Results
Flow Regimes
A flow regime analysis is shown in Figure 2 (left column), where the Fr
number is plotted as a function of the Fl number. Measurements at 81
operating points were performed for each impeller level. The analysis
reveals that the flow regimes VC, LC and RC occurred at all impeller
levels, depending on the operating parameters. The position of the
transition lines was further analyzed and is displayed in Figure 3
(left). Only at high Fr numbers (> 0.72), all impellers
exhibit the transition from the vortex to the loaded cavity regime at
similar stirring and aeration conditions. For the bottom impeller, the
vortex-loaded-transition (cavity line) can be expected to occur at the
same Fl number, independent of the Fr number as gas is applied without
pre-dispersion to the bottom impeller and the gas load becomes too high.
The cavity line moves towards higher Flow numbers, with the increase of
fermenter height and number of impellers. This study demonstrates for
the first time that this shift of the transition becomes stronger with
each impeller level and is most pronounced at the lowest Fr number of
0.18, where the transition moves from a Fl number of 0.03 for the first,
to 0.08 for the second, 0.09 for the third and 0.11 for the fourth
impeller. This significant difference between the cavity lines of the
bottom impeller and the three upper impellers is of particular interest
for understanding the dispersion behavior of the whole bioreactor. A
straightforward explanation might be that in the non-coalescing media
applied in the present study, each impeller stage disperses the rising
bubbles more effectively and distributes the gas more homogeneously.
Thus, smaller bubbles are observed along the reactor height. This
hypothesis helps explaining the individual shift of the
vortex-loaded-transition at each impeller level.
When the stirrer speed is high, small bubbles are strongly pumped and
accumulate in the recirculation flow. Therefore, the upper impellers
become loaded already at lower Fl numbers, and, the cavity line of the
bottom and the upper impellers approach each other and intersect at a Fl
number of 0.03 (Figure 3, left). The observation of an individual and
more pronounced shift for the upper impellers is contrary to the results
of Smith et al. (1987). These authors used water in a three level
reactor for their experiments, which leads to coalescence of the rising
air bubbles and could explain why their cavity lines of the upper two
impellers were similar to each other.
Despite the experimental differences in their study, the results can be
explained in a similar way. These authors (Smith et al., 1987) assumed
that the gas in the upper compartments is more uniformly distributed,
leading to a lower gas density at the impeller, and thus to a shift in
the vortex-loaded-transition. The increase of rotation rate and Fr
number, leads to an increased circulation and a concentration of the gas
stream arriving at the impeller, and thus to the lack of the shift for
high Fr numbers. However, for the non-coalescent medium applied in the
present study, the observed shift is individual and more pronounced for
the upper impellers (Figure 3) since each compartment contributes to the
dispersion of gas bubbles and the impellers of higher levels become less
loaded.
A shift towards higher Fl numbers also applies for the transition from
the loaded to the flooded flow regime (flooding line) which moves from a
Fl number of 0.13 for the bottom impeller, to 0.22 for the second, 0.31
for the third and 0.34 for the fourth impeller at a similar Fr number of
0.26 (Figure 2 and 3). Our analysis of the flooding line at each
impeller level extends the results of Bombac and Zun (2006) by using a
fourth impeller level. As can be seen, there is a further shift of the
flooding line to higher Fl numbers with an increase in impeller level.
At the flooded state of the bottom impeller, large bubbles are visible,
not being dispersed and rising through the reactor (visible inspection,
data not shown). Thus, not all air can be dispersed by the second and
following impellers even though they are still in the loaded regime
(Figure 2).This phenomenon was already observed by Nocentini et al.
(1988) for a lab scale reactor filled with tap and distilled water.
In contrast, the upper impellers still showed a radial gas flow despite
the impeller’s probe indicated a flooded impeller (visible inspection,
data not shown). This raises the question if the upper impellers
actually reached a flooded state comparable to the bottom impeller
flooding. Detached small bubbles that are formed from large, buoyancy
driven bubbles may lead to the observed minor circulation flow in the
radial direction.
In conclusion, the upper Rushton turbines of the multistage aerated
bioreactor exhibit a shift in the cavity and flooding lines towards
higher Fl numbers. While an equal shift of vortex-cavity-transition can
be expected for all upper impeller stages in coalescent (water) medium
according to Smith et al. (1987), the gas pre-dispersion by the lower
impellers appears to cumulatively shift this transition for the upper
impellers in the non-coalescent (salt) medium applied in the present
study. This individual shift is demonstrated for the first time and its
explanation will be critically analyzed in the below CFD simulation
study.
Power Input
In Figure 2 (middle column), the relative power input by each of the
impellers (with respect to the unaerated case P0) is
shown as a function of \(u_{g}\). Without aeration (data not shown),
every impeller stage draws the same power. Under aerated conditions, the
bottom impeller shows a well-known distinct decrease of the relative
power input already at low aeration rates. The power decrease is most
pronounced at the occurrence of cavities around the transition to the
loading regime (square shape in Figure 2). Once every impeller blade has
a cavity attached and the cavities grow with an increase in aeration
rate (Fl number ≥ 0.07), the power decrease is less pronounced.
