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Fri, 16 Sep 2016 12:50:46 +0200Fri, 16 Sep 2016 12:50:46 +0200Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4448
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.
Wolfgang Dornisch; Sven Klinkelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4448Fri, 16 Sep 2016 12:50:46 +0200Isogeometric Reissner–Mindlin shell analysis with exactly calculated director vectors
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4447
An isogeometric Reissner-Mindlin shell derived from the continuum theory is presented. The geometry is described by NURBS surfaces. The kinematic description of the employed shell theory requires the interpolation of the director vector and of a local basis system. Hence, the definition of nodal basis systems at the control points is necessary for the proposed formulation. The control points are in general not located on the shell reference surface and thus, several choices for the nodal values are possible. The proposed new method uses the higher continuity of the geometrical description to calculate nodal basis system and director vectors which lead to geometrical exact interpolated values thereof. Thus, the initial director vector coincides with the normal vector even for the coarsest mesh. In addition to that a more accurate interpolation of the current director and its variation is proposed. Instead of the interpolation of nodal director vectors the new approach interpolates nodal rotations. Account is taken for the discrepancy between interpolated basis systems and the individual nodal basis systems with an additional transformation. The exact evaluation of the initial director vector along with the interpolation of the nodal rotations lead to a shell formulation which yields precise results even for coarse meshes. The convergence behavior is shown to be correct for k-refinement allowing the use of coarse meshes with high orders of NURBS basis functions. This is potentially advantageous for applications with high numerical effort per integration point. The geometrically nonlinear formulation accounts for large rotations. The consistent tangent matrix is derived. Various standard benchmark examples show the superior accuracy of the presented shell formulation. A new benchmark designed to test the convergence behavior for free form surfaces is presented. Despite the higher numerical effort per integration point the improved accuracy yields considerable savings in computation cost for a predefined error bound.
Wolfgang Dornisch; Sven Klinkel; Bernd Simeonpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4447Mon, 12 Sep 2016 10:12:58 +0200The weak substitution method – An application of the mortar method for patch coupling in NURBS-based isogeometric analysis
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4436
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.Wolfgang Dornisch; Gennaro Vitucci; Sven Klinkelpreprinthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4436Fri, 09 Sep 2016 08:57:48 +0200A Phase Field Model for the Evolution of Martensite Microstructures in Metastable Austenites
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4438
This thesis is concerned with a phase field model for martensitic transformations in metastable austenitic steels. Within the phase field approach an order parameter is introduced to indicate whether the present phase is austenite or martensite. The evolving microstructure is described by the evolution of the order parameter, which is assumed to follow the time-dependent Ginzburg-Landau equation. The elastic phase field model is enhanced in two different ways to take further phenomena into account. First, dislocation movement is considered by a crystal plasticity setting. Second, the elastic model for martensitic transformations is combined with a phase field model for fracture. Finite element simulations are used to study the single effects separately which contribute to the microstructure formation.Regina Müllerdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4438Tue, 06 Sep 2016 17:37:25 +0200Morphology and Morphology Formation of Injection Molded PP-based Nanocomposites
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4433
The mechanical properties of semi-crystalline polymers depend extremely on their
morphology, which is dependent on the crystallization during processing. The aim of
this research is to determine the effect of various nanoparticles on morphology
formation and tensile mechanical properties of polypropylene under conditions
relevant in polymer processing and to contribute ultimately to the understanding of
this influence.
Based on the thermal analyses of samples during fast cooling, it is found that the
presence of nanoparticle enhances the overall crystallization process of PP. The results
suggest that an increase of the nucleation density/rate is a dominant process that
controls the crystallization process of PP in this work, which can help to reduce the
cycle time in the injection process. Moreover, the analysis of melting behaviors
obtained after each undercooling reveals that crystal perfection increases significantly
with the incorporation of TiO2 nanoparticles, while it is not influenced by the SiO2
nanoparticles.
