## Fachbereich Maschinenbau und Verfahrenstechnik

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- On the Extended Finite Element Method for the Elasto-Plastic Deformation of Heterogeneous Materials (2015)
- This thesis is concerned with the extended finite element method (XFEM) for deformation analysis of three-dimensional heterogeneous materials. Using the "enhanced abs enrichment" the XFEM is able to reproduce kinks in the displacements and therewith jumps in the strains within elements of the underlying tetrahedral finite element mesh. A complex model for the micro structure reconstruction of aluminum matrix composite AMC225xe and the modeling of its macroscopic thermo-mechanical plastic deformation behavior is presented, using the XFEM. Additionally, a novel stabilization algorithm is introduced for the XFEM. This algorithm requires preprocessing only.

- Effects of Waterjet Treatment on Surface Integrity of Metals and its Optimization (2014)
- The study addresses the effect of multiple jet passes and other parameters namely feedrate, water pressure and standoff distance in waterjet peening of metallic surfaces. An analysis of surface integrity was used to evaluate the performance of different parameters in the process. An increase in the number of jet passes and pressure leads to a higher roughness and more erosion and also a higher hardness. In contrast, the feedrate shows a reverse effect on those surface characteristics. There exists a specific value of standoff distance that results in the maximum surface roughness, erosion as well as hardness. Analysis of the surface microstructure gave a good insight into the mechanism material removal process involving initial and evolved damage. Also, the waterjet peening process was optimized based on the design of experiment approach. The developed empirical models had shown reasonable correlations between the measured and predicted responses. A proper selection of waterjet peening parameters can be formulated to be used in practical works.

- Solid-Solid Phase Transitions in Iron Systems (2014)
- In the present work, the phase transitions in different Fe/FeC systems were studied by using the molecular dynamics simulation and the Meyer-Entel interaction potential (also the Johnson potential for Fe-C interaction). Fe-bicrystal, thin film, Fe-C bulk and Fe-C nanowire systems were investigated to study the behaviour of the phase transition, where the energetics, dynamics and transformations pathways were analysed.

- Continuum Mechanical Modeling of Dry Granular Systems: From Dilute Flow to Solid-Like Behavior (2014)
- In this thesis, we develop a granular hydrodynamic model which covers the three principal regimes observed in granular systems, i.e. the dilute flow, the dense flow and the solid-like regime. We start from a kinetic model valid at low density and extend its validity to the granular solid-like behavior. Analytical and numerical results show that this model reproduces a lot of complex phenomena like for instance slow viscoplastic motion, critical states and the pressure dip in sand piles. Finally we formulate a 1D version of the full model and develop a numerical method to solve it. We present two numerical examples, a filling simulation and the flow on an inclined plane where the three regimes are included.

- Sound Simulation and Visualization in virtual Manufacturing Systems (2013)
- The noise issue in manufacturing system is widely discussed from legal and health aspects. Regarding the existing laws and guidelines, various investigation methods are implemented in industry. The sound pressure level can be measured and reduced by using established approaches in reality. However, a straightforward and low cost approach to study noise issue using existing digital factory models is not found. This thesis attempts to develop a novel concept for sound pressure level investigation in a virtual environment. With this, the factory planners are able to investigate the noise issue during factory design and layout planning phase. Two computer aided tools are used in this approach: acoustic simulation and virtual reality (VR). The former enables the planner to simulate the sound pressure level by given factory layout and facility sound features. And the latter provides a visualization environment to view and explore the simulation results. The combination of these two powerful tools provides the planners a new possibility to analyze the noise in a factory. To validate the simulations, the acoustic measurements are implemented in a real factory. Sound pressure level and sound intensity are determined respectively. Furthermore, a software tool is implemented using the introduced concept and approach. With this software, the simulation results are represented in a Cave Automatic Virtual Environment (CAVE). This thesis describes the development of the approach, the measurement of sound features, the design of visualization framework, and the implementation of VR software. Based on this know-how, the industry users are able to design their own method and software for noise investigation and analysis.

