## Fachbereich Maschinenbau und Verfahrenstechnik

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- Wetting of Structured Packing Elements - CFD and Experiment (2006)
- Wetting of a solid surface with liquids is an important parameter in the chemical engineering process such as distillation, absorption and desorption. The degree of wetting in packed columns mainly contributes in the generating of the effective interfacial area and then enhancing of the heat and mass transfer process. In this work the wetting of solid surfaces was studied in real experimental work and virtually through three dimensional CFD simulations using the multiphase flow VOF model implemented in the commercial software FLUENT. That can be used to simulate the stratified flows [1]. The liquid rivulet flow which is a special case of the film flow and mostly found in packed columns has been discussed. Wetting of a solid flat and wavy metal plate with rivulet liquid flow was simulated and experimentally validated. The local rivulet thickness was measured using an optically assisted mechanical sensor using a needle which is moved perpendicular to the plate surface with a step motor and in the other two directions using two micrometers. The measured and simulated rivulet profiles were compared to some selected theoretical models founded in the literature such as Duffy & Muffatt [2], Towell & Rothfeld [3] and Al-Khalil et al. [4]. The velocity field in a cross section of a rivulet flow and the non-dimensional maximum and mean velocity values for the vertical flat plate was also compared with models from Al-Khalil et al. [4] and Allen & Biggin [5]. Few CFD simulations for the wavy plate case were compared to the experimental findings, and the Towel model for a flat plate [3]. In the second stage of this work 3-D CFD simulations and experimental study has been performed for wetting of a structured packing element and packing sheet consisting of three elements from the type Rombopak 4M, which is a product of the company Kuhni, Switzerland. The hydrodynamics parameters of a packed column, e. i. the degree of wetting, the interfacial area and liquid hold-up have been depicted from the CFD simulations for different liquid systems and liquid loads. Flow patterns on the degree of wetting have been compared to that of the experiments, where the experimental values for the degree of wetting were estimated from the snap shooting of the flow on the packing sheet in a test rig. A new model to describe the hydrodynamics of packed columns equipped with Rombopak 4M was derived with help of the CFD–simulation results. The model predicts the degree of wetting, the specific or interfacial area and liquid hold-up at different flow conditions. This model was compared to Billet & Schultes [6], the SRP model Rocha et al. [7-9], to Shi & Mersmann [10] and others. Since the pressure drop is one of the most important parameter in packed columns especially for vacuum operating columns, few CFD simulations were performed to estimate the dry pressure drop in a structured and flat packing element and were compared to the experimental results. It was found a good agreement from one side, between the experimental and the CFD simulation results, and from the other side between the simulations and theoretical models for the rivulet flow on an inclined plate. The flow patterns and liquid spreading behaviour on the packing element agrees well with the experimental results. The VOF (Volume of Fluid) was found very sensitive to different liquid properties and can be used in optimization of the packing geometries and revealing critical details of wetting and film flow. An extension of this work to perform CFD simulations for the flow inside a block of the packing to get a detailed picture about the interaction between the liquid and packing surfaces is recommended as further perspective.

- Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework (2014)
- This work presents a framework for the computation of complex geometries containing intersections of multiple patches with Reissner-Mindlin shell elements. The main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization, nor user interaction to quantify the number of rotational degrees of freedom for every node. For this purpose, the following set of methods is presented. Control points with corresponding physical location are assigned to one common node for the finite element solution. A nodal basis system in every control point is defined, which ensures an exact interpolation of the director vector throughout the whole domain. A distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented. An isogeometric Reissner-Mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches. The parametrization of adjacent patches along the interface has to be conforming. The shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector. The nonlinear kinematic allows the computation of large deformations and large rotations. Two concepts for the description of rotations are presented. The first one uses an interpolation which is commonly used in standard Lagrange-based shell element formulations. The second scheme uses a more elaborate concept proposed by the authors in prior work, which increases the accuracy for arbitrary curved geometries. Numerical examples show the high accuracy and robustness of both concepts. The applicability of the proposed framework is demonstrated.

- 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.