This work also comprises an analysis of the influence of nanoparticles on the
microstructure of injection-molded parts. The results clearly show multi-layers along
the wall thickness. The spherulite size and the degree of crystallinity continuously
decrease from the center to the edge. Generally both the spherulite size and the degree
of crystallinity decrease with higher the SiO2 loading. In contrast, an increase in the
degree of crystallinity with an increasing TiO2 nanoparticle loading was detected.
The tensile properties exhibit a tendency to increase in the tensile strength as the core
is reached. The tensile strength decreases with the addition of nanoparticles, while the
elongation at break of nanoparticle-filled PP decreases from the skin to the core. With
increasing TiO2 loading, the elongation at break decreases.Buncha Suksutdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4433Thu, 25 Aug 2016 09:19:31 +0200Development of nano/micro hybrid susceptor sheet for induction heating applications
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4405
Thermoplastic composite materials are being widely used in the automotive and aerospace industries. Due to the limitations of shape complexity, different components
need to be joined. They can be joined by mechanical fasteners, adhesive bonding or
both. However, these methods have several limitations. Components can be joined
by fusion bonding due to the property of thermoplastics. Thermoplastics can be melted on heating and regain their shape on cooling. This property makes them ideal for
joining through fusion bonding by induction heating. Joining of non-conducting or
non-magnetic thermoplastic composites needs an additional material that can generate heat by induction heating.
Polymers are neither conductive nor electromagnetic so they don’t have inherent potential for inductive heating. A susceptor sheet having conductive materials (e.g. carbon fiber) or magnetic materials (e.g. nickel) can generate heat during induction. The
main issues related with induction heating are non-homogeneous and uncontrolled
heating.
In this work, it was observed that to generate heat with a susceptor sheet depends
on its filler, its concentration, and its dispersion. It also depends on the coil, magnetic
field strength and coupling distance. The combination of different fillers not only increased the heating rate but also changed the heating mechanism. Heating of 40ºC/
sec was achieved with 15wt.-% nickel coated short carbon fibers and 3wt.-% multiwalled carbon nanotubes. However, only nickel coated short carbon fibers (15wt-.%)
attained the heating rate of 24ºC/ sec. In this study, electrical conductivity, thermal
conductivity and magnetic properties testing were also performed. The results also
showed that electrical percolation was achieved around 15wt.-% in fibers and (13-
6)wt.-% with hybrid fillers. Induction heating tests were also performed by making
parallel and perpendicular susceptor sheet as fibers were uni-directionally aligned.
The susceptor sheet was also tested by making perforations.
The susceptor sheet showed homogeneous and fast heating, and can be used for
joining of non-conductive or non-magnetic thermoplastic composites.Muhammad Muddassirdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4405Thu, 30 Jun 2016 13:47:41 +0200Centimeter-Level Accuracy Path Tracking Control of Tractors and Actively Steered Implements
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4401
Accurate path tracking control of tractors became a key technology for automation in agriculture. Increasingly sophisticated solutions, however, revealed that accurate path tracking control of implements is at least equally important. Therefore, this work focuses on accurate path tracking control of both tractors and implements. The latter, as a prerequisite for improved control, are equipped with steering actuators like steerable wheels or a steerable drawbar, i.e. the implements are actively steered. This work contributes both new plant models and new control approaches for those kinds of tractor-implement combinations. Plant models comprise dynamic vehicle models accounting for forces and moments causing the vehicle motion as well as simplified kinematic descriptions. All models have been derived in a systematic and automated manner to allow for variants of implements and actuator combinations. Path tracking controller design begins with a comprehensive overview and discussion of existing approaches in related domains. Two new approaches have been proposed combining the systematic setup and tuning of a Linear-Quadratic-Regulator with the simplicity of a static output feedback approximation. The first approach ensures accurate path tracking on slopes and curves by including integral control for a selection of controlled variables. The second approach, instead, ensures this by adding disturbance feedforward control based on side-slip estimation using a non-linear kinematic plant model and an Extended Kalman Filter. For both approaches a feedforward control approach for curved path tracking has been newly derived. In addition, a straightforward extension of control accounting for the implement orientation has been developed. All control approaches have been validated in simulations and experiments carried out with a mid-size tractor and a custom built demonstrator implement. Roland Wernerdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4401Wed, 22 Jun 2016 11:18:09 +0200Evaluation of whole-body vibrations and improvement of the driver’s seat performance on a compact wheel loader
