502
Chapter 11
Fig. 11.10. Calculated velocity profiles in a round-bottom stirred tank reactor equipped with a Rushton
turbine, (from Lunden (1994)).
solution of the flow field: 1.) The flow is normally turbulent. 2). The flow is not a one-phase
flow, since both gas and liquid are present. This makes it necessary to introduce modelling
assumptions concerning both turbulence and two-phase flow before a numerical flow pattern can
be calculated (See Note 11.5). Simulated flow patterns in bioreactors are thus to be seen only as
approximations. Even so these simulations can be highly illustrative for showing flow patterns,
and thereby help to identify possible scale-up problems (see e.g, Kelly and Humphrey, 1998). An
example of a flow pattern obtained in a CFD simulation is shown in Fig. 11.10.
Note. 11.5. Modelling of turbulent flow
The turbulence of the flow in stirred tank reactors does not invalidate Eq. (11.25), and time resolved
simulations of the turbulent flow have indeed been made (Revstedt et al., 1998). However, to resolve the
turbulent flow, which contains highly irregular flow patterns down to the Kolmogorov size, a grid size of
the same length scale is needed, which is computationally very expensive. In practice, the fine details in
the turbulent flow are therefore not resolved, but are instead treated by a simplified model, in which the
time-averaged flow pattern is shown. The velocity is in these simulations divided into a time-averaged
velocity and a fluctuating (turbulent) velocity according to:
u = u + u
where
(1)
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