Scale-up of Bioprocesses
489
Increasing
Froude number
T
i
i
t
0
0.01
0.02
0.03
0.04
A eration num ber,
NA
0.05
Fig. 11.7. The ratio
Npg/Np
shown (qualitatively) as a function of the aeration number for a six-bladed
Rushton turbine. The Froude number is given in Eq. (11.28). (Adapted from Ekato, Handbook of mixing
technology
(
www.EKATO.com1).
The cavities will grow with increasing
Na
until eventually the impeller becomes fully immersed
in gas, a condition called flooding. The power number
Np_g
gradually falls with increasing
Na
in a
manner shown by Fig. 11.7. Typically, a fluid foil impeller will have a significantly smaller drop
in the ratio
NpJNp
with increasing aeration rate than a Rushton turbine (see Problem 10.2).
An approximate empirical correlation describing the relation between aerated,
P*
and unaerated,
P,
power consumption is (Michel and Miller, 1962):
where the value of
k
depends on the impeller type.
Power input in bubble columns
The power input by the aeration is normally small in stirred tank reactors. In a bubble column, on
the other hand, all mixing energy is supplied by the aeration. The compression power input for
aeration in a bubble column operating at moderate superficial velocities can be expressed as
(Chisti and Moo-Young, 2001)
(
11
.
10
)
Pcomp = gPl“sV
comp
(
1 1
-
1 1
)
where g is the gravitational acceleration (9.82 m s'2).
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