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4265
Whole-body vibrations (WBV) have adverse effects on ride comfort and human health. Suspension seats have an important influence on the WBV severity. In this study, WBV were measured on a medium-sized compact wheel loader (CWL) in its typical operations. The effect of short-term exposure to the WBV on the ride comfort was evaluated according to ISO 2631-1:1985 and ISO 2631-1:1997. ISO 2631-1:1997 and ISO 2631-5:2004 were adopted to evaluate the effect of long-term exposure to the WBV on the human health. Reasons for the different evaluation results obtained according to ISO 2631-1:1997 and ISO 2631-5:2004 were explained in this study. The WBV measurements were carried out in cases where the driver wore a lap belt or a four-point seat harness and in the case where the driver did not wear any safety belt. The seat effective amplitude transmissibility (SEAT) and the seat transmissibility in the frequency domain in these three cases were analyzed to investigate the effect of a safety belt on the seat transmissibility. Seat tests were performed on a multi-axis shaking table in laboratory to study the dynamic behavior of a suspension seat under the vibration excitations measured on the CWL. The WBV intensity was reduced by optimizing the vertical and the longitudinal seat suspension systems with the help of computational simulations. For the optimization multi-body models of the seat-dummy system in the laboratory seat tests and the seat-driver system in the field vibration measurements were built and validated. Xiaojing Zhaodoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4265Tue, 12 Jan 2016 15:04:57 +0100Dynamic, Continuous, and Center of Gravity Independent Weighing with a Loader
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4243
This thesis deals with the development of a tractor front loader scale which measures payload continuously, independent of the center of gravity of the payload, and unaffected of the position and movements of the loader. To achieve this, a mathematic model of a common front loader is simplified which makes it possible to identify its parameters by a repeatable and automatic procedure. By measuring accelerations as well as cylinder forces, the payload is determined continuously during the working process. Finally, a prototype was build and the scale was tested on a tractor.Frederic Ballairedoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4243Mon, 04 Jan 2016 08:35:36 +0100Fracture Mechanical Analysis of Failure Processes in Antarctic Ice Shelves
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4236
This thesis treats the application of configurational forces for the evaluation of fracture processes in Antarctic ice shelves. FE simulations are used to analyze the influence of geometric scales, material parameters and boundary conditions on single surface cracks. A break-up event at the Wilkins Ice Shelf that coincided with a major temperature drop motivates the consideration of frost wedging as a mechanism for ice shelf disintegration. An algorithm for the evaluation of the crack propagation direction is used to analyze the horizontal growth of rifts. Using equilibrium considerations for a viscoelastic fluid, a method is introduced to compute viscous volume forces from measured velocity fields as loads for a linear elastic fracture mechanical analysis.Carolin Platedoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4236Mon, 30 Nov 2015 14:32:59 +0100Computational Homogenization of Piezoelectric Materials using FE² Methods and Configurational Forces
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4174
Piezoelectric materials are electro-mechanically coupled materials. In these materials it is possible to produce an electric field by applying a mechanical load. This phenomenon is known as the piezoelectric effect. These materials also exhibit a mechanical deformation in response to an external electric loading, which is known as the inverse piezoelectric effect. By using these smart properties of piezoelectric materials, applications are possible in sensors and actuators. Ferroelectric or piezoelectric materials show switching behavior of the polarization in the material under an external loading. Due to this property, these materials are used to produce random access memory (RAM) for the non-volatile storage of data in computing devices. It is essential to understand the material responses of piezoelectric materials properly in order to use them in the engineering applications in innovative manners. Due to the growing interest in determining the material responses of smart material (e.g., piezoelectric material), computational methods are becoming increasingly important.
