- Datum: 19.01.2018
- Uhrzeit: 10:00 - 11:00
- Vortragende(r): Prof. Dr. Menwer Attarakih,
- The University of Jordan, School of Engineering, Department of Chemical Engineering, Amman, Jordanien, und Chair of Separation Science and Technology, TU Kaiserslautern
- Ort: Max-Planck-Institut Magdeburg
- Raum: Großer Seminarraum "Prigogine"
- Kontakt: sek-pcg@mpi-magdeburg.mpg.de

The presentation will focus on the fundamental mathematical framework elucidated by success stories with real applications in Chemical Engineering and Computational Fluid Dynamics. The key points include: Introduction to the Population Balance Equation: Importance and Applications, Frequent Solution Methods, SQMOM: Model Concept, PPBLab Software Implementation, From SQMOM to OPOSPM, Mathematical Foundation and Hyperbolic Analysis, OPOSPM: A Nonlinear Autocorrelation Model with real applications, OPOSPM Validation using CFD Solvers: FLUENT, OpenFoam, COMSOL and FPM (Finite Point Set Method), Implementation of OPOSPM in SIMULINK , Dynamic and Steady State Experimental Validation, and finally Conclusions.

In this presentation, I deal with a critical
problem in the numerical modelling of the dispersed multiphase flow systems,
which is composed of dispersed particles in a continuous phase. The numerical modelling of such systems
calls for the population balance equation (PBE) which is an integro-partial
differential equation with no general analytical solution. In spite of the
intensive research in the last two decades, which is concerned with fast
numerical solvers based on the moment methods, numerical solutions which are
able to conserve particle integral properties are still expensive from CPU time
point of view and suffer from losing the particle size distribution. The latter
is required in industrial particulate systems where it is used to determine
mechanical and physiochemical properties and for online control purposes. Therefore,
I will introduce a numerical framework for solving
the PBE based on the selective conservation of the total number and volume
concentrations of the particulate system population. In one-dimensional
particle property space, the key idea is to represent the population by a
single Lagrange particle which moves along the positive real axis to conserve
two low-order moments of the underlying particle distribution. The mean
position of the particle is related algebraically to the total volume and number
concentrations. In multi-particle property space, these particles carry
information about the distribution as it evolves in space and time. This
information includes averaged quantities such as total number, volume and
solute concentrations, which are tracked directly through a system of coupled
hyperbolic conservation laws with nonlinear source terms. In the framework of
the Sectional Quadrature Method of Moments (*Attarakih, M, Drumm, C., and
Bart, H.-J., 2009, Solution of the population balance equation using the
sectional quadrature method of moments (SQMOM). Chemical Engineering Science,
64, 742--752*), this moving particle is called the “Secondary Particle”
where its position coincides exactly with that of the “Primary Particle”.
Therefore, the method is called the One Primary and One Secondary Particle Method
(OPOSPM) where the resulting discrete hydrodynamic model for the PBE consist of
two continuity equations for the total number and volume concentrations in the
most general case. These equations are
found exact when compared to those derived from the continuous PBE for many
popular breakage, aggregation and growth functions. The accuracy of the method can
be easily improved by increasing the number of primary particles in case it
deviates from the exact solution. The method has been proved as an efficient
engineering model and stable numerical tool for modeling physical and
engineering problems that have discrete and multi-scale nature with
multivariate internal particle properties.

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