In power plants using large utility coal-fired boilers for generation of electricity the coal is pulverised in coal mills and then it has to be pneumatically transported and distributed to a larger number of burners (e.g. 30-40) circumferentially arranged in several rows around the burning chamber of the boiler. Besides the large pipework flow splitting devices are necessary for distribution of an equal amount of pulverised fuel (PF) to each of the burners. So called trifurcators (without inner fittings or guiding vanes) and ''riffle'' type bifurcators are commonly used to split the gas-coal particle flow into two or three pipes/channels with an equal amount of PF mass flow rate in each outflow cross section of the flow splitting device. These PF flow splitting devices are subject of a number of problems. First of all an uneven distribution of PF over the burners of a large utility boiler leads to operational and maintenance problems, increased level of unburned carbon and higher rates of NOX emissions. Maldistribution of fuel between burners caused by non uniform concentration of the PF (particle roping) in pipe and channel bends prior to flow splitting devices leads to uncontrolled differences in the fuel to air ratio between burners. This results in localised regions in the furnace which are fuel rich, where insufficient air causes incomplete combustion of the fuel. Other regions in the furnace become fuel lean, forming high local concentrations of NOX due to the high local concentrations of O2. Otherwise PF maldistribution can impact on power plant maintenance in terms of uneven wear on PF pipework, flow splitters as well as the effects on boiler panels (PF deposition, corrosion, slagging). In order to address these problems in establishing uniform PF distribution over the outlet cross sections of flow splitting devices in the pipework of coal-fired power plants the present paper deals with numerical prediction and analysis of the complex gas and coal particle (PF) flow through trifurcators and ''riffle'' type bifurcators. The numerical investigation is based on a 3-dimensional Eulerian- Lagrangian approach (MISTRAL/PartFlow-3D) developed by Frank et al. The numerical method is capable to predict isothermal, incompressible, steady gas- particle flows in 3-dimensional, geometrically complex flow geometries using boundary fitted, block-structured, numerical grids. Due to the very high numerical effort of the investigated gas-particle flows the numerical approach has been developed with special emphasis on efficient parallel computing on clusters of workstations or other high performance computing architectures. Besides the aerodynamically interaction between the carrier fluid phase and the PF particles the gas-particle flow is mainly influenced by particle-wall interactions with the outer wall boundaries and the inner fittings and guiding vanes of the investigated flow splitting devices. In order to allow accurate quantitative prediction of the motion of the disperse phase the numerical model requires detailed information about the particle-wall collision process. In commonly used physical models of the particle-wall interaction this is the knowledge or experimental prediction of the restitution coefficients (dynamic friction coefficient, coefficient of restitution) for the used combination of particle and wall material, e.g. PF particles on steel. In the present investigation these parameters of the particle-wall interaction model have been obtained from special experiments in two test facilities. Basic experiments to clarify the details of the particle-wall interaction process were made in a test facility with a spherical disk accelerator. This test facility furthermore provides the opportunity to investigate the bouncing process under normal pressure as well as under vacuum conditions, thus excluding aerodynamically influences on the motion of small particles in the near vicinity of solid wall surfaces (especially under small angles of attack). In this experiments spherical glass beads were used as particle material. In a second test facility we have investigated the real impact of non-spherical pulverised fuel particles on a steel/ceramic target. In this experiments PF particles were accelerated by an injector using inert gas like e.g. CO2 or N2 as the carrier phase in order to avoid dust explosion hazards. The obtained data for the particle-wall collision models were compared to those obtained for glass spheres, where bouncing models are proofed to be valid. Furthermore the second test facility was used to obtain particle erosion rates for PF particles on steel targets as a function of impact angles and velocities. The results of experimental investigations has been incorporated into the numerical model. Hereafter the numerical approach MISTRAL/PartFlow-3D has been applied to the PF flow through a ''riffle'' type bifurcator. Using ICEM/CFD-Hexa as grid generator a numerical mesh with approximately 4 million grid cells has been designed for approximation of the complex geometry of the flow splitting device with all its interior fittings and guiding vanes. Based on a predicted gas flow field a large number of PF particles are tracked throughout the flow geometry of the flow-splitter. Besides mean quantities of the particle flow field like e.g. local particle concentrations, mean particle velocities, distribution of mean particle diameter, etc. it is now possible to obtain information about particle erosion on riffle plates and guiding vanes of the flow splitting device. Furthermore the influence of different roping patterns in front of the flow splitter on the uniformness of PF mass flow rate splitting after the bifurcator has been investigated numerically. Results show the efficient operation of the investigated bifurcator in absence of particle roping, this means under conditions of an uniform PF particle concentration distribution in the inflow cross section of the bifurcator. If particle roping occurs and particle concentration differs over the pipe cross section in front of the bifurcator the equal PF particle mass flow rate splitting can be strongly deteriorated in dependence on the location and intensity of the particle rope or particle concentration irregularities. The presented results show the importance of further development of efficient rope splitting devices for applications in coal-fired power plants. Numerical analysis can be used as an efficient tool for their investigation and further optimisation under various operating and flow conditions.