Many engineering materials possess inhomogeneities on the micro level. These inhomogeneities in the materials cause some difficulties in the determination of the material responses computationally as well as experimentally. But on the other hand, sometimes these inhomogeneities help the materials to render some good physical properties, e.g., glass or carbon fiber reinforced composites are light weight, but show higher strength. Piezoelectric materials also exhibit intense inhomogeneities on the micro level. These inhomogeneities are originating from the presence of domains, domain walls, grains, grain boundaries, micro cracks, etc. in the material. In order to capture the effects of the underlying microstructures on the macro quantities, it is essential to homogenize material parameters and the physical responses. There are several approaches to perform the homogenization. A two-scale classical (first-order) homogenization of electro-mechanically coupled materials using a FE²-approach is discussed in this work. The main objective of this work is to investigate the influences of the underlying micro structures on the macro Eshelby stress tensor and on the macro configurational forces. The configurational forces are determined in certain defect situations. These defect situations include the crack tip of a sharp crack in the macro specimen.
A literature review shows that the macro strain tensor is used to determine the micro boundary condition for the FE²-based homogenization in a small strain setting. This approach is capable to determine the consistent homogenized physical quantities (e.g., stress, strain) and the homogenized material quantities (e.g., stiffness tensor). But the application of these type of micro boundaries for the homogenization does not generate physically consistent macro Eshelby stress tensor or the macro configurational forces. Even in the absence of the micro volume configurational forces, this approach of the homogenization of piezoelectric materials produces unphysical volume configurational forces on the macro level. After a thorough investigation of the boundary conditions on the representative volume elements (RVEs), it is found that a displacement gradient driven micro boundary conditions remedy this issue. The use of the displacement gradient driven micro boundary conditions also satisfies the Hill-Mandel condition. The macro Eshelby stress tensor of a pure mechanical problem in a small deformation setting can be determined in two possible ways: by using the homogenized mechanical quantities (displacement gradient and stress tensor), or by homogenizing the Eshelby stress tensor on the micro level by volume averaging. The first approach does not satisfy the Hill-Mandel condition incorporating the Eshelby stress tensor in the energy term, on the other hand, the Hill-Mandel condition is satisfied in the second approach. In the case of homogenized Eshelby stress tensor determined from the homogenized physical quantities, the Hill-Mandel condition gives an additional energy term. A body in a small deformation setting is deformed according to the displacement gradient. If the homogenization is done using strain driven micro boundary conditions, the micro domain is deformed according to the macro strain, but the tiny vicinity around the corresponding Gauß point is deformed according to the macro displacement gradient. This implies that some restrictions are imposed at every Gauß point on the macro level. This situation helps the macro system to produce nonphysical volume configurational forces.
A FE²-based computational homogenization technique is also considered for the homogenization of piezoelectric materials. In this technique a representative volume element, which comprises of the micro structural features in the material, is assigned to every Gauß point of the macro domain. The macro displacement gradient and the macro electric field, or the macro stress tensor and the macro electric displacement are passed to the RVEs at every macro Gauß point. After determining boundary conditions on the RVEs, the homogenization process is performed. The homogenized physical quantities and the homogenized material parameters are passed back to macro Gauß points. In this work numerical investigations are carried out for two distinct situations of the microstructures of the piezoelectric materials regarding the evolution on the micro level: a) homogenization by using stationary microstructures, and b) homogenization by using evolving microstructures.
For the first case, the domain walls remain at fixed positions through out the simulations for the homogenization of piezoelectric materials. For a considerably large external loading, the real situation is different. But to understand the effects of the underlying microstructures on the macro configurational forces, to some extent it is sufficient to do the homogenization with fixed or stationary microstructures. The homogenization process is carried out for different microstructures and for different loading conditions. If the mechanical load is applied in the direction of the polarization, a smaller crack tip configurational force is observed in comparison to the configurational force determined for a mechanical loading perpendicular to the polarization. If the polarizations in the microstructures are parallel or perpendicular to the applied electric field and the applied displacement, configurational forces parallel to the crack ligament of the macro crack are observed only. In the case of inclined polarizations in the microstructures, configurational forces inclined to the crack ligament are obtained. The simulation results also reveal that an application of an external electric field to the material reduces the value of the nodal configurational forces at the crack tip.
