We present, extend, and apply a method to extract the contribution of a subregion of a data set to the global flow. To isolate this contribution, we decompose the flow in the subregion into a potential flow that is induced by the original flow on the boundary and a localized flow. The localized flow is obtained by subtracting the potential flow from the original flow. Since the potential flow is free of both divergence and rotation, the localized flow retains the original features and captures the region-specific flow that contains the local contribution of the considered subdomain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions for steady and unsteady flow fields. We discuss the application of some widely used feature extraction methods on the localized flow and describe applications like reverse-flow detection using the potential flow. Finally, we show that our algorithm is robust and scalable by applying it to various flow data sets and giving performance figures.

Surface water is essential for the eco-environment and provides various purposes and functions in anthropogenic activities such as domestic water supply, agriculture irrigation and drainage, and energy creation. Due to its important role in human health and ecosystem, it is essential to establish effective models to study the water quantity and quality through systematic research. In this dissertation, machine learning (ML) has been investigated as a modelling approach to simulate water quality and quantity of rivers. It includes the analysis of river pollution sources, downstream river flow prediction, long-term river heavy metal prediction and the influence of environmental factors on river heavy metals. This research was conducted to combine ML methods to enhance the accuracy and applicability of models in water environment studies and further assist relevant sectors to strengthen the management of surface water quantity and quality. (1) The primary source contributors of trace metals in surface water were identified based on the trained optimal model. This study trained and evaluated the typical shallow and deep learning approaches to identifying and classifying source contributors based on a database and analyzed the source apportionment of trace metals in the main stream and tributaries of river basin by the proposed approaches. (2) The interpretable ML models were developed to overcome the under-appreciated issue of the model for predicting heavy metals that are both predictive and transparent. This study employed and compared five tree-based machine learning models and then performed global and local feature importance analyses with the optimum models to predict the most important environmental factors for heavy metals management. (3) The performance of conventional or hybrid ML models with time series decomposition technology was developed and compared for long term prediction of heavy metals. This study examined the effect of inputs time-series data of selection and division on the performance of conventional and hybrid models and evaluated the long-term fore-casts by standard metrics to select the optimum approaches for typical metal long term prediction. (4) The downstream river flow was predicted based on the combined ML models. This study established the hybrid CNN-LSTM model to process the 2D rainfall radar information by convolutional neural network (CNN) and the time series information by long short-term memory (LSTM), and explored the capacity of the hybrid model for river flow forecasting.:Table of Content List of Abbreviations V List of Publications on the Ph.D. Topic VII List of Co-authored Publications during the Ph.D. VII 1 General Introduction 1 1.1 Background 1 1.2 Aim and Objective 3 1.3 Innovation and Contribution 3 1.4 Outline 4 1.5 References 5 2 Traceability Study of Metals 9 2.1 Introduction 10 2.2 Materials and Methods 11 2.2.1 Study Area 11 2.2.2 Ecological Risk Assessment 12 2.2.3 Model Development 13 2.2.4 The Classification Supervised ML Models 14 2.2.5 Model Evaluation 15 2.3 Results 16 2.3.1 Metal Characteristics of the Registered Dataset and Applicable Area 16 2.3.2 Spatial Assessment of Ecological Risk 20 2.3.3 Temporal Trend in Ecologic Risk 21 2.3.4 Performance Analysis of Classification Models 22 2.3.5 Resource Analysis Based on the Trained Model 23 2.4 Discussion 24 2.4.1 RF Outperformed the Other Models 24 2.4.2 Potential Sources of Metals in the Given Area 25 2.5 Conclusion 27 2.6 References 27 3 Elucidation of Environmental Factors’ Influence on Metals 33 3.1 Introduction 34 3.2 Materials and Methods 36 3.2.1 Study Sites and Data 36 3.2.2 Indexing Approach 39 3.2.3 Regression Models 40 3.2.4 Model Performance Metrics and Hyperparameter Tuning 41 3.2.5 SHapley Additive exPlanations (SHAP) 42 3.2.6 The Partial Dependence Plot (PDP) 42 3.3 Results 43 3.3.1 HPI and Environmental Variables 43 3.3.2 Assessment of Approaches 44 3.3.3 Global Feature Importance 46 3.3.4 Local Feature Importance 47 3.3.5 Sensitive Factor Analysis 49 3.4 Discussion 49 3.4.1 SHAP Outperformed the Other Importance Method 49 3.4.2 Robust Association of Top Variables with HPI 50 3.5 Conclusion 51 3.6 References 51 4 Long-Term Prediction of Metals Concentration 57 4.1 Introduction 58 4.2 Materials and Methods 60 4.2.1 Study Area and Water Quality Data 60 4.2.2 Input Identification 61 4.2.3 Wavelet Transform 63 4.2.4 Back-Propagation Neural Network (BPNN) Model 63 4.2.5 Nonlinear Autoregressive Exogenous (NARX) Model 65 4.2.6 Wavelet and BPNN (WNN) Hybrid Model 65 4.2.7 Wavelet and NARX (WNARX) Hybrid Model 66 4.2.8 Model Performance Evaluation 66 4.3 Results 67 4.3.1 Model Establishment 67 4.3.2 Performance Analysis of the Optimal Scenarios 70 4.4 Discussion 74 4.5 Conclusion 75 4.6 References 76 5 Prediction of Downstream River Flow 79 5.1 Introduction 80 5.2 Materials and Methods 82 5.2.1 Study Area and Data Acquisition 82 5.2.2 Convolutional Neural Network (CNN) 83 5.2.3 Long Short-Term Memory (LSTM) 83 5.2.4 River Flow Simulation 84 5.2.5 Performance Evaluation 84 5.3 Results 85 5.3.1 Flow Time Series 85 5.3.2 Input Selection 86 5.3.3 Flow Simulation 87 5.4 Discussion 90 5.5 Conclusion 91 5.6 References 92 6 Conclusions and Future Research 97 6.1 Traceability Study of Metals 97 6.2 Elucidation of Environmental Factors’ Influence on Metals 97 6.3 Long-Term Prediction of Metals Concentration 98 6.4 Prediction of River Flow 98 6.5 Discussion and Future Research 98 6.5.1 Discussion 99 6.5.2 Future Research 100 7 Appendices 103 7.1 Supporting Information for Traceability Study of Metals 103 7.1.1 Naive Bayes 103 7.1.2 Support Vector Machine 103 7.1.3 Neural Network 105 7.1.4 Random Forest 106 7.1.5 Long Short-Term Memory 106 7.1.6 Convolutional Neural Network 107 7.2 Supporting Information for Elucidation of Environmental Factors’ Influence on Metals 108 7.3 Supporting Information for Long-Term Prediction of Metals Concentration 109 7.3.1 Figures 109 7.4 References 120

