13 Morphological Modelling and Simulation …
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5.1 MSMPR Crystallizer
The central equation of the mixed suspension mixed product removal (MSMPR)
crystallizer model is again a population balance equation. In this case growth of
spherical particles (diameter d ) with a growth rate G, and nucleation with a birth
rate B were considered. In addition, the crystallizer accepts a feed stream and has a
vapor and a product stream as output.
∂n(d )
∂t
+
∂(G(d )n(d ))
∂d
+
1
V
n streams
j
n j (d ) ˙
V j
+ n(d )
d ln V
dt
=
∂B(d , n)
∂d
(38)
Growth and nucleation kinetics were as proposed by Jones and Mydlarz [52].
The discretization as done with the method of classes and a flux limiter was used as
proposed by Qamar [53]. Additionally, mass balances were introduced. The resulting
set of differential algebraic equations is then solved using Dyssol [54].
5.2 Hydrocyclone
The implementation of the hydrocyclone is based on the work of Braun [55] and the
descriptions of Kulikov et al. [50]. The static model proposed by Braun divides a
hydrocyclone into four zones (c.f. Fig. 27): Zone A is a tube-like inlet zone to which
a suspension is fed and forced onto a circular downward movement. The suspension
then enters an outer tube-like zone B where the fluid continues to move downward on
Fig. 27 Abstraction of the
hydrocyclone as proposed by
Braun [55]