488
Chapter 11
Table 113. Power number at fully turbulent flow for various impeller designs in a bioreactor system
equipped with baffles.
Im peller type
Np
Reference
Rushton
5.20
Nienow (1990)
Intermig
0.35
Nienow (1990)
Prochem
1.0 0
Nienow (1990)
Marine impeller
0.35
Schügerl (1991)
for stirred tank bioreactors. In a baffled reactor, only the inertial forces are important for a fully
turbulent flow, and
Np
has a constant value independent of
Res.
The power number will,
however, depend on the impeller type (see Table 11.3). In the laminar flow regime,
Res
< 10,
viscous forces dominate and the power dissipation will depend on
Res.
For laminar flow it has
been shown (Rushton et al, 1950a) that
NBoc—
(11.7)
'
Re,
In between fully laminar flow and fully turbulent flow, there is a transition regime, in which both
inertial and viscous forces need to be considered (Rushton et al, 1950b). The functional relation is
more complex in this case. For a known power number, the power consumption can obviously be
calculated from:
P = N pp,N,d;
(11.8)
Influence o f multiple impellers
Equation (11.8) holds for single-impeller systems. In practice, several impellers are normally put on
the same shaft. For systems with multiple impellers, the situation is more complicated (see e.g.,
Nienow and Lilly, 1979), but as a first approximation the power input can be calculated by just
multiplying the power consumption for a single impeller with the number of impellers. This is an
overestimation, since the power consumption increases slightly less than proportional to the number
of impellers.
Influence o f aeration
The power consumption for stirring is affected by aeration. The dispersion of gas in the liquid
causes a decrease in liquid density. Furthermore, when gas is sparged to a tank, gas bubbles are
drawn to regions of low pressure. This results in the formation of gas-filled areas (called
cavities)
behind the stirrer blades. The formation of these cavities depends on the ratio between the
volumetric gas flow rate and the pump capacity. This ratio is often expressed as a dimensionless
group, the so-called
aeration number Na
:
N
A
where
N f
is the flow number, (Eq. 11.3).
Nd;
■Ni
(11.9)