In order to investigate the two-phase flow behaviour in a complex reactor-typical geometry and to supply suitable data for CFD code validation, a model of the hot leg of a pressurised water reactor was built at FZD. The hot leg model is operated in the pressure chamber of the TOPFLOW test facility, which is used to perform high-pressure experiments under pressure equilibrium with the inside atmosphere of the chamber. This technique makes it possible to visualise the two-phase flow through large windows, also at reactor-typical pressure levels. In order to optimise the optical observation possibilities, the test section was designed with a rectangular cross-section. Experiments were performed with air and water at 1.5 and 3.0 bar at room temperature as well as with steam and water at 15, 30 and 50 bar and the corresponding saturation temperature (i.e. up to 264°C). The total of 194 runs are divided into 4 types of experiments covering stationary co-current flow, counter-current flow, flow without water circulation and transient counter-current flow limitation (CCFL) experiments. This report provides a detailed documentation of the experiments including information on the experimental setup, experimental procedure, test matrix and on the calibration of the measuring devices. The available data is described and data sheets were arranged for each experiment in order to give an overview of the most important parameters. For the cocurrent flow experiments, water level histograms were arranged and used to characterise the flow in the hot leg. In fact, the form of the probability distribution was found to be sensitive to the boundary conditions and, therefore, is useful for the CFD comparison. Furthermore, the flooding characteristics of the hot leg model plotted in terms of the classical Wallis parameter or Kutateladze number were found to fail to properly correlate the data of the air/water and steam/water series. Therefore, a modified Wallis parameter is proposed, which takes the effect of viscosity into account.