In contrast, the upper impellers show a moderate decrease of the
relative power input. This behavior is most pronounced at higher
impeller levels (3 & 4), indicating that the cavity formation of the
upper impellers is spread over a larger range of aeration rates. This
moderate relative power decrease mainly occurs in the LC regime, but is
present in all studied flow regimes. This makes evident that the drop in
the power draw of the upper impellers may not be attributed to specific
flow regimes as previously postulated for example by Smith et al.
(1987). Our approach of studying the individual power draw of each
impeller stage together with the respective flow regime enables this new
view on the effect of aeration on power input (Figure 2). Again, the
differences between the bottom and the upper impellers may be due to the
occurrence of less air bubbles close to the upper impellers, leading to
a higher density of the gas-liquid dispersion around the impeller, which
results in higher power inputs. The below CFD analysis will embrace this
hypothesis in more detail.
Gas Hold-up
In Figure 2, right column, the gas hold-up is shown as a function of\(u_{g}\) for each impeller level and for all operating conditions. The
upper impellers exhibit a higher gas hold-up than the bottom impeller as
expected (Figure 2, right column). Interestingly, the generally desired
positive effect on gas hold-up of increasing the impeller speed (Fr) is
stronger for the upper impellers compared to the bottom level stirrer.
The increase of aeration rate (i.e. \(u_{g}\)) has a positive impact on
the gas hold-up and this is individual for each impeller. Both the
bottom and second impeller level exhibit only a minor dependence on
aeration and thus show a low aeration efficiency. This demonstrates that
these impellers are not capable of dispersing the supplied air
efficiently, and the surplus air is transferred to the next compartment.
A reason for this may be that gas bubbles in the lower two compartments
are larger, more buoyancy driven and therefore are not following the
recirculation flow to the same extent as the smaller bubbles of the
upper compartments. The upper two impellers show a very good aeration
efficiency that is illustrated by the steep slope of gas hold-up when
increasing aeration rate (Figure 2 , right column).
Moreover, the upper impellers and predominantly the fourth level show an
interesting behavior when the bottom impeller is flooded: The aeration
efficiency is lower when the bottom impeller is in the flooded state. In
particular on the fourth level, the gas hold-up stays almost constant
with increase in aeration rate (Figure 2, right column, blue lines) and
demonstrates that a substantial part of the introduced airflow does not
contribute to the gas hold-up. This implies that large bubbles rise to
the top of the reactor in case of a flooded bottom impeller, and lead to
a low dispersion efficiency for the upper impeller levels.
The observations of the gas hold-up distribution are in contrast to
other publications (Linek et al., 1996; Nocentini, Fajner, Pasquali, &
Magelli, 1993), which assumed a similar gas hold-up for the upper
impeller levels. Our study thus draws a novel picture of a strong
dependency of the upper impellers’ gas dispersion performance on the
flow regime of the bottom impeller.
Figure 3 (right) summarizes the higher gas hold-up within the upper
impeller compartments (as detailed in Figure 2). Besides the gas
hold-up, the relative power input also increases with the impeller
level. This is an interesting finding as high gas hold-up is usually
associated with low power input. Although this is true for the
individual stirrer levels, it is not between levels (Figure 3). It may
be again concluded that the upper compartments profit from the
aforementioned pre-dispersed air rising from the lower compartments, and
the resulting homogenous dispersion may correspond with a lower local
gas hold-up in the immediate vicinity of the upper impellers. Thus, the
individual local gas hold-up at the impeller discs might explain the
expected power drop for each impeller, when the compartment gas hold-up
increases, and, the better power input for upper impellers compared with
lower impellers. Figure 3 (right) illustrates this behavior for a Fr
number of 0.46. The qualitatively described behavior was observed over
the complete experimental area between Fr number of 0.28 and 0.87. The
following CFD simulation supports these findings and enables studying
the complex mechanism leading to this dispersion behavior.
Computational Analysis
The experimental results of each impeller’s flow regime, power input and
gas hold-up show drastic differences between the impeller levels. They
further indicate that the local gas bubble distribution within each
compartment changes from the bottom to the top compartment. Therefore,
we analyzed the local bubble distribution and movement in the individual
impeller compartments by means of a two-phase CFD simulation.
Furthermore, the estimation of the local gas hold-up throughout the
reactor based on the number of bubbles, their size and volume was
performed. Such information, to the best of our knowledge, has not yet
been applied in this detail before for studying gas dispersion in
pilot-scale bioreactors.