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

L'implantation en Virgule Flottante (VF) d'une fonction à valeurs réelles est réalisée avec arrondi correct si le résultat calculé est toujours égal à l'arrondi de la valeur exacte, ce qui présente de nombreux avantages. Mais pour implanter une fonction avec arrondi correct de manière fiable et efficace, il faut résoudre le "dilemme du fabricant de tables" (TMD en anglais). Deux algorithmes sophistiqués (L et SLZ) ont été conçus pour résoudre ce problème, via des calculs longs et complexes effectués par des implantations largement optimisées. D'où la motivation d'apporter des garanties fortes sur le résultat de ces pré-calculs coûteux. Dans ce but, nous utilisons l'assistant de preuves Coq. Tout d'abord nous développons une bibliothèque d'"approximation polynomiale rigoureuse", permettant de calculer un polynôme d'approximation et un intervalle bornant l'erreur d'approximation à l'intérieur de Coq. Cette formalisation est un élément clé pour valider la première étape de SLZ, ainsi que l'implantation d'une fonction mathématique en général (avec ou sans arrondi correct). Puis nous avons implanté en Coq, formellement prouvé et rendu effectif 3 vérifieurs de certificats, dont la preuve de correction dérive du lemme de Hensel que nous avons formalisé dans les cas univarié et bivarié. En particulier, notre "vérifieur ISValP" est un composant clé pour la certification formelle des résultats générés par SLZ. Ensuite, nous nous sommes intéressés à la preuve mathématique d'algorithmes VF en "précision augmentée" pour la racine carré et la norme euclidienne en 2D. Nous donnons des bornes inférieures fines sur la plus petite distance non nulle entre sqrt(x²+y²) et un midpoint, permettant de résoudre le TMD pour cette fonction bivariée. Enfin, lorsque différentes précisions VF sont disponibles, peut survenir le phénomène de "double-arrondi", qui peut changer le comportement de petits algorithmes usuels en arithmétique. Nous avons prouvé en Coq un ensemble de théorèmes décrivant le comportement de Fast2Sum avec double-arrondis.

Ce mémoire présente le travail de recherche effectué pour la conception d'une stratégie de commande originale, destinée aux systèmes de puissance hybrides en sites isolés. Le système considéré, voué à l'alimentation électrique d'une habitation, comprend deux sources, un groupe de panneaux photovoltaïques et une petite éolienne, et deux types de stockage, un banc de batteries lithium-ion et un de supercondensateurs. Face au problème de gestion de l'énergie dans un système hybride, et aux enjeux de maximisation de sa puissance produite, nous proposons de développer une stratégie de commande basée sur les flux d'énergie. pour cela, nous présentons dans un premier temps les modélisations d'Euler-Lagrange et hamiltonienne du système. Ces modèles permettent d'utiliser la propriété de passivité de celui-ci, et ainsi de synthétiser des commandes par injection d'amortissement pour chaque source, afin de maximiser sa production, et pour les supercondensateurs, dans le but d'assurer une répartition cohérente des flux d'énergie entre eux et les batteries. Les commandes sont finalement mises en œuvre dans un simulateur, puis dans un banc d'essai expérimental, afin d'une part de comparer leurs performances à celles de solutions préexistantes, et d'autre part de valider le bon fonctionnement du système hybride complet les utilisant.

