uni- and bi-variate population balance systems; direct discretizations; aggregation; accuracy of numerical results
Population balance systems model the interaction of the surrounding medium
and the particles which are described by the particle size distribution (PSD).
This way of modeling results in a system of partial differential equations where
the incompressible Navier–Stokes equations for the fluid velocity and pressure
are coupled to convection-diffusion equations for species concentration and the
system temperature, and a transport equation for the PSD. The equation for the
PSD may even contain an integral operator that models, e.g., the aggregation of
the particles. Whereas the flow field, the concentration of dissolved species, and
temperature are defined in a three-dimensional spatial domain, the PSD depends
also on the internal coordinates, which are used to describe additional properties
of the particles (e.g., diameter, volume). In particular, uni-variate and
bi-variate population balance models are based on one- and two-dimensional
geometrical characterizations of the individual particles (diameter, volume, or
main axis in the case of anisotropic particles), resulting in four-dimensional
(4D) and five-dimensional (5D) population balance systems. There are several
classes of numerical methods for solving population balance systems. With the
ongoing rise of computer power, the option of using direct discretizations for
simulating those systems becomes more and more interesting since these discretizations
do not introduce an additional error by circumventing the solution
of the higher-dimensional equation for PSD, like momentum-based methods or
operator-splitting schemes. In this thesis, it is shown for uni-variate population
balance systems that for an appropriate choice of the unknown model
parameters in aggregation kernel good agreements can be achieved between the
experimental data and the numerical results computed by the numerical methods.
A mixed finite difference/finite volume method is used for discretizing
the PSD equation in the case of bi-variate population balance systems. In this
case, it is demonstrated that even in the class of direct discrerizations, different
numerical methods lead to qualitatively different numerical solutions.
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