Stratified two-phase flows were investigated at different test facilities with horizontal test sections in order to provide an experimental database for the development and validation of computational fluid dynamics (CFD) codes. These channels were designed with rectangular cross-sections to enable optimal observation conditions for the application of optical measurement techniques. Consequently, the local flow structure was visualised with a high-speed video camera, delivering data with high-resolution in space and time as needed for CFD code validation. Generic investigations were performed at atmospheric pressure and room temperature in two air/water channels made of acrylic glass. Divers preliminary experiments were conducted with various measuring systems in a test section mounted between two separators. The second test facility, the Horizontal Air/Water Channel (HAWAC), is dedicated to co-current flow investigations. The hydraulic jump as the quasi-stationary discontinuous transition between super- and subcritical flow was studied in this closed channel. Moreover, the instable wave growth leading to slug flow was investigated from the test section inlet. For quantitative analysis of the optical measurements, an algorithm was developed to recognise the stratified interface in the camera frames, allowing statistical treatments for comparison with CFD calculation results. The third test apparatus was installed in the pressure chamber of the TOPFLOW test facility in order to be operated at reactor typical conditions under pressure equilibrium with the vessel atmosphere. The test section representing a flat model of the hot leg of the German Konvoi pressurised water reactor (PWR) scaled at 1:3 is equipped with large glass side walls in the region of the elbow and of the steam generator inlet chamber to allow visual observations. The experiments were conducted with air and water at room temperature and maximum pressures of 3 bar as well as with steam and water at boundary conditions of up to 50 bar and 264°C. Four types of experiments were performed, including generic test cases as well as transient validation cases of typical nuclear reactor safety issues. As an example, the co-current flow experiments simulate the two-phase natural circulation in the primary circuit of a PWR. The probability distribution of the water level measured in the reactor pressure vessel simulator was used to characterise the flow in the hot leg. Moreover, the flooding behaviour in this conduit was investigated with dedicated counter-current flow limitation experiments. A comparison of the flooding characteristics with similar experimental data and correlations available in the literature shows that the channel height is the characteristic length to be used in the Wallis parameter for channels with rectangular cross-sections. Furthermore, for the analysis of steam/water experiments, condensation effects had to be taken into account. Finally, the experimental results confirm that the Wallis similarity is appropriate to scale flooding in the hot leg of a PWR over a large range of pressure and temperature conditions. Not least, different examples of comparison between experiment and simulation demonstrate the possibilities offered by the data to support the development and validation of CFD codes. Besides the comparison of qualitative aspects, it is shown exemplarily how to treat the CFD results in order to enable quantitative comparisons with the experiments.

Auf dem Gebiet der mobilen Arbeitsmaschinen und Nutzfahrzeuge zeigen aktuelle Arbeiten weltweit ein verstärktes Interesse an leistungsverzweigten Antriebskonzepten auf Basis elektrischer und hydraulischer Hybridlösungen. Die Kombination beider Technologien verspricht wartungsarme, energieeffiziente Antriebssyteme mit hoher Steuer- und Regelbarbeit sowie hoher Kraftdichte. Die primär erzeugte mechanische Antriebsleistung der Wärmekraftmaschine kann meist für die Arbeitsprozesse und zur Versorgung zugehöriger Hilfsfunktionen nicht direkt verwendet werden. Diese muss je nach Anforderungen gewandelt bzw. angepasst oder bedarfsgerecht mittels zusätzlichen, wiederaufladbaren Speichern bereitgestellt werden. Solche hybriden Lösungsansätze führen jedoch gegenüber konventionellen Antrieben zu einer steigenden Komplexität sowie einem erhöhten technischen Aufwand. Nach dem Stand der Technik erfolgt die Erzeugung hydraulischer und elektrischer Leistung mit Hilfe mindestens dreier Komponenten: Verbrennungsmotor, Hydraulikpumpe und Generator. Für künftige antriebstechnische Innovationen ist daher aus funktionellen und energetischen Gründen ein einfaches, preiswertes Primäraggregat zur gleichzeitigen, bedarfsgerechten Bereitstellung hydraulischer und elektrischer Leistung wünschenswert, welches unnötige Umwandlungsverluste vermeidet und zusätzlich Kosten spart. Das Forschungsprojekt „Theoretische Grundlagen zur Verknüpfung von thermohydraulischer und thermoelektrischer Leistungswandlung in einem Aggregat – Thermohydraulischer Lineargenerator“ befasst sich mit einer belastbaren Abschätzung der technischen Realisierbarkeit und des technischen Aufwands eines derartigen neuen Antriebskonzeptes mit frei wählbarer Bereitstellung hydraulischer und elektrischer Leistung auf Basis des Freikolbenprinzips. Die grundlegenden Untersuchungen widmen sich der Kopplung zweier unterschiedlicher Leistungswandlungen, einer stabilen Prozessführung sowie der Analyse und Bewertung der physikalischen Prozessgrößen in Bezug auf eine zukünftige Auslegung eines Prototyps. Der Beitrag erklärt das Grundkonzept, zeigt den aktuellen Stand des Projekts auf und stellt die zum gegenwärtigen Zeitpunkt vorliegenden Ergebnisse vor.