In the second case, the interfaces of the micro structures are allowed to move from their initial positions at every step of the applied incremental external loading. Thus, at every step of the application of the external loading, the microstructures are changed when the external loading is larger than the coercive field. The movement of the interfaces is realized through the nodal configurational forces on the micro level. At every step of the application of the external loading, the nodal configurational forces per unit length on the domain walls are determined in the post-processing of the FE-simulation on the micro domain. With the help of the domain wall kinetics, the new positions of the domain walls are determined. Numerical results show that the crack tip region is the most affected area in the macro domain. For that reason a very different distribution of the macro electric displacement is observed comparing the same produced by using fixed microstructures. Due to the movement of the domain walls, the energy is dissipated in the system. As a result, a smaller configurational force appears at the crack tip on the macro level in the case of the homogenization by using evolving microstructures. By using the homogenization technique involving the evolution of the microstructures, it is possible to produce the electric displacement vs. electric field hysteresis loop on the macro level. The shape of the hysteresis loop depends on the value of the rate of application of the external electric loading. A faster deployment of the external electric field widens the hysteresis loop. Md Khalaquzzamandoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4174Wed, 16 Sep 2015 16:20:09 +0200A Viscosity Adaptive Lattice Boltzmann Method
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4058
The present thesis describes the development and validation of a viscosity adaption method for the numerical simulation of non-Newtonian fluids on the basis of the Lattice Boltzmann Method (LBM), as well as the development and verification of the related software bundle SAM-Lattice.
By now, Lattice Boltzmann Methods are established as an alternative approach to classical computational fluid dynamics
methods. The LBM has been shown to be an accurate and efficient tool for the numerical simulation of weakly compressible or incompressible fluids. Fields of application reach from turbulent simulations through thermal problems to acoustic calculations among others. The transient nature of the method and the need for a regular grid based, non body conformal discretization makes the LBM ideally suitable for simulations involving complex solids. Such geometries are common, for instance, in the food processing industry, where fluids are mixed by static mixers or agitators. Those fluid flows are often laminar and non-Newtonian.
This work is motivated by the immense practical use of the Lattice Boltzmann Method, which is limited due to stability issues. The stability of the method is mainly influenced by the discretization and the viscosity of the fluid. Thus, simulations of non-Newtonian fluids, whose kinematic viscosity depend on the shear rate, are problematic. Several authors have shown that the LBM is capable of simulating those fluids. However, the vast majority of the simulations in the literature are carried out for simple geometries and/or moderate shear rates, where the LBM is still stable. Special care has to be taken for practical non-Newtonian Lattice Boltzmann simulations in order to keep them stable. A straightforward way is to truncate the modeled viscosity range by numerical stability criteria. This is an effective approach, but from the physical point of view the viscosity bounds are chosen arbitrarily. Moreover, these bounds depend on and vary with the grid and time step size and, therefore, with the simulation Mach number, which is freely chosen at the start of the simulation. Consequently, the modeled viscosity range may not fit to the actual range of the physical problem, because the correct simulation Mach number is unknown a priori. A way around is, to perform precursor simulations on a fixed grid to determine a possible time step size and simulation Mach number, respectively. These precursor simulations can be time consuming and expensive, especially for complex cases and a number of operating points. This makes the LBM unattractive for use in practical simulations of non-Newtonian fluids.
The essential novelty of the method, developed in the course of this thesis, is that the numerically modeled viscosity range is consistently adapted to the actual physically exhibited viscosity range through change of the simulation time step and the simulation Mach number, respectively, while the simulation is running. The algorithm is robust, independent of the Mach number the simulation was started with, and applicable for stationary flows as well as transient flows. The method for the viscosity adaption will be referred to as the "viscosity adaption method (VAM)" and the combination with LBM leads to the "viscosity adaptive LBM (VALBM)".
