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A generalized population balance model for the simulation of polydisperse multiphase flows within the Euler-Euler framework

Lehnigk, R.


Polydisperse multiphase flows appear in a multitude of industrial processes. Depending on the application, the fluid or solid particles differ not only in size, but also with respect to other variables such as their velocity, shape, temperature, crystal structure or chemical composition. These secondary properties can significantly influence the corresponding process or the performance of the end product. An example are bubbly flows in vertical channels. The velocity vectors of the individual bubbles depend on their size, which ultimately determines the gas phase distribution in the pipe cross-section. Another example is the gas phase synthesis of ceramic powder in high temperature processes. The resulting particle aggregates are usually non-spherical due to the competition of aggregation and sintering of primary particles. The aggregate morphology affects the likelihood of collisions and the primary particle size determines the characteristics of the product powder. The evolution of property distributions within the dispersed phase can be described with the population balance equation. Its coupled solution with the governing equations of fluid flow allows to consider spatial dependencies. In the present thesis, a flexible population balance model has been developed and combined with a multifluid solver within the open source Computational Fluid Dynamics library OpenFOAM. The population balance equation is solved with the method of classes. The applied technique preserves the total mass and number of particles and allows for an arbitrary discretization of the distribution function. A new formulation that allows a direct implementation of binary breakup models with an implicitly given daughter size distribution is proposed which eliminates the need for an additional numerical integration. Further, a general approach for predicting the evolution of secondary size-conditioned properties is presented. The flexibility of the developed population balance model is demonstrated by applying it to two fundamentally different problems. First, the cocurrent flow of air and water in a vertical pipe is simulated. Predicting the development of the lateral void fraction profile is still a largely unsolved problem and requires proper modeling of several physical mechanisms. In dealing with the complexity a stepwise validation strategy is adopted, whereby the limits of each model layer are determined for a large matrix of measured superficial velocities. By employing an established model for the momentum exchange between the phases it is shown that, in the case of a nearly developed flow, especially the transition region between bubbly and slug flow can be simulated reliably. Next, using volume-averaged flow parameters, the performance of several coalescence and breakup model combinations is assessed. Promising results are obtained for some cases, albeit the models still require further development and calibration. Finally, the developing flow is simulated and it is shown that a complete model for predicting transitions between flow regimes must account for the size dependency of the bubble motion, as possible with the developed population balance model. The second application is the synthesis of titania in an aerosol reactor. The specific surface area of the aggregates is considered as a secondary property here. In combination with a constant fractal dimension their collision diameter can be modeled. The mean primary particle diameter can be inferred from it as well. The created model helps in explaining the trends observed in the experiment, which is not possible on the basis of considering merely the aggregate size distribution or using a simplified description of the reactor geometry.

Related publications

  • Doctoral thesis
    TU Dresden, 2020
    Mentor: Prof. Dr.-Ing. habil. Dr. h. c. Uwe Hampel
    127 Seiten


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