Construction of structural computational model of the tank with fluid using program package ANSYS based on the Finite Element Method. Solve eigen-vibration of the tank with or without effects of fluid. Application of Euler and Lagrange method for modeling fluid. Solve seismic response using response spectra. Verify of the tank in accordance to EC 3 and EC8.

In power plants using large utility coal-fired boilers for generation of electricity the coal is pulverised in coal mills and then it has to be pneumatically transported and distributed to a larger number of burners (e.g. 30-40) circumferentially arranged in several rows around the burning chamber of the boiler. Besides the large pipework flow splitting devices are necessary for distribution of an equal amount of pulverised fuel (PF) to each of the burners. So called trifurcators (without inner fittings or guiding vanes) and ''riffle'' type bifurcators are commonly used to split the gas-coal particle flow into two or three pipes/channels with an equal amount of PF mass flow rate in each outflow cross section of the flow splitting device. These PF flow splitting devices are subject of a number of problems. First of all an uneven distribution of PF over the burners of a large utility boiler leads to operational and maintenance problems, increased level of unburned carbon and higher rates of NOX emissions. Maldistribution of fuel between burners caused by non uniform concentration of the PF (particle roping) in pipe and channel bends prior to flow splitting devices leads to uncontrolled differences in the fuel to air ratio between burners. This results in localised regions in the furnace which are fuel rich, where insufficient air causes incomplete combustion of the fuel. Other regions in the furnace become fuel lean, forming high local concentrations of NOX due to the high local concentrations of O2. Otherwise PF maldistribution can impact on power plant maintenance in terms of uneven wear on PF pipework, flow splitters as well as the effects on boiler panels (PF deposition, corrosion, slagging). In order to address these problems in establishing uniform PF distribution over the outlet cross sections of flow splitting devices in the pipework of coal-fired power plants the present paper deals with numerical prediction and analysis of the complex gas and coal particle (PF) flow through trifurcators and ''riffle'' type bifurcators. The numerical investigation is based on a 3-dimensional Eulerian- Lagrangian approach (MISTRAL/PartFlow-3D) developed by Frank et al. The numerical method is capable to predict isothermal, incompressible, steady gas- particle flows in 3-dimensional, geometrically complex flow geometries using boundary fitted, block-structured, numerical grids. Due to the very high numerical effort of the investigated gas-particle flows the numerical approach has been developed with special emphasis on efficient parallel computing on clusters of workstations or other high performance computing architectures. Besides the aerodynamically interaction between the carrier fluid phase and the PF particles the gas-particle flow is mainly influenced by particle-wall interactions with the outer wall boundaries and the inner fittings and guiding vanes of the investigated flow splitting devices. In order to allow accurate quantitative prediction of the motion of the disperse phase the numerical model requires detailed information about the particle-wall collision process. In commonly used physical models of the particle-wall interaction this is the knowledge or experimental prediction of the restitution coefficients (dynamic friction coefficient, coefficient of restitution) for the used combination of particle and wall material, e.g. PF particles on steel. In the present investigation these parameters of the particle-wall interaction model have been obtained from special experiments in two test facilities. Basic experiments to clarify the details of the particle-wall interaction process were made in a test facility with a spherical disk accelerator. This test facility furthermore provides the opportunity to investigate the bouncing process under normal pressure as well as under vacuum conditions, thus excluding aerodynamically influences on the motion of small particles in the near vicinity of solid wall surfaces (especially under small angles of attack). In this experiments spherical