- Analysis of Off-Road Tire-Soil Interaction through Analytical and Finite Element Methods (2013)
- Tire-soil interaction is important for the performance of off-road vehicles and the soil compaction in the agricultural field. With an analytical model, which is integrated in multibody-simulation software, and a Finite Element model, the forces and moments generated on the tire-soil contact patch were studied to analyze the tire performance. Simulations with these two models for different tire operating conditions were performed to evaluate the mechanical behaviors of an excavator tire. For the FE model validation a single wheel tester connected to an excavator arm was designed. Field tests were carried out to examine the tire vertical stiffness, the contact pressure on the tire – hard ground interface, the longitudinal/vertical force and the compaction of the sandy clay from the test field under specified operating conditions. The simulation and experimental results were compared to evaluate the model quality. The Magic Formula was used to fit the curves of longitudinal and lateral forces. A simplified tire-soil interaction model based on the fitted Magic Formula could be established and further applied to the simulation of vehicle-soil interaction.

- Computational Fluid Dynamics Aided Design of Stirred Liquid-Liquid Extraction Columns (2013)
- Aim of this work was the extension and development of a coupled Computational Fluid Dynamics (CFD) and population balance model (PBM) solver to enable a simulation aided design of stirred liquid-liquid extraction columns. The principle idea is to develop a new design methodology based on a CFD-PBM approach and verify it with existing data and correlations. On this basis, the separation performance in any apparatus geometry should be possible to predict without any experimental input. Reliable “experiments in silico” (computer calculations) should give the engineer a valuable and user-friendly tool for early design studies at minimal costs. The layout of extraction columns is currently based on experimental investigations from miniplant to pilot plant and a scale-up to the industrial scale. The hydrodynamic properties can be varied by geometrical adjustments of the stirrer diameter, the stirrer height, the free cross sectional area of the stator, the compartment height as well as the positioning and the size of additional baffles. The key parameter for the liquid–liquid extraction is the yield which is mainly determined at the in- and outlets of the column. Local phenomena as the swirl structure are influenced by geometry changes. However, these local phenomena are generally neglected in state-of-the are design methodologies due to the complex required measurement techniques. A geometrical optimization of the column therefore still results in costs for validation experiments as assembly and operation of the column, which can be reduced by numerical investigations. The still mainly in academics used simulation based layout of counter-current extraction columns is based at the beginning of this work on one dimensional simulations of extraction columns and first three dimensional simulations. The one dimensional simulations are based on experimental derived, geometrical dependent correlations for the axial backmixing (axial dispersion), the hold-up, the phase fraction, the droplet sedimentation and the energy dissipation. A combination of these models with droplet population balance modeling resulted in a description of the complex droplet-droplet interactions (droplet size) along the column height. The three dimensional CFD simulations give local information about the flow field (velocity, swirl structure) based on the used numerical mesh corresponding to the real geometry. A coupling of CFD with population balance modeling further provides information about the local droplet size. A backcoupling of the droplet size with the CFD (drag model) results in an enhancement of the local hydrodynamics (e.g. hold-up, dispersed phase velocity). CFD provided local information about the axial dispersion coefficient of simple geometrical design (e.g. Rotating Disc Contactor (RDC) column). First simulations of the RDC column using a two dimensional rotational geometry combined with population balance modeling were performed and gave local information about the droplet size for different boundary conditions (rotational speed, different column sizes). In this work, two different column types were simulated using an extended OpenSource CFD code. The first was the RDC column, which were mainly used for code development due to its simple geometry. The Kühni DN32 column is equipped with a six-baffled stirring device and flat baffles for disturbing the flow and requires a full three dimensional description. This column type was mainly used for experimental validation of the simulations due to the low required volumetric flow rate. The Kühni DN60 column is similar to the Kühni DN32 column with slight changes to the stirring device (4-baffles) and was used for scale up investigations. For the experimental validation of the hydrodynamics, laser based measurement techniques as Particle Image Velocimetry (PIV) and Laser Induced Fluorescence (LIF) were