In this contribution, a methodology for particle tracing based on computed tomography and digital image processing is presented. It enables the tracing of particles in opaque structures using laboratory X-ray microcomputed tomography (μCT) systems that are not capable of time-resolved particle tracking. Through the development, it becomes apparent that an X-ray source with a cone beam geometry and the ability to perform fast, dynamic scans is a prerequisite for generating parabolic motion artefacts. Moreover, experimental tests are used to acquire data from simple particle sedimentations as well as from self-developed filter structures based on deep bed filtration. These experiments confirm that the particle position is located at the apex of the motion artefacts. Following the data assessment, multiple options for the particle coordinate extraction are discussed, and strategies thoroughly examined. A combination of random sample consensus (RANSAC) and the least squares method proves to be the most useful for determining the particle position. Besides, the developed methodology is validated using artificially generated data in which the motion artefact parameters of size, spatial orientation, and curvature, as well as noise, are varied. Supplementary, data is analysed manually in order to draw a comparison. In addition, to the presentation and discussion of the application of the methodology, a comparison with an artificial neural network (ANN) and the advantages and disadvantages of both methods are discussed. Finally, a first comparison of an extracted particle trace with a flow simulation through the complex structure is carried out, which shows that the particle trace follows the flow.:Table of Contents List of Figures ............................................................................................................................. i List of Tables ............................................................................................................................. vi List of Formula Symbols ......................................................................................................... vii List of Abbreviations ................................................................................................................. x 1 Introduction ....................................................................................................................... 1 2 Fundamentals .................................................................................................................... 5 2.1 Methods for Particle Tracking and Tracing .............................................................. 5 2.2 Computed Tomography .......................................................................................... 10 2.2.1 Tomography Design and Functional Principle ................................................ 10 2.2.2 Data Reconstruction ......................................................................................... 15 2.3 Digital Image Processing .......................................................................................... 18 3 Material............................................................................................................................. 30 3.1 Laboratory X-ray Tomography System TomoTU ................................................... 30 3.2 Experimental Setup .................................................................................................. 33 3.3 Choice of Particles and Medium ............................................................................. 34 4 Method development ...................................................................................................... 36 4.1 Characterisation of the Motion Artefacts ............................................................... 38 4.2 Method Consideration ............................................................................................. 45 4.3 Pre-processing .......................................................................................................... 46 4.4 Combination of Random Sample Consensus and Least Squares Method.......... 48 4.5 Multiple Particle Tracing .......................................................................................... 51 4.6 Coordinate Processing ............................................................................................. 53 4.7 Method Validation .................................................................................................... 53 5 Results and Discussion .................................................................................................... 59 5.1 Evaluation experimental data ................................................................................. 59 5.2 Comparison with Computational Fluid Dynamics (CFD) ....................................... 68 5.3 Comparison of Artificial Neural Networks with the Developed Classical Digital Image Processing Approach ............................................................................................... 70 6 Summary, Conclusion and Outlook ............................................................................... 74 7 References ........................................................................................................................ 