Besides the introduction of the VALBM, a goal of this thesis is to offer assistance in the spirit of a theory guide to students and assistant researchers concerning the theory of the Lattice Boltzmann Method and its implementation in SAM-Lattice. In Chapter 2, the mathematical foundation of the LBM is given and the route from the BGK approximation of the Boltzmann equation to the Lattice Boltzmann (BGK) equation is delineated in detail.
The derivation is restricted to isothermal flows only. Restrictions of the method, such as low Mach number flows are highlighted and the accuracy of the method is discussed.
SAM-Lattice is a C++ software bundle developed by the author and his colleague Dipl.-Ing. Andreas Schneider. It is a highly automated package for the simulation of isothermal flows of incompressible or weakly compressible fluids in 3D on the basis of the Lattice Boltzmann Method. By the time of writing of this thesis, SAM-Lattice comprises 5 components. The main components are the highly automated lattice generator SamGenerator and the Lattice Boltzmann solver SamSolver. Postprocessing is done with ParaSam, which is our extension of the
open source visualization software ParaView. Additionally, domain decomposition for MPI
parallelism is done by SamDecomposer, which makes use of the graph partitioning library MeTiS. Finally, all mentioned components can be controlled through a user friendly GUI (SamLattice) implemented by the author using QT, including features to visually track output data.
In Chapter 3, some fundamental aspects on the implementation of the main components, including the corresponding flow charts will be discussed. Actual details on the implementation are given in the comprehensive programmers guides to SamGenerator and SamSolver.
In order to ensure the functionality of the implementation of SamSolver, the solver is verified in Chapter 4 for Stokes's First Problem, the suddenly accelerated plate, and for Stokes's Second Problem, the oscillating plate, both for Newtonian fluids. Non-Newtonian fluids are modeled in SamSolver with the power-law model according to Ostwald de Waele. The implementation for non-Newtonian fluids is verified for the Hagen-Poiseuille channel flow in conjunction with a convergence analysis of the method. At the same time, the local grid refinement as it is implemented in SamSolver, is verified. Finally, the verification of higher order boundary conditions is done for the 3D Hagen-Poiseuille pipe flow for both Newtonian and non-Newtonian fluids.
In Chapter 5, the theory of the viscosity adaption method is introduced. For the adaption process, a target collision frequency or target simulation Mach number must be chosen and the distributions must be rescaled according to the modified time step size. A convenient choice is one of the stability bounds. The time step size for the adaption step is deduced from the target collision frequency \(\Omega_t\) and the currently minimal or maximal shear rate in the system, while obeying auxiliary conditions for the simulation Mach number. The adaption is done in the collision step of the Lattice Boltzmann algorithm. We use the transformation matrices of the MRT model to map from distribution space to moment space and vice versa. The actual scaling of the distributions is conducted on the back mapping, because we use the transformation matrix on the basis of the new adaption time step size. It follows an additional rescaling of the non-equilibrium part of the distributions, because of the form of the definition for the discrete stress tensor in the LBM context. For that reason it is clear, that the VAM is applicable for the SRT model as well as the MRT model, where there is virtually no extra cost in the latter case. Also, in Chapter 5, the multi level treatment will be discussed.
Depending on the target collision frequency and the target Mach number, the VAM can be used to optimally use the viscosity range that can be modeled within the stability bounds or it can be used to drastically accelerate the simulation. This is shown in Chapter 6. The viscosity adaptive LBM is verified in the stationary case for the Hagen-Poiseuille channel flow and in the transient case for the Wormersley flow, i.e., the pulsatile 3D Hagen-Poiseuille pipe flow. Although, the VAM is used here for fluids that can be modeled with the power-law approach, the implementation of the VALBM is straightforward for other non-Newtonian models, e.g., the Carreau-Yasuda or Cross model. In the same chapter, the VALBM is validated for the case of a propeller viscosimeter developed at the chair SAM. To this end, the experimental data of the torque on the impeller of three shear thinning non-Newtonian liquids serve for the validation. The VALBM shows excellent agreement with experimental data for all of the investigated fluids and in every operating point. For reasons of comparison, a series of standard LBM simulations is carried out with different simulation Mach numbers, which partly show errors of several hundred percent. Moreover, in Chapter 7, a sensitivity analysis on the parameters used within the VAM is conducted for the simulation of the propeller viscosimeter.