used. A good agreement between the experimental derived values for velocity, hold-up and energy dissipation, experimentally derived correlations from literature and the simulations with a modified Euler-Euler based OpenSource CFD code could be found. The experimental derived axial dispersion coefficient was further compared to Euler-Lagrange simulations. The experimental derived correlations for the Kühni DN32 in literature fit to the simulated values. Also the axial dispersion coefficient for the dispersed phase satisfied a correlation from literature. However, due to the complexity of the dispersed phase axial dispersion coefficient measurement, the available correlations gave no distinct agreement to each other. A coupling of the modified Euler-Euler OpenSource CFD code was done with a one group population balance model. The implementation was validated to the analytical solution of the population balance equation for constant breakage and coalescence kernels. A further validation of the population balance transport equation was done by comparing the results of a five compartment section to the results of the commercial CFD code FLUENT using the Quadrature Method of Moments (QMOM). For the simulation of the droplet-droplet interactions in liquid-liquid extraction columns, several breakage and coalescence models are available in the literature. The models were compared to each other using the one-group population balance model in Matlab which allows the determination of the minimum stable droplet diameter at a certain energy dissipation. Based on this representation, it was possible to determine the parameters for a specific breakage and coalescence model combination which allowed the simulation of a Kühni miniplant column at different rotational speeds. The resulting simulated droplet size was in very good agreement to the experimental derived droplet size from literature. Several column designs of the DN32 were investigated by changing the compartment height and the axial stirrer position. It could be shown that a decrease of the stirrer position increases the phase fraction inside the compartment. At the same time, the droplet size decreases inside the compartment, which allows a higher mass transfer due to a higher available interfacial area. However, the shifting results in an expected earlier flooding of the column due to a compressed flow structure underneath the stirring device. In a next step, the code was further extended by mass transfer equations based on the two-film theory. Mass transfer coefficient models for the dispersed and continuous phase were investigated for the RDC column design. A first mass transfer simulation of a full miniplant column was done. The change in concentration was accounted by the mixture density, viscosity and interfacial tension in dependence of the concentration, which affects the calculation of the droplet size. The results of the column simulation were compared to own experimental data of the column. It could be shown that the concentration profile along the column height can be predicted by the presented CFD/population balance/mass transfer code. The droplet size decreases corresponding to the interfacial tension along the column height. Compared to the experimental derived droplet size at the outlet, the simulation is in good agreement. Besides the occurrence of a mono dispersed droplet size, high breakage may lead to the generation of small satellite droplets and coalescence underneath the stator leads to larger droplets inside the column and hence to a change of the hold-up and of the flooding point. A multi-phase code was extended by the Sectional Quadrature Method of Moment (SQMOM) allowing a modeling of the droplet interactions of bimodal droplet interactions or multimodal distributions. The implementations were in good agreement to the analytical solution. In addition, the simulation of an RDC column section showed the different distribution of the smaller droplets and larger droplets. The smaller droplets tend to follow the continuous phase flow structure and show a higher distribution of inside the column. The larger droplets tend to rise directly through the column and show only a low influence to the continuous phase flow. The current results strengthen the use of CFD for the layout of liquid-liquid extraction columns in future. The coupling of CFD/PBM and mass transfer using an OpenSource CFD code allows the investigation of computational intensive column designs (e.g. pilot plant columns). Furthermore the coupled code enhances the accuracy of the hydrodynamics simulations and leads to a better understanding of counter-current liquid-liquid extraction columns. The gained correlation were finally used as an input for one dimensional mass transfer simulations, where a perfect fit of the concentration profiles at varied boundary conditions could be obtained. By using the multi-scale approach, the computational time for mass transfer simulations could be reduced to minutes. In future, with increasing computational power, a further extend of the multiphase CFD/SQMOM model including mass transfer equation will provide an efficient tool to model multimodal and multivariate systems as bubble column reactors.