glass beads were used as particle material. In a second test facility we have investigated the real impact of non-spherical pulverised fuel particles on a steel/ceramic target. In this experiments PF particles were accelerated by an injector using inert gas like e.g. CO2 or N2 as the carrier phase in order to avoid dust explosion hazards. The obtained data for the particle-wall collision models were compared to those obtained for glass spheres, where bouncing models are proofed to be valid. Furthermore the second test facility was used to obtain particle erosion rates for PF particles on steel targets as a function of impact angles and velocities. The results of experimental investigations has been incorporated into the numerical model. Hereafter the numerical approach MISTRAL/PartFlow-3D has been applied to the PF flow through a ''riffle'' type bifurcator. Using ICEM/CFD-Hexa as grid generator a numerical mesh with approximately 4 million grid cells has been designed for approximation of the complex geometry of the flow splitting device with all its interior fittings and guiding vanes. Based on a predicted gas flow field a large number of PF particles are tracked throughout the flow geometry of the flow-splitter. Besides mean quantities of the particle flow field like e.g. local particle concentrations, mean particle velocities, distribution of mean particle diameter, etc. it is now possible to obtain information about particle erosion on riffle plates and guiding vanes of the flow splitting device. Furthermore the influence of different roping patterns in front of the flow splitter on the uniformness of PF mass flow rate splitting after the bifurcator has been investigated numerically. Results show the efficient operation of the investigated bifurcator in absence of particle roping, this means under conditions of an uniform PF particle concentration distribution in the inflow cross section of the bifurcator. If particle roping occurs and particle concentration differs over the pipe cross section in front of the bifurcator the equal PF particle mass flow rate splitting can be strongly deteriorated in dependence on the location and intensity of the particle rope or particle concentration irregularities. The presented results show the importance of further development of efficient rope splitting devices for applications in coal-fired power plants. Numerical analysis can be used as an efficient tool for their investigation and further optimisation under various operating and flow conditions.

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

Many fluid flow processes in nature and technology are characterized by the presence and coexistence of two ore more phases. These two- or multiphase flows are furthermore characterized by a greater complexity of possible flow phenomena and phase interactions then in single phase flows and therefore the numerical simulation of these multiphase flows is usually demanding a much higher numerical effort. The presented work summarizes the research and development work of the author and his research group on "Numerical Methods for Multiphase Flows" at the University of Technology, Chemnitz over the last years. This work was focussed on the development and application of numerical approaches for the prediction of disperse fluid-particle flows in the field of fluid mechanics and process technology. A main part of the work presented here is concerned with the modelling of different physical phenomena in fluid-particle flows under the paradigm of the Lagrangian treatment of the particle motion in the fluid. The Eulerian-Lagrangian approach has proved to be an especially well suited numerical approach for the simulation of disperse multiphase flows. On the other hand its application requires a large amount of (parallel) computational power and other computational ressources. The models described in this work give a mathematical description of the relevant forces and momentum acting on a single spherical particle in the fluid flow field, the particle-wall interaction and the particle erosion to the wall. Further models has been derived in order to take into account the influence of particle-particle collisions on the particle motion as well as the interaction of the fluid flow turbulence with the particle motion. For all these models the state-of-the-art from literature is comprehensively discussed. The