|Title:||Numerical aspects of population balance equations coupled to computational fluid dynamics|
|Abstract:||It can be the motion of clouds, the movement of a smoke plume, or the dynamics of fluids in processes which are interesting to food, petroleum, chemical, pharmaceutical and many other industries; they are all governed by the same physical laws: fluid dynamics and population balances. Numerical solution of Population Balance Equations (PBE) coupled to Computational Fluid Dynamics (CFD) is a promising approach to simulate liquid/gas-liquid dispersed flows, for which the governing physical phenomena are breakup and coalescence of bubbles/droplets, additional to transport phenomena of fluids. In the literature, there are many breakup and coalescence models to close the PBE. Unfortunately, there is no unified framework for these closures; and, it is one of our objectives: to determine appropriate coalescence and breakage kernels for liquid/gas-liquid dispersions. Another objective is to investigate numerical techniques for one-way coupled CFD and PBE, and to develop a computational tool. The developed tool is based on the incompressible flow solver FeatFlow which is extended with Chien's Low-Reynolds number k-epsilon turbulence model and PBE. The presented implementation ensures strictly conservative treatment of sink and source terms which is enforced even for geometric discretization of the internal coordinate. The validation of our implementation which covers a wide range of computational and experimental problems enables us to proceed into three-dimensional applications as, turbulent flows in a pipe and through static mixers. Regarding the studies on static mixers, not only we have obtained numerical results; we have conducted comprehensive experimental studies in the Sulzer Chemtech Ltd. laboratories (Winterthur, Switzerland). The inclusive experimental results has offered a good ground for verifying the adopted mathematical models and numerical techniques. The obtained satisfactory results in the studies for one-way coupled CFD and PBE has motivated us to study two-way coupled CFD-PBE models. The so far developed numerical recipe of which main ingredients are the method of classes, positivity-preserving linearization and the high-order FEM-AFC with FeatFlow including the standard k-epsilon solver has been extended to cover bubble induced turbulence and mixture-model with algebraic slip relation. A smart algorithm is developed, offering a compromise between the computational cost and the accuracy. Numerical simulation of air-in-water dispersed phase systems in a flat bubble column which is, numerically, a very challenging case-study and is experimentally studied by Becker et al. has been performed with the developed computational tool. The dynamic movement of the bubble swarm which is observed in the experiments have been successfully simulated. Keywords: computational fluid dynamics (CFD), population balances, coalescence, breakage, numerical solution, method of classes, parallel parent daughter classes, simulation, static mixers, multiphase flows.|
|Subject Headings:||Computatiional fluid dynamics (CFD)|
|Appears in Collections:||Lehrstuhl III Angewandte Mathematik und Numerik|
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