For comparison, two simulations were conducted, one in the VC and one in
the LC flow regime of the bottom impeller. The simulated total gas
hold-up was 15 % in test case 2 (LC), and 5 % in test case 1 (VC). The
simulation exhibits a reasonable correlation with measured gas hold-up
values (with a relative standard error of 14 % for test case 1 and 19
% for test case 2). The detailed analysis of the bubble properties and
distribution for each impeller level and for both test cases is shown in
Figure 4. The number of bubbles, nBub. increase (Figure
4, A) and diameter, dBub. decrease (Figure 4, B) from
level one to level three supports the aforementioned assumption of a
better gas dispersion with increasing level. Along with the increase in
bubble velocity vBub. (Figure 4, C), these results
substantially support our aforementioned hypothesis for the shifting
cavity lines for each additional impeller stage. In test case 1, a
decrease in bubble number and an increase in diameter can be seen from
level three to level four (Figure 4 A and B), which may be due to gas
recirculation from the level above and leading to a lower amount of
bubbles in the fourth compartment. This could not be verified in the
experimental set-up. However, in the experiments the gas hold-up of each
compartment was derived by a differential approach. The gas hold-up for
each level was determined without the presence of the respective next
compartment on top of the one studied. In test case 2, this phenomenon
cannot be observed in the computations, which can be explained by less
recirculation due to larger and thus more buoyancy-driven gas bubbles.
The experimentally observed increasing gas hold-up from impeller one to
four was also observed in the simulations (Figure 4 F). The difference
in the bubble size between the impeller levels of test case 1 is only
minor and may be explained by reaching a stable droplet size (Figure 4
B).
A comparison of the local gas hold-up, εImp., in the
disk volume of (Figure 4 D) and of the local gas pumping capacity,
QImp., through each impeller (Figure 4 E) reveal a new
picture on the dispersion behavior of the multistage impeller
bioreactor. From the first to the second level a significant drop in
these key figures can be observed, which implies that the upper
impellers are exposed to less gas (i.e., the gas load is lower compared
with the bottom impeller). A large fraction of recirculating gas bubbles
in the upper compartment seem to bypass the impeller region. This might
explain why the local gas hold-up at the impeller is low although the
compartment gas hold-up, εComp., is high (Figure 4 F).
The higher velocity of bubbles (Figure 4 C) within the upper impeller
levels results in a better gas recirculation and explains the increase
in gas hold-up. Test case 1 shows an increase of local gas hold-up and
local aeration rate (gas load) from the second to the fourth impeller.
This is accompanied by an increase in bubble velocity.
The results of a low local gas hold-up in the impeller region, as well
as the significant lower local aeration rate (gas loading) for the upper
impellers, agree to our experimental results (Figure 2 and Figure 3) and
the assumption of a less pronounced power decrease due to a higher
gas-liquid density paired with a higher compartment gas hold-up.
The simulation approach also allows a detailed analysis of the impeller
cavities by displaying the simulated gas fraction isosurface (Khopkar &
Tanguy, 2008).
Figure 5 (left) shows the bottom view of each impeller level with the
isosurface of a 15 % void fraction (corresponding to the gas hold-up of
>15 %). Test case 1 with a high Fr number shows large
cavities at all impeller levels. The bubbles velocity increases from
second to fourth level. Test case 2 with low Fr number shows large
cavities at the bottom impeller and vortex cavities for upper impellers.
The velocity is lower compared to test case 1. These results are
remarkable as they correspond to the experimentally determined complex
flow regimes for these conditions and reinforce the simulations
validity. It must be noted that this approximative approach of choosing
15 % void fraction for illustration enables directly comparing gas
accumulation for both test cases, although gas cavities exhibit a void
fraction of 100 %.
The estimated local aeration rates of each impeller level (Figure 4 E)
revealed large differences between the bottom and the upper impellers.
Following these results, it is to question if the flow rate introduced
by the sparger and the resulting Fl number is the correct quantity to
describe the upper impellers flow regimes. The local aeration rates
allow the calculation of each impellers actual Fl number and an
adjustment of the positions on the flow map. This is illustrated for the
two test cases in
Figure 5 (right), where a shift of the adjusted Fl numbers (colored
symbols) towards lower values compared to the Fl number calculated for
the gas inlet aeration rate (black symbols). This shift is more
pronounced for the test case 2 with low impeller speed and shows that
the differences of aeration between the upper and the bottom impeller is
larger at low Fr numbers. These results support substantially the above
experimental flow regime analysis (Figure 2): The shift of the cavity
lines is larger at small Fr numbers and the cavity lines of all impeller
levels intersect at high Fr numbers. We postulate that the observed
shifts in the flow regime maps can be explained by the differences in
the effective gas flow resulting from pre-dispersed gas from the lower
level. Moreover, at higher stirrer speed, the recirculation is stronger
and more gas bubbles are drawn into this flow. Consequently, for the
higher local gas hold-up that is observed at the upper impeller levels
even more gas bubbles follow this flow. This might lead to the observed
intersection of cavity lines at all impeller levels for high Fr numbers.