main field of interest of the work presented here is in the area of development, implementation, investigation and comparative evaluation of parallelization methods for the Eulerian-Lagrangian approach for the simulation of disperse multiphase flows. Most of the priorly existing work of other authors is based on shared-memory approaches, quasi-serial or static domain decomposition approaches. These parallelization methods are mostly limited in theire applicability and scalability to parallel computer architectures with a limited degree of parallelism (a few number of very powerfull compute nodes) and to more or less homogeneous multiphase flows with uniform particle concentration distribution and minor complexity of phase interactions. This work now presents a novel parallelization method developed by the author, realizing a dynamic load balancing for the Lagrangian approach (DDD - Dynamic Domain Decomposition) and therefore leading to a substantial decrease in total computation time necessary for multiphase flow computations with the Eulerian-Lagrangian approach. Finally, the developed and entirely parallelized Eulerian-Lagrangian approach MISTRAL/PartFlow-3D offers the opportunity of efficient investigation of disperse multiphase flows with higher concentrations of the disperse phase and the resulting strong phase interaction phenomena (four-way coupling). / Viele der in Natur und Technik ablaufenden Strömungsvorgänge sind durch die Koexistenz zweier oder mehrerer Phasen gekennzeichnet. Diese sogenannten Zwei- oder Mehrphasensysteme zeichnen sich durch ein hohes Maß an Komplexität aus und erfordern oft einen sehr hohen rechentechnischen Aufwand zu deren numerischer Simulation. Die vorliegende Arbeit faßt langjährige Forschungs- und Entwicklungsarbeiten des Autors und seiner Forschungsgruppe "Numerische Methoden für Mehrphasenströmungen" an der TU Chemnitz zusammen, die sich mit der Entwicklung und Anwendung numerischer Berechnungsverfahren für disperse Fluid-Partikel-Strömungen auf dem Gebiet der Strömungs- und Verfahrenstechnik befassen. Ein wesentlicher Teil der Arbeit befaßt sich mit der Modellierung unterschiedlicher physikalischer Phänomene in Fluid-Partikel-Strömungen unter dem Paradigma der Lagrange'schen Betrachtungsweise der Partikelbewegung. Das Euler-Lagrange-Verfahren hat sich als besonders geeignetes Berechnungsverfahren für die numerische Simulation disperser Mehrphasenströmungen erwiesen, stellt jedoch in seiner Anwendung auch höchste Anforderungen an die Ressourcen der verwendeten (parallelen) Rechnerarchitekturen. Die näher ausgeführten mathematisch-physikalischen Modelle liefern eine Beschreibung der auf eine kugelförmige Einzelpartikel im Strömungsfeld wirkenden Kräfte und Momente, der Partikel-Wand-Wechselwirkung und der Partikelerosion. Weitere Teilmodelle dienen der Berücksichtigung von Partikel-Partikel-Stoßvorgängen und der Wechselwirkung zwischen Fluidturbulenz und Partikelbewegung. Der Schwerpunkt dieser Arbeit liegt im Weiteren in der Entwicklung, Untersuchung und vergleichenden Bewertung von Parallelisierungsverfahren für das Euler-Lagrange-Verfahren zur Berechnung von dispersen Mehrphasenströmungen. Zuvor von anderen Autoren entwickelte Parallelisierungsmethoden für das Lagrange'sche Berechnungsverfahren basieren im Wesentlichen auf Shared-Memory-Ansätzen, Quasi-Seriellen Verfahren oder statischer Gebietszerlegung (SDD) und sind somit in ihrer Einsetzbarkeit und Skalierbarkeit auf Rechnerarchitekturen mit relativ geringer Parallelität und auf weitgehend homogene Mehrphasenströmungen mit geringer Komplexität der Phasenwechselwirkungen beschränkt. In dieser Arbeit wird eine vom Autor entwickelte, neuartige Parallelisierungsmethode vorgestellt, die eine dynamische Lastverteilung für das Lagrange-Verfahren ermöglicht (DDD - Dynamic Domain Decomposition) und mit deren Hilfe eine deutliche Reduzierung der Gesamtausführungszeiten einer Mehrphasenströmungsberechnung mit dem Euler-Lagrange-Verfahren möglich ist. Im Ergebnis steht mit dem vom Autor und seiner Forschungsgruppe entwickelten vollständig parallelisierten Euler-Lagrange-Verfahren MISTRAL/PartFlow-3D ein numerisches Berechnungsverfahren zur Verfügung, mit dem disperse Mehrphasenströmungen mit höheren Konzentrationen der dispersen Phase und daraus resultierenden starken Phasenwechselwirkungen (Vier-Wege-Kopplung) effektiv untersucht werden können.