- Numerical and Analytical Investigation of a Phase Field Model for Fracture (2013)
- This thesis is concerned with a phase field model for brittle fracture. The high potential of phase field modeling in computational fracture mechanics lies in the generality of the approach and the straightforward numerical implementation, combined with a good accuracy of the results in the sense of continuum fracture mechanics. However, despite the convenient numerical application of phase field fracture models, a detailed understanding of the physical properties is crucial for a correct interpretation of the numerical results. Therefore, the driving mechanisms of crack propagation and nucleation in the proposed phase field fracture model are explored by a thorough numerical and analytical investigation in this work.

- Transient processes with hydrogels (2013)
- Hydrogels are known to be covalently or ionic cross-linked, hydrophilic three-dimensional polymer networks, which exist in our bodies in a biological gel form such as the vitreous humour that fills the interior of the eyes. Poly(N-isopropylacrylamide) (poly(NIPAAm)) hydrogels are attracting more interest in biomedical applications because, besides others, they exhibit a well-defined lower critical solution temperature (LCST) in water, around 31–34°C, which is close to the body temperature. This is considered to be of great interest in drug delivery, cell encapsulation, and tissue engineering applications. In this work, the poly(NIPAAm) hydrogel is synthesized by free radical polymerization. Hydrogel properties and the dimensional changes accompanied with the volume phase transition of the thermosensitive poly(NIPAAm) hydrogel were investigated in terms of Raman spectra, swelling ratio, and hydration. The thermal swelling/deswelling changes that occur at different equilibrium temperatures and different solutions (phenol, ethanol, propanol, and sodium chloride) based on Raman spectrum were investigated. In addition, Raman spectroscopy has been employed to evaluate the diffusion aspects of bovine serum albumin (BSA) and phenol through the poly(NIPAAm) network. The determination of the mutual diffusion coefficient, \(D_{mut}\) for hydrogels/solvent system was achieved successfully using Raman spectroscopy at different solute concentrations. Moreover, the mechanical properties of the hydrogel, which were investigated by uniaxial compression tests, were used to characterize the hydrogel and to determine the collective diffusion coefficient through the hydrogel. The solute release coupled with shrinking of the hydrogel particles was modelled with a bi-dimensional diffusion model with moving boundary conditions. The influence of the variable diffusion coefficient is observed and leads to a better description of the kinetic curve in the case of important deformation around the LCST. A good accordance between experimental and calculated data was obtained.