76 / Die vorliegende Arbeit stellt eine auf Computertomografie und digitaler Bildverarbeitung basierte Methodik für die Partikelverfolgung dar. Diese ermöglicht es, mittels Labor- Microcomputertomografie (μCT) Anlagen, welche nicht dazu in der Lage sind, zeitaufgelöste Partikelverfolgung zu realisieren, Partikel in opaken Strukturen zu verfolgen. Durch die Methodenentwicklung ergibt sich, dass eine Röntgenquelle mit Kegelstrahlgeometrie sowie die Durchführungsmöglichkeit von schnellen, dynamischen Scans Voraussetzungen sind, um parabelförmige Bewegungsartefakte zu erzeugen. Dafür werden durch experimentelle Untersuchungen Daten erzeugt, die sowohl von einfachen Partikelsedimentationen als auch von eigens entwickelten Filterstrukturen, die sich an der Tiefenfiltration orientieren, abgeleitet werden. Diese Experimente bestätigen, dass sich die Partikelposition am Scheitelpunkt der Bewegungsartefakte befindet. Auf Grundlage der ersten Messungen werden verschiedene Möglichkeiten für die Partikelkoordinatenbestimmung diskutiert und Ansätze kritisch betrachtet. Dabei hat sich eine Kombination aus dem Random Sample Consensus (RANSAC) Algorithmus und der Methode der kleinsten Quadrate als am sinnvollsten für die Bestimmung der Partikelposition ergeben. Zudem wird die entwickelte Methodik anhand von künstlich erzeugten Daten validiert, bei welchen die Bewegungsartefakt-Parameter Größe, Raumorientierung und Krümmung sowie Rauschen variiert werden. Zusätzlich werden auch Daten manuell ausgewertet, um einen Vergleich ziehen zu können. Neben der Präsentation und Diskussion der Anwendung der Methodik wird außerdem ein Vergleich zu künstlichen neuronalen Netzen (KNNs) und die Vor- und Nachteile beider Methoden diskutiert. Abschließend wird ein erster Vergleich einer extrahierten Partikelspur mit einer Strömungssimulation durch die komplexe Struktur durchgeführt, welche zeigt, dass die Partikelspur der Strömung folgt.:Table of Contents List of Figures ............................................................................................................................. i List of Tables ............................................................................................................................. vi List of Formula Symbols ......................................................................................................... vii List of Abbreviations ................................................................................................................. x 1 Introduction ....................................................................................................................... 1 2 Fundamentals .................................................................................................................... 5 2.1 Methods for Particle Tracking and Tracing .............................................................. 5 2.2 Computed Tomography .......................................................................................... 10 2.2.1 Tomography Design and Functional Principle ................................................ 10 2.2.2 Data Reconstruction ......................................................................................... 15 2.3 Digital Image Processing .......................................................................................... 18 3 Material............................................................................................................................. 30 3.1 Laboratory X-ray Tomography System TomoTU ................................................... 30 3.2 Experimental Setup .................................................................................................. 33 3.3 Choice of Particles and Medium ............................................................................. 34 4 Method development ...................................................................................................... 36 4.1 Characterisation of the Motion Artefacts ............................................................... 38 4.2 Method Consideration ............................................................................................. 45 4.3 Pre-processing .......................................................................................................... 46 4.4 Combination of Random Sample Consensus and Least Squares Method.......... 48 4.5 Multiple Particle Tracing .......................................................................................... 51 4.6 Coordinate Processing ............................................................................................. 53 4.7 Method Validation .................................................................................................... 53 5 Results and Discussion .................................................................................................... 59 5.1 Evaluation experimental data ................................................................................. 59 5.2 Comparison with Computational Fluid Dynamics (CFD) ....................................... 68 5.3 Comparison of Artificial Neural Networks with the Developed Classical Digital Image Processing Approach ............................................................................................... 70 6 Summary, Conclusion and Outlook ............................................................................... 74 7 References ........................................................................................................................ 76

The transport or the separation of solid particles or droplets suspended in a fluid flow is a common task in mechanical and process engineering. To improve machinery and physical processes (e.g. for coal combustion, reduction of NO_x and soot) an optimization of complex phenomena by simulation applying the fundamental conservation equations is required. Fluid-particle flows are characterized by the ratio of density of the two phases gamma=rho_P/rho_F, by the Stokes number St=tau_P/tau_F and by the loading in terms of void and mass fraction. Those numbers (Stokes number, gamma) define the flow regime and which relevant forces are acting on the particle. Dependent on the geometrical configuration the particle-wall interaction might have a heavy impact on the mean flow structure. The occurrence of particle-particle collisions becomes also more and more important with the increase of the local void fraction of the particulate phase. With increase of the particle loading the interaction with the fluid phase can not been neglected and 2-way or even 4-way coupling between the continous