This thesis describes the design, implementation and analysis for a preliminary study for DLR's MASCOT lander's next mission to Small Solar System Bodies (SSSB). MASCOT (Mobile Asteroid Surface Scout) is a nano-lander that flew aboard Hayabusa2 (JAXA) to an asteroid, Ryugu. It is a passive nano-spacecraft that can only be deployed ballistically from a hovering spacecraft. Current research focusses on optimizing similar close-approach missions for deploying landers or small cubesats into periodic orbits but does not provide solutions with semi-autonomous small landers deployed from farther distances. This study aims to overcome this short-coming by proposing novel yet simple Guidance, Navigation and Control (GNC) and Propulsion systems for MASCOT. Due to its independent functioning and customisable anatomy, MASCOT can be adapted for several mission scenarios. In this thesis, a particular case-study is modelled for the HERA (ESA) mission. The first phase of the study involves the design of a landing trajectory to the moon of the Didymos binary asteroid system. For a preliminary analysis, the system - Didymain (primary body), Didymoon (secondary body) and MASCOT (third body) - are modelled as a Planar Circular Restricted Three Body Problem (PCR3BP). The numerical integration methodology used for the trajectory is the variable-step Dormand–Prince (Runge Kutta) ODE-4,5 (Ordinary Differential Equation) solver. The model is built in MATLAB-Simulink (2019a) and refined iteratively by conducting a Monte Carlo analysis using the Sensitivity Analysis Tool. Two models - a thruster-controlled system and an alternative hybrid propulsion system of solar sails and thrusters - are simulated and proven to be feasible. The results show that the stable manifold near Lagrange 2 points proposed by Tardivel et. al. for ballistic landings can still be exploited for distant deployments if a single impulse retro-burn is done at an altitude of 65 m to 210 m above ground with error margins of 50 m in position, 5 cm/s in velocity and 0.1 rad in attitude. The next phase is the conceptual design of a MASCOT-variant with GNC abilities. Based on the constraints and requirements of the flown spacecraft, novel GNC and Propulsion systems are chosen. To identify the overriding factors in using commercial-off-the-shelf (COTS) for MASCOT, a market survey is conducted and the manufacturers of short-listed products are consulted. The final phase of the study is to analyse the proposed equipment in terms of parameter scope and capability-oriented trade-offs. Two traceability matrices, one for devised solutions and system and another for solutions versus capabilities, are constructed. The final proposed system is coherent with the given mass, volume and power constraints. A distant deployment of MASCOT-like landers for in-situ observation is suggested as an advantageous and risk-reducing addition to large spacecraft missions to unknown micro-gravity target bodies. Lastly, the implications of this study and the unique advantages of an enhanced MASCOT lander are explored for currently planned SSSB missions ranging from multiple rendezvous, fly-by or sample-return missions. Concluding, this study lays the foundation for future work on advanced GNC concepts for unconventional spacecraft topology for the highly integrated small landers. / <p>This thesis is submitted as per the requirements for the Spacemaster (Round 13) dual master's degree under the Erasmus Mundus Joint Master's Degree Programme. </p> / MASCOT team, DLR

The goal of this thesis is two-fold. On the one hand, it pursues to provide a contribution to the conjugate duality by proposing a new duality concept, which can be understood as an umbrella for different meaningful perturbation methods. On the other hand, this thesis aims to investigate minimax location problems by means of the duality concept introduced in the first part of this work, followed by a numerical approach using epigraphical splitting methods. After summarizing some elements of the convex analysis as well as introducing important results needed later, we consider an optimization problem with geometric and cone constraints, whose objective function is a composition of n+1 functions. For this problem we propose a conjugate dual problem, where the functions involved in the objective function of the primal problem are decomposed. Furthermore, we formulate generalized interior point regularity conditions for strong duality and give necessary and sufficient optimality conditions. As applications of this approach we determine the formulae of the conjugate as well as the biconjugate of the objective function of the primal problem and analyze an optimization problem having as objective function the sum of reciprocals of concave functions. In the second part of this thesis we discuss in the sense of the introduced duality concept three classes of minimax location problems. The first one consists of nonlinear and linear single minimax location problems with geometric constraints, where the maximum of nonlinear or linear functions composed with gauges between pairs of a new and existing points will be minimized. The version of the nonlinear location problem is additionally considered with set-up costs. The second class of minimax location problems deals with multifacility location problems as suggested by Drezner (1991), where for each given point the sum of weighted distances to all facilities plus set-up costs is determined and the maximal value of these sums is to be minimized. As the last and third class the classical multifacility location problem with geometrical constraints is considered in a generalized form where the maximum of gauges between pairs of new facilities and the maximum of gauges between pairs of new and existing facilities will be minimized. To each of these location problems associated dual problems will be formulated as well as corresponding duality statements and necessary and sufficient optimality conditions. To illustrate the results of the duality approach and to give a more detailed characterization of the relations between the location problems and their corresponding duals, we consider examples in the Euclidean space. This thesis ends with a numerical approach for solving minimax location problems by epigraphical splitting methods. In this framework, we give formulae for the projections onto the epigraphs of several sums of powers of weighted norms as well as formulae for the projection onto the epigraphs of gauges. Numerical experiments document the usefulness of our approach for the discussed location problems.