfer
Oxygen represents a critical parameter in the cultivation of human cells because it is
essential for mitochondrial respiration and oxidative phosphorylation. Hence, the
determination of the oxygen mass transfer (OTR) represents an important aspect.
However, many of the small-scale bioreactor systems frequently used for the
expansion of hMSCs are not equipped with oxygen sensors, which makes it impossible to experimentally determine the oxygen transfer. In such cases, multi-phase
CFD simulations can be used to estimate the oxygen mass transfer coefficient (k L a),
which is shown in the following representative for the SP100.
The multi-phase VOF approach, which takes the headspace into account, was
used for the prediction of the k L a in the spinner flasks. Figure 8 (a) shows the
stationary fluid flow pattern (N ¼ 49 rpm) obtained from the multi-phase VOF
model, without significant differences to that derived from the single-phase simulations (see Sect. 3.2.2). This conformity between the single and multi-phase simulations was due to the fact that the transport equations for mass and momentum were
corrected only at the phase boundary where both the liquid and the gaseous phase
were within the control volume. Since only low impeller speeds ( 120 rpm) were
used in the SP100, marginal changes in the fluid surface with relative low interactions between the liquid and gaseous phases occurred. As a result, the multi-phase
VOF model also provided reliable predictions for the fluid flow as well as the fluid
surface.
The calculation of the k L a value by means of CFD is usually performed in
surface-aerated systems using Higbie’s penetration model. In this approach, the
mass transport is modelled by surface renewal, whereby a characteristic contact
time between fluid elements and the phase boundary is calculated (see Eq. (3)).
Numerical Methods for the Design and Description of In Vitro Expansion. . .
207