and disperse phases has to be taken into account. For dilute to moderate dense particle flows the Euler-Lagrange method is capable to resolve the main flow mechanism. An accurate computation needs unfortunately a high number of numerical particles (1,...,10^7) to get the reliable statistics for the underlying modelling correlations. Due to the fact that a Lagrangian algorithm cannot be vectorized for complex meshes the only way to finish those simulations in a reasonable time is the parallization applying the message passing paradigma. Frank et al. describes the basic ideas for a parallel Eulererian-Lagrangian solver, which uses multigrid for acceleration of the flow equations. The performance figures are quite good, though only steady problems are tackled. The presented paper is aimed to the numerical prediction of time-dependend fluid-particle flows using the simultanous particle tracking approach based on the Eulerian-Lagrangian and the particle-source-in-cell (PSI-Cell) approach. It is shown in the paper that for the unsteady flow prediction efficiency and load balancing of the parallel numerical simulation is an even more pronounced problem in comparison with the steady flow calculations, because the time steps for the time integration along one particle trajectory are very small per one time step of fluid flow integration and so the floating point workload on a single processor node is usualy rather low. Much time is spent for communication and waiting time of the processors, because for cold flow particle convection not very extensive calculations are necessary. One remedy might be a highspeed switch like Myrinet or Dolphin PCI/SCI (500 MByte/s), which could balance the relative high floating point performance of INTEL PIII processors and the weak capacity of the Fast-Ethernet communication network (100 Mbit/s) of the Chemnitz Linux Cluster (CLIC) used for the presented calculations. Corresponding to the discussed examples calculation times and parallel performance will be presented. Another point is the communication of many small packages, which should be summed up to bigger messages, because each message requires a startup time independently of its size. Summarising the potential of such a parallel algorithm, it will be shown that a Beowulf-type cluster computer is a highly competitve alternative to the classical main frame computer for the investigated Eulerian-Lagrangian simultanous particle tracking approach.

The transport or the separation of solid particles or droplets suspended in a fluid flow is a common task in mechanical and process engineering. To improve machinery and physical processes (e.g. for coal combustion, reduction of NO_x and soot) an optimization of complex phenomena by simulation applying the fundamental conservation equations is required. Fluid-particle flows are characterized by the ratio of density of the two phases gamma=rho_P/rho_F, by the Stokes number St=tau_P/tau_F and by the loading in terms of void and mass fraction. Those numbers (Stokes number, gamma) define the flow regime and which relevant forces are acting on the particle. Dependent on the geometrical configuration the particle-wall interaction might have a heavy impact on the mean flow structure. The occurrence of particle-particle collisions becomes also more and more important with the increase of the local void fraction of the particulate phase. With increase of the particle loading the interaction with the fluid phase can not been neglected and 2-way or even 4-way coupling between the continous and disperse phases has to be taken into account. For dilute to moderate dense particle flows the Euler-Lagrange method is capable to resolve the main flow mechanism. An accurate computation needs unfortunately a high number of numerical particles (1,...,10^7) to get the reliable statistics for the underlying modelling correlations. Due to the fact that a Lagrangian algorithm cannot be vectorized for complex meshes the only way to finish those simulations in a reasonable time is the parallization applying the message passing paradigma. Frank et al. describes the basic ideas for a parallel Eulererian-Lagrangian solver, which uses multigrid for acceleration of the flow equations. The performance figures are quite good, though only steady problems are tackled. The presented paper is aimed to the numerical prediction of time-dependend fluid-particle flows using the simultanous particle tracking approach based on the Eulerian-Lagrangian and the particle-source-in-cell (PSI-Cell) approach. It is shown in the paper that for the unsteady flow prediction efficiency and load balancing of the parallel numerical simulation is an even more pronounced problem in comparison with the steady flow calculations, because the time steps for the time integration along one particle trajectory are very small per one time step of fluid flow integration and so the floating point workload on a single processor node is usualy rather low. Much time is spent for communication and waiting time of the processors, because for cold flow particle convection not very extensive calculations are necessary. One remedy might be a highspeed switch like Myrinet or Dolphin PCI/SCI (500 MByte/s), which could balance the relative high floating point performance of INTEL PIII processors and the weak capacity of the Fast-Ethernet communication network (100 Mbit/s) of the Chemnitz Linux Cluster (CLIC) used for the presented calculations. Corresponding to the discussed examples calculation times and parallel performance will be presented. Another point is the communication of many small packages, which should be summed up to bigger messages, because each message requires a startup time independently of its size. Summarising the potential of such a parallel algorithm, it will be shown that a Beowulf-type cluster computer is a highly competitve alternative to the classical main frame computer for the investigated Eulerian-Lagrangian simultanous particle tracking approach.