In der vorliegenden Arbeit wurde das Verhalten dünner Flüssigkeitsfilme an gekrümmten Substratoberflächen durch experimentelle Beschichtungsversuche basierend auf der non-invasiven laserinduzierten Fluoreszenzmesstechnik und durch numerische Filmsimulationen mit Hilfe des Volume-of-Fluid Mehrphasenmodells untersucht. Besonderes Interesse galt dabei dem Finden optimaler Einflussgrößenkombinationen zur Reduzierung des Fettkanten-Effekts. In der hierfür durchgeführten Parameterstudie wurden sowohl Applikationsparameter wie der Kantenrundungsradius und die Applikationsschichtdicke als auch Stoffparameter der untersuchten Flüssigkeit wie die Viskosität und die Oberflächenspannung variiert. Neben qualitativen Beschreibungen der entstandenen Fettkantengestalten sind als Resultate auch Größen zur Quantifizierung der Fettkanten festgelegt worden und systematisch dargestellt. Es konnte nachgewiesen werden, dass ungünstige und geeignete Parameterkonfigurationen existieren, welche prägnante bzw. kaum auffällige Fettkanten erzeugen, insbesondere im Experiment. Über die dabei eingreifenden Mechanismen der zugrundeliegenden Strömungen wurden konkrete Hypothesen aufgestellt, auch um die resultierenden Proportionalitäten der Fettkantengrößen bezüglich der Einflussgrößen zu plausibilisieren. Weiterhin konnte eine Aussage über die Signifikanz der untersuchten Einflussgrößen getroffen werden. Abschließend wurde eine geeignete dimensionslose Kenngröße generiert, um den Fettkanten-Effekt parameterübergreifend beschreiben zu können, wodurch mittels der Ähnlichkeitstheorie auch eine gewisse Abschätzung des Fettkanten-Effekts ermöglicht wird. / In this study the behaviour of a thin liquid layer at a curved solid edge was examined by experimental coating investigations based on the laser-induced fluorescence technique and by numerical film simulations based on the Volume-of-Fluid multiphase flow model, respectively. The main motivation was to find optimal combinations of influencing quantities to reduce the fat-edge effect. Therefore a study of these quantities was performed, in which application parameters like edge radii of curvature and application layer thicknesses as well as determining liquid properties like viscosity and surface tension have been varied. Results are described qualitatively at corresponding fat-edge shapes and quantified by suitable fat-edge parameters, which had to be identified and selected. It could be shown that adverse and appropriate influencing parameter combinations exist, which generate conspicuous and less distinctive fat-edges, respectively - especially in laboratory experiments. The experimental findings and proportionalities regarding fat-edge shapes and dimensions are found to be physically plausible. Furthermore an order of significance of the influencing quantities established. Eventually, a dimensionless quantity was derived by dimensional analysis, which describes the fat-edge effect. Thus, the fat-edge effect has also been described by the application of similarity theory and the corresponding dimenionless number, respectively.