- Towards Material Modelling within Continuum-Atomistics (2006)
- With the burgeoning computing power available, multiscale modelling and simulation has these days become increasingly capable of capturing the details of physical processes on different scales. The mechanical behavior of solids is oftentimes the result of interaction between multiple spatial and temporal scales at different levels and hence it is a typical phenomena of interest exhibiting multiscale characteristic. At the most basic level, properties of solids can be attributed to atomic interactions and crystal structure that can be described on nano scale. Mechanical properties at the macro scale are modeled using continuum mechanics for which we mention stresses and strains. Continuum models, however they offer an efficient way of studying material properties they are not accurate enough and lack microstructural information behind the microscopic mechanics that cause the material to behave in a way it does. Atomistic models are concerned with phenomenon at the level of lattice thereby allowing investigation of detailed crystalline and defect structures, and yet the length scales of interest are inevitably far beyond the reach of full atomistic computation and is rohibitively expensive. This makes it necessary the need for multiscale models. The bottom line and a possible avenue to this end is, coupling different length scales, the continuum and the atomistics in accordance with standard procedures. This is done by recourse to the Cauchy-Born rule and in so doing, we aim at a model that is efficient and reasonably accurate in mimicking physical behaviors observed in nature or laboratory. In this work, we focus on concurrent coupling based on energetic formulations that links the continuum to atomistics. At the atomic scale, we describe deformation of the solid by the displaced positions of atoms that make up the solid and at the continuum level deformation of the solid is described by the displacement field that minimize the total energy. In the coupled model, continuum-atomistic, a continuum formulation is retained as the overall framework of the problem and the atomistic feature is introduced by way of constitutive description, with the Cauchy-Born rule establishing the point of contact. The entire formulation is made in the framework of nonlinear elasticity and all the simulations are carried out within the confines of quasistatic settings. The model gives direct account to measurable features of microstructures developed by crystals through sequential lamination.

- Thermo-Mechanical Modelling of Solids and Interfaces -Theory, Numerics and Applications (2007)
- In the present work the modelling and numerical treatment of discontinuities in thermo-mechanical solids is investigated and applied to diverse physical problems. From this topic a structure for this work results, which considers the formulation of thermo-mechanical processes in continua in the first part and which forms the mechanical and thermodynamical framework for the description of discontinuities and interfaces, that is performed in the second part. The representation of the modelling of solid materials bases on the detailed derivation of geometrically nonlinear kinematics, that yields different strain and stress measures for the material and spatial configuration. Accordingly, this results in different formulations of the mechanical and thermodynamical balance equations. On these foundations we firstly derive by means of the concepts of the plasticity theory an elasto-plastic prototype-model, that is extended subsequently. In the centre of interest is the formulation of damage models in consideration of rate-dependent material behaviour. In the next step follows the extension of the isothermal material models to thermo-mechanically coupled problems, whereby also the special case of adiabatic processes is discussed. Within the representation of the different constitutive laws, the importance is attached to their modular structure. Moreover, a detailed discussion of the isothermal and the thermo-mechanically coupled problem with respect to their numerical treatment is performed. For this purpose the weak forms with respect to the different configurations and the corresponding linearizations are derived and discretized. The derived material models are highlighted by numerical examples and also proved with respect to plausibility. In order to take discontinuities into account appropriate kinematics are introduced and the mechanical and thermodynamical balance equations have to be modified correspondingly. The numerical description is accomplished by so-called interface-elements, which are based on an adequate discretization. In this context two application fields are distinguished. On the one side the interface elements provide a tool for the description of postcritical processes in the framework of localization problems, which include material separation and therefore they are appropriate for the description of cutting processes. Here in turn one has to make the difference between the domain-dependent and the domain-independent formulation, which mainly differ in the definition of the interfacial strain measure. On the other side material properties are attached to the interfaces whereas the spatial extension is neglectable. A typical application of this type of discontinuities can be found in the scope of the modelling of composites, for instance. In both applications the corresponding thermo-mechanical formulations are derived. Finally, the different interface formulations are highlighted by some numerical examples and they are also proved with respect to plausibility.

- Theory and numerics of three-dimensional strong discontinuities at finite strains (2009)
- Within this thesis we present a novel approach towards the modeling of strong discontinuities in a three dimensional finite element framework for large deformations. This novel finite element framework is modularly constructed containing three essential parts: (i) the bulk problem, ii) the cohesive interface problem and iii) the crack tracking problem. Within this modular design, chapter 2 (Continuous solid mechanics) treats the behavior of the bulk problem (i). It includes the overall description of the continuous kinematics, the required balance equations, the constitutive setting and the finite element formulation with its corresponding discretization and required solution strategy for the emerging highly non-linear equations. Subsequently, we discuss the modeling of strong discontinuities within finite element discretization schemes in chapter 3 (Discontinuous solid mechanics). Starting with an extension of the continuous kinematics to the discontinuous situation, we discuss the phantom-node discretization scheme based on the works of Hansbo & Hansbo. Thereby, in addition to a comparison with the extended finite element method (XFEM), importance is attached to the technical details for the adaptive introduction of the required discontinuous elements: The splitting of finite elements, the numerical integration, the visualization and the formulation of geometrical correct crack tip elements. In chapter 4 (The cohesive crack concept), we consider the treatment of cohesive process zones and the associated treatment of cohesive tractions. By applying this approach we are able to merge all irreversible, crack propagation accompanying, failure mechanisms into an arbitrary traction separation relation. Additionally, this concept ensures bounded crack tip stresses and allows the use of stress-based failure criteria for the determination of crack growth. In summary, the use of the discontinuous elements in conjunction with cohesive traction separation allows the mesh-independent computation of crack propagation along pre-defined crack paths. Therefore, this combination is defined as the interface problem (ii) and represents the next building block in the modular design of this thesis. The description and the computation of the evolving crack surface, based on the actual status of a considered specimen is the key issue of chapter 5 (Crack path tracking strategies). In contrast to the two-dimensional case, where tracking the path in a C0-continuous way is straightforward, three-dimensional crack path tracking requires additional strategies. We discuss the currently available approaches regarding this issue and further compare the approaches by means of usual quality measures. In the modular design of this thesis these algorithms represent the last main part which is classified as the crack tracking problem (iii). Finally chapter 6 (Representative numerical examples) verifies the finite element tool by comparisons of the computational results which experiments and benchmarks of engineering fracture problems in concrete. Afterwards the finite element tool is applied to model folding induced fracture of geological structures.