- Dynamic Modelling and Simulation of (Pulsed and Stirred) Liquid-Liquid Extraction Columns using the Population Balance Equation (2012)
- The discrete nature of the dispersed phase (swarm of droplet) in stirred and pulsed liquid-liquid extraction columns makes its mathematical modelling of such complex system a tedious task. The dispersed phase is considered as a population of droplets distributed randomly with respect to their internal properties (such as: droplet size and solute concentration) at a specific location in space. Hence, the population balance equation has been emerged as a mathematical tool to model and describe such complex behaviour. However, the resulting model is too complicated. Accordingly, the analytical solution of such a mathematical model does not exist except for particular cases. Therefore, numerical solutions are resorted to in general. This is due to the inherent nonlinearities in the convective and diffusive terms as well as the appearance of many integrals in the source term. However, modelling and simulation of liquid extraction columns is not an easy task because of the discrete nature of the dispersed phase, which consist of population of droplets. The natural frame work for taking this into account is the population balance approach. In part of this doctoral thesis work, a rigours mathematical model based on the bivariate population balance frame work (the base of LLECMOD ‘‘Liquid-Liquid Extraction Column Module’’) for the steady state and dynamic simulation of pulsed (sieve plate and packed) liquid-liquid extraction columns is developed. The model simulates the coupled hydrodynamic and mass transfer for pulsed (packed and sieve plate) extraction columns. The model is programmed using visual digital FORTRAN and then integrated into the LLECMOD program. Within LLECMOD the user can simulate different types of extraction columns including stirred and pulsed ones. The basis of LLECMOD depends on stable robust numerical algorithms based on an extended version of a fixed pivot technique after Attarakih et al., 2003 (to take into account interphase solute transfer) and advanced computational fluid dynamics numerical methods. Experimental validated correlations are used for the estimation of the droplet terminal velocity in extraction columns based on single and swarm droplet experiments in laboratory scale devices. Additionally, recent published correlations for turbulent energy dissipation, droplet breakage and coalescence frequencies are discussed as been used in this version of LLECMOD. Moreover, coalescence model from literature derived from a stochastical description have been modified to fit the deterministic population model. As a case study, LLECMOD is used here to simulate the steady state performance of pulsed extraction columns under different operating conditions, which include pulsation intensity and volumetric flow rates are simulated. The effect of pulsation intensity (on the holdup, mean droplet diameter and solute concentration) is found to have more profound effect on systems of high interfacial tension. On the hand, the variation of volumetric flow rates have substantial effect on the holdup, mean droplet diameter and solute concentration profiles for chemical systems with low interfacial tension. Two chemical test systems recommended by the European Federation of Chemical Engineering (water-acetone (solute)-n-butyl acetate and water-acetone (solute)-toluene) and an industrial test system are used in the simulation. Model predictions are successfully validated against steady state and transient experimental data, where good agreements are achieved. The simulated results (holdup, mean droplet diameter and mass transfer profiles) compared to the experimental data show that LLECMOD is a powerful simulation tool, which can efficiently predict the dynamic and steady state performance of pulsed extraction columns. In other part of this doctoral thesis work, the steady state performance of extraction columns is studied taking into account the effect of dispersed phase inlet condition (light or heavy phase is dispersed) and the direction of mass transfer (from continuous to dispersed phase and vice versa) using the population balance framework. LLECMOD, a program that uses multivariate population balance models, is extended to take into account the direction of mass transfer and the dispersed phase inlet. As a case study, LLECMOD is used to simulate pilot plant RDC columns where the steady state mean flow properties (dispersed phase hold up and droplet mean diameter) and the solute concentration profiles are compared to the available experimental data. Three chemical systems were used: sulpholane–benzene–n-heptane, water–acetone–toluene and water–acetone–n-butyl acetate. The dispersed phase inlet and the direction of mass transfer as well as the chemical system physical properties are found to have profound effect on the steady state performance of the RDC column. For example, the mean droplet diameter is found to persist invariant when the heavy phase is dispersed and the extractor efficiency is higher when the direction of mass transfer is from the continuous to the dispersed phase. For the purpose of experimental validation, it is found that LLECMOD predictions are in good agreement with the available experimental data concerning the dispersed phase hold up, mean droplet diameter and solute concentration profiles in both phases. In a further part of this doctoral thesis, a mathematical model is developed for liquid extraction columns based on the multivariate population balance equation (PBE) and the primary secondary particle method (PSPM) introduced by Attarakih, 2010 (US Patent Application: 0100106467). It is extended to include the momentum balance for the dispersed phase. The advantage of momentum balance is to eliminate the need for often conflicting correlations used in estimating the terminal velocity of single and swarm of droplets. The resulting mathematical model is complex due to the integral nature of the population balance equation. To reduce the complexity of this model, while maintaining most of the information drawn from the continuous population balance equation, the concept of the PSPM is used. Based on the multivariate population balance equation and the PSPM a mathematical model is developed for any liquid extraction column. The secondary particle could be envisaged as a fluid particle carrying information about the distribution as it is evolved in space and time, in the meanwhile the primary particles carry the mean properties of the population such as total droplet concentration; mean droplet diameter dispersed phase hold up and so on. This information reflects the particle-particle interactions (breakage and coalescence) and transport (convection and diffusion). The developed model is discretized in space using a first-order upwind method, while semi-implicit first-order scheme in time is used to simulate a pilot plant RDC extraction column. Here the effect of the number of primary particles (classes) on the final predicted solution is investigated. Numerical results show that the solution converge fast even as the number of primary particle is increased. The terminal droplet velocity of the individual primary particle is found the most sensitive to the number of primary particles. Other mean population properties like the droplet mean diameter, mean hold up and the concentration profiles are also found to converge along the column height by increasing the number of primary particles. The predicted steady state profiles (droplet diameter, holdup and the concentration profiles) along a pilot RDC extraction column are compared to the experimental data where good agreement is achieved. In addition to this a robust rigorous mathematical model based on the bivariate population balance equation is developed to predict the steady state and dynamic behaviour of the interacting hydrodynamics and mass transfer in Kühni extraction columns. The developed model is extended to include the momentum balance for the calculation of the droplet velocity. The effects of step changes in the important input variables (such as volumetric flow rates, rotational speed, inlet solute concentrations etc.) on the output variables (dispersed phase holdup, mean droplet diameter and the concentration profiles) are investigated. The last topic of this doctoral thesis is developed to transient problems. The unsteady state analysis reveals the fact that the largest time constant (slowest response) is due to the mass transfer. On the contrary, the hydrodynamic response of the dispersed phase holdup is very fast when compared to the mass transfer due to the relative fast motion of the dispersed droplets with respect to the continuous phase. The dynamic behaviour of the dispersed and continuous phases shows a lag time that increases away from the feed points of both phases. Moreover, the solute concentration response shows a highly nonlinear behaviour due to both positive and negative step changes in the input variables. The simulation results are in good agreement with the experimental ones and show the usefulness of the model.