Die Charakterisierung hochdimensionaler Systeme mit Lyapunov-Instabilität wird durch das Lyapunov-Spektrum und die zugehörigen Lyapunov-Vektoren ermöglicht. Für eine Vielzahl von derartigen Systemen (Coupled-Map-Lattices, Hartkugel-Systeme, Systeme mit ausgedehnten Potentialen ...) konnte durch die Untersuchung der Lyapunov-Vektoren die Existenz von hydrodynamischen Lyapunov-Moden nachgewiesen werden. Diese kollektiven Anregungen zeigen sich in Lyapunov-Vektoren, deren Lyapunov-Exponenten dem Betrage nach am kleinsten sind. Da Lyapunov-Exponenten charakteristische Zeitskalen innerhalb der Systeme repräsentieren, ist durch die Lyapunov-Moden eine Untersuchung des Langzeitverhaltens möglich. In dieser Arbeit werden die hydrodynamischen Lyapunov-Moden durch Molekulardynamiksimulationen von mehrkomponentigen Lennard-Jones-Flüssigkeiten untersucht. Die Charakterisierung der Lyapunov-Moden zeigt im weiteren eine Ähnlichkeit zu Dispersionsrelationen von Phononen.

Die vorliegende Arbeit beschäftigt sich mit der analytischen Modellierung und Optimierung synthetischer Jet-Aktuatoren, welche zur aktiven Strömungsbeeinflussung genutzt werden können. Ein in der Literatur bekanntes eindimensionales Modell wird ausführlich hergeleitet und an gemessene Geschwindigkeitsspektren verschiedener Jet-Aktuatoren angepasst. Der Einfluss jedes Modellparameters wird separat untersucht. Außerdem wird ein empirischer Zusammenhang zwischen Membranresonanzfrequenz und Luftkammervolumen angegeben, mit dessen Hilfe synthetische Jet-Aktuatoren mit größtmöglichen Strömungsgeschwindigkeiten durch die Düse konstruiert werden können.:Abkürzungsverzeichnis Symbolverzeichnis 1 Einleitung 2 Physikalische Grundlagen 2.1 Aufbau und Funktionsweise der betrachteten synthetischen Jet-Aktuatoren 2.2 Grundlagen aus der Mechanik 2.3 Grundlagen aus der Hydrodynamik 2.4 Analytisches Modell für synthetische Jet-Aktuatoren 3 Numerische Grundlagen 3.1 Zur Lösung von Differentialgleichungssystemen 3.2 Grundlagen der Optimierung 4 Beschreibung von Messdaten mit Hilfe des Modells 4.1 Reproduktion der Ergebnisse der Veröffentlichungen von Sharma 4.2 Anpassung des Modells an Messdaten weiterer Aktuatoren 5 Parametervariation und Optimierung 5.1 Separate Variation jedes Parameters 5.2 Brute-force-Optimierung von Luftkammervolumen und Membranresonanzfrequenz 6 Zusammenfassung und Ausblick Anhang Abbildungsverzeichnis Tabellenverzeichnis Literaturverzeichnis Danksagung Selbstständigkeitserklärung

Measuring the liquid velocity and turbulence parameters in multiphase flows is a challenging task. In general, measurements based on optical methods are hindered by the presence of the gas phase. In the present work, it is shown that this leads to a sampling bias. Here, particle image velocimetry (PIV) is used to measure the liquid velocity and turbulence in a bubble column for different gas volume flow rates. As a result, passing bubbles lead to a significant sampling bias, which is evaluated by the mean liquid velocity and Reynolds stress tensor components. To overcome the sampling bias a window averaging procedure that waits a time depending on the locally distributed velocity information (hold processor) is derived. The procedure is demonstrated for an analytical test function. The PIV results obtained with the hold processor are reasonable for all values. By using the new procedure, reliable liquid velocity measurements in bubbly flows, which are vitally needed for CFD validation and modeling, are possible. In addition, the findings are general and can be applied to other flow situations and measuring techniques.

The main goal of our thesis is to understand qualitative properties of solutions to the Cauchy problem for the semi-linear wave model with time-dependent speed and dissipation. We greatly benefited from very precise estimates for the corresponding linear problem in order to obtain the global existence (in time) of small data solutions. This reason motivated us to introduce very carefully a complete description for classification of our models: scattering, non-effective, effective, over-damping. We have considered those separately.