- Theory and Numerics of Open System Thermodynamics (2004)
- A general framework for the thermodynamics of open systems is developed in the spatial and the material setting. Special emphasis is placed on the balance of mass which is enhanced by additional source and flux terms. Different solution strategies within the finite element technique are derived and compared. A number of numerical examples illustrates the features of the proposed approach.

- Theory and numerics of non-classical thermo-hyperelasticity (2007)
- Thermoelasticity represents the fusion of the fields of heat conduction and elasticity in solids and is usually characterized by a twofold coupling. Thermally induced stresses can be determined as well as temperature changes caused by deformations. Studying the mutual influence is subject of thermoelasticity. Usually, heat conduction in solids is based on Fourier’s law which describes a diffusive process. It predicts unnatural infinite transmission speed for parts of local heat pulses. At room temperature, for example, these parts are strongly damped. Thus, in these cases most engineering applications are described satisfactorily by the classical theory. However, in some situations the predictions according to Fourier’s law fail miserable. One of these situations occurs at temperatures near absolute zero, where the phenomenon of second sound1 was discovered in the 20th century. Consequently, non-classical theories experienced great research interest during the recent decades. Throughout this thesis, the expression “non-classical” refers to the fact that the constitutive equation of the heat flux is not based on Fourier’s law. Fourier’s classical theory hypothesizes that the heat flux is proportional to the temperature gradient. A new thermoelastic theory, on the one hand, needs to be consistent with classical thermoelastodynamics and, on the other hand, needs to describe second sound accurately. Hence, during the second half of the last century the traditional parabolic heat equation was replaced by a hyperbolic one. Its coupling with elasticity leads to non-classical thermomechanics which allows the modeling of second sound, provides a passage to the classical theory and additionally overcomes the paradox of infinite wave speed. Although much effort is put into non-classical theories, the thermoelastodynamic community has not yet agreed on one approach and a systematic research is going on worldwide.Computational methods play an important role for solving thermoelastic problems in engineering sciences. Usually this is due to the complex structure of the equations at hand. This thesis aims at establishing a basic theory and numerical treatment of non-classical thermoelasticity (rather than dealing with special cases). The finite element method is already widely accepted in the field of structural solid mechanics and enjoys a growing significance in thermal analyses. This approach resorts to a finite element method in space as well as in time.

- Theory and numerics of higher gradient inelastic material behavior (2003)
- The goal of this thesis is a physically motivated and thermodynamically consistent formulation of higher gradient inelastic material behavior. Thereby, the influence of the material microstructure is incorporated. Next to theoretical aspects, the thesis is complemented with the algorithmic treatment and numerical implementation of the derived model. Hereby, two major inelastic effects will be addressed: on the one hand elasto-plastic processes and on the other hand damage mechanisms, which will both be modeled within a continuum mechanics framework.

- The weak substitution method – An application of the mortar method for patch coupling in NURBS-based isogeometric analysis (2015)
- In this contribution a mortar-type method for the coupling of non-conforming NURBS surface patches is proposed. The connection of non-conforming patches with shared degrees of freedom requires mutual refinement, which propagates throughout the whole patch due to the tensor-product structure of NURBS surfaces. Thus, methods to handle non-conforming meshes are essential in NURBS-based isogeometric analysis. The main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation. The deformations of the interface control points of adjacent patches are interrelated with a master-slave relation. This relation is established numerically using the weak form of the equality of mutual deformations along the interface. With the help of this relation the interface degrees of freedom of the slave patch can be condensated out of the system. A natural connection of the patches is attained without additional terms in the weak form. The proposed method is also applicable for nonlinear computations without further measures. Linear and geometrical nonlinear examples show the high accuracy and robustness of the new method. A comparison to reference results and to computations with the Lagrange multiplier method is given.