Finally, the accuracy of non-Newtonian Lattice Boltzmann simulations with the SRT and the MRT model is analyzed in detail. Previous work for Newtonian fluids indicate that depending on the numerical value of the collision frequency \(\Omega\), additional artificial viscosity is introduced due to the finite difference scheme, which negatively influences the accuracy. For the non-Newtonian case, an error estimate in the form of a functional is derived on the basis of a series expansion of the Lattice Boltzmann equation. This functional can be solved analytically for the case of the Hagen-Poiseuille channel flow of non-Newtonian fluids. The estimation of the error minimum is excellent in regions where the \(\Omega\) error is the dominant source of error as opposed to the compressibility error.
Result of this dissertation is a verified and validated software bundle on the basis of the viscosity adaptive Lattice Boltzmann Method. The work restricts itself on the simulation of isothermal, laminar flows with small Mach numbers. As further research goals, the testing of the VALBM with minimal error estimate and the investigation of the VALBM in the case of turbulent flows is suggested.Daniel Conraddoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4058Mon, 27 Apr 2015 08:33:27 +0200A Consistent Large Eddy Approach for Lattice Boltzmann Methods and its Application to Complex Flows
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4056
Lattice Boltzmann Methods have shown to be promising tools for solving fluid flow problems. This is related to the advantages of these methods, which are among others, the simplicity in handling complex geometries and the high efficiency in calculating transient flows. Lattice Boltzmann Methods are mesoscopic methods, based on discrete particle dynamics. This is in contrast to conventional Computational Fluid Dynamics methods, which are based on the solution of the continuum equations. Calculations of turbulent flows in engineering depend in general on modeling, since resolving of all turbulent scales is and will be in near future far beyond the computational possibilities. One of the most auspicious modeling approaches is the large eddy simulation, in which the large, inhomogeneous turbulence structures are directly computed and the smaller, more homogeneous structures are modeled.
In this thesis, a consistent large eddy approach for the Lattice Boltzmann Method is introduced. This large eddy model includes, besides a subgrid scale model, appropriate boundary conditions for wall resolved and wall modeled calculations. It also provides conditions for turbulent domain inlets. For the case of wall modeled simulations, a two layer wall model is derived in the Lattice Boltzmann context. Turbulent inlet conditions are achieved by means of a synthetic turbulence technique within the Lattice Boltzmann Method.
The proposed approach is implemented in the Lattice Boltzmann based CFD package SAM-Lattice, which has been created in the course of this work. SAM-Lattice is feasible of the calculation of incompressible or weakly compressible, isothermal flows of engineering interest in complex three dimensional domains. Special design targets of SAM-Lattice are high automatization and high performance.
Validation of the suggested large eddy Lattice Boltzmann scheme is performed for pump intake flows, which have not yet been treated by LBM. Even though, this numerical method is very suitable for this kind of vortical flows in complicated domains. In general, applications of LBM to hydrodynamic engineering problems are rare. The results of the pump intake validation cases reveal that the proposed numerical approach is able to represent qualitatively and quantitatively the very complex flows in the intakes. The findings provided in this thesis can serve as the basis for a broader application of LBM in hydrodynamic engineering problems.Andreas Schneiderdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/4056Mon, 27 Apr 2015 08:24:57 +0200An Efficient Multiscale Method for Modeling Progressive Damage in Composite Materials
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3980
An efficient multiscale approach is established in order to compute the macroscopic response of nonlinear composites. The micro problem is rewritten in an integral form of the Lippmann-Schwinger type and solved efficiently by Fast Fourier Transforms. Using realistic microstructure models complex nonlinear effects are reproduced and validated with measured data of fiber reinforced plastics. The micro problem is integrated in a Finite Element framework which is used to solve the macroscale. The scale coupling technique and a consistent numerical algorithm is established. The method provides an efficient way to determine the macroscopic response considering arbitrary microstructures, constitutive behaviors and loading conditions.Johannes Spahndoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3980Mon, 02 Feb 2015 08:46:45 +0100On the Extended Finite Element Method for the Elasto-Plastic Deformation of Heterogeneous Materials
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3962
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.Tobias Zangmeisterdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3962Wed, 07 Jan 2015 11:05:26 +0100Effects of Waterjet Treatment on Surface Integrity of Metals and its Optimization
