Modeling and Simulation of Drop Size Distributions in Stirred Liquid-Liquid Systems

Abstract

In this thesis, the modeling and numerical simulation of drop size distributions in stirred liquid-liquid systems is considered. Therefore, the turbulent flow field in the stirred tank as well as the behavior of the drops is investigated. The turbulent flow field is modeled by means of the Reynolds-averaged Navier-Stokes equations in combination with a k-e turbulence model. The population dynamical processes, i. e., the behavior of the drops, are described by an averaged population balance equation, where the coalescence and breakage phenomena are modeled via integral terms. In order to investigate the dynamical behavior of the coupled system, the index of the underlying differential algebraic equations, which are obtained after space-discretization, is determined. This analysis shows that the index of the semi-discretized Navier-Stokes equations is not increased by the coupling with the population balance equation, which means that a solver that is suitable for the solution of the Navier-Stokes equations can be extended so that it can also be used for the solution of the coupled system. However, since the effort to build such a solver is immense, in this thesis, the coupling is realized by means of a simulator coupling approach. In this approach, the CFD code FeatFlow is used for the flow simulation, whereas the population balance solver Parsival is applied for the calculation of the drop size distributions. Since it is justified for the considered application to neglect the influence of the drops on the flow field, only a one-way coupling is considered, regarding the modeling as well as the numerical simulation. As far as the numerical simulation is concerned, this means that only the results of the flow simulation are used for the calculation of the drop size distributions and not vice versa. According to these results, the stirred tank is then subdivided into compartments, and the data from the flow simulation are averaged with respect to these compartments so that they can be used for the simulation with Parsival. Both, the results of the flow simulation as well as the drop size distributions derived by the simulation with Parsival, are validated by comparison with experimental data, which are taken from the literature or obtained by the experimental part of a joint project, respectively. Besides the realization of the coupling, in this thesis, we also investigate the occurring difficulties in order to demonstrate the possibilities, but also the restrictions, of the presented approach and to discuss alternatives, like the use of the (direct) quadrature method of moments as another way to solve the population balance equation.