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3854
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.MOHD AZMIR MOHD AZHARIdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3854Tue, 19 Aug 2014 10:24:13 +0200Solid-Solid Phase Transitions in Iron Systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3706
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. Binjun Wangdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3706Thu, 06 Feb 2014 12:48:45 +0100Continuum Mechanical Modeling of Dry Granular Systems: From Dilute Flow to Solid-Like Behavior
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3696
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.Clément Zemerlidoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3696Wed, 29 Jan 2014 11:01:06 +0100Sound Simulation and Visualization in virtual Manufacturing Systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3668
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. Xiang Yangdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3668Mon, 16 Dec 2013 11:26:00 +0100Analysis of Off-Road Tire-Soil Interaction through Analytical and Finite Element Methods
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3644
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.Hao Lidoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3644Thu, 31 Oct 2013 11:32:49 +0100Computational Fluid Dynamics Aided Design of Stirred Liquid-Liquid Extraction Columns
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3633
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.
Mark Hlawitschkadoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3633Wed, 23 Oct 2013 13:11:12 +0200Numerical and Analytical Investigation of a Phase Field Model for Fracture
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3525
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.Charlotte Kuhndoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3525Mon, 03 Jun 2013 15:52:20 +0200Transient processes with hydrogels
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3489
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.Aisha Ahmad Naddafdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3489Mon, 22 Apr 2013 12:53:38 +0200Dynamic Modelling and Simulation of (Pulsed and Stirred) Liquid-Liquid Extraction Columns using the Population Balance Equation
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3268
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.
Moutasem Jaradatdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/3268Tue, 25 Sep 2012 07:23:03 +0200On optimal control simulations for mechanical systems
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2761
The primary objective of this work is the development of robust, accurate and efficient simulation methods for the optimal control of mechanical systems, in particular of constrained mechanical systems as they appear in the context of multibody dynamics. The focus is on the development of new numerical methods that meet the demand of structure preservation, i.e. the approximate numerical solution inherits certain characteristic properties from the real dynamical process.
This task includes three main challenges. First of all, a kinematic description of multibody systems is required that treats rigid bodies and spatially discretised elastic structures in a uniform way and takes their interconnection by joints into account. This kinematic description must not be subject to singularities when the system performs large nonlinear dynamics. Here, a holonomically constrained formulation that completely circumvents the use of rotational parameters has proved to perform very well. The arising constrained equations of motion are suitable for an easy temporal discretisation in a structure preserving way. In the temporal discrete setting, the equations can be reduced to minimal dimension by elimination of the constraint forces. Structure preserving integration is the second important ingredient. Computational methods that are designed to inherit system specific characteristics – like consistency in energy, momentum maps or symplecticity – often show superior numerical performance regarding stability and accuracy compared to standard methods. In addition to that, they provide a more meaningful picture of the behaviour of the systems they approximate. The third step is to take the previ- ously addressed points into the context of optimal control, where differential equation and inequality constrained optimisation problems with boundary values arise. To obtain meaningful results from optimal control simulations, wherein energy expenditure or the control effort of a motion are often part of the optimisation goal, it is crucial to approxi- mate the underlying dynamics in a structure preserving way, i.e. in a way that does not numerically, thus artificially, dissipate energy and in which momentum maps change only and exactly according to the applied loads.
The excellent numerical performance of the newly developed simulation method for optimal control problems is demonstrated by various examples dealing with robotic systems and a biomotion problem. Furthermore, the method is extended to uncertain systems where the goal is to minimise a probability of failure upper bound and to problems with contacts arising for example in bipedal walking.Sigrid Leyendeckerhabilitationhttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2761Thu, 06 Oct 2011 10:39:24 +0000