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L'objectif de cette thèse est d'analyser l'influence des non linéarités, du comportement rhéologique des fluides rhéofluidifiants, sur les conditions de stabilité et de transition vers la turbulence. Dans un premier temps, une analyse linéaire de stabilité avec une approche modale a été réalisée. Les résultats obtenus mettent clairement en évidence l'effet stabilisant de la rhéofluidification. Ensuite, une analyse faiblement non linéaire de stabilité a été menée en vue d'examiner l'influence de la perturbation de la viscosité sur la stabilité vis à vis de perturbations d'amplitude finie. L'analyse de la contribution des termes non linéaires d'inertie et visqueux montre que, contrairement aux termes d'inertie, les termes non linéaires visqueux ont tendance à accélérer l'écoulement et favoriser une bifurcation sur-critique. Les effets rhéofluidifiants tendent à réduire la dissipation visqueuse. Finalement, une analyse fortement non linéaire de stabilité a été conduite en utilisant les techniques de suivi de branches de solutions par des méthodes de continuation. Pour pouvoir traiter les termes visqueux fortement non linéaires, un code de calcul pseudo-spectral a été développé. Des solutions non linéaires d'équilibre ont été obtenues et caractérisées pour différentes valeurs des paramètres rhéologiques / The aim of this study is to understand the influence of the nonlinear rheological behaviour of the shear-thinning fluids on the flow stability and transition to turbulence. First, a linear stability analysis using modal approach was carried out. Results clearly highlight the stabilizing effect of shear-thinning. Then, as a first approach to take into account nonlinear effects of viscosity perturbation on the flow stability, a weakly nonlinear stability analysis is performed in the neighbourhood of the critical conditions. Results indicate that shear-thinning reduces the viscous dissipation and, in contrast to inertial terms, the nonlinear viscous terms tend to accelerate the flow and act in favour of supercritical bifurcation. Finally, a nonlinear stability analysis is done by following solution branches in the parameter space using continuation techniques. To deal with highly nonlinear viscous terms, a pseudo-spectral code is developed. Nonlinear equilibrium solutions was found and characterized for various values of the rheological parameters

Este trabalho aborda o escoamento incompressível ao redor de um cilindro circular. A tese que se quer defender, com base em experimentos numéricos, é: A equação de Landau pode ser obtida a partir das equações de Navier-Stokes por uma análise de estabilidade não-linear global. A teoria produz um procedimento bem-definido para determinação dos coeficientes da equação de Landau, permitindo assim a sua interpretação como um modelo simplificado (equações reduzidas de Navier-Stokes) para a predição das forças aplicadas pelo fluido ao cilindro, que podem ser comparados com resultados experimentais. O modelo não-linear se baseia em uma teoria assintótica que, como se sabe, tem sua faixa de validade no espaço de parâmetros determinada a posteriori, por meio da própria comparação com dados de laboratório. Resultados na faixa 46 <= Re <= 80 são apresentados. Descobriu-se, que a faixa de aplicabilidade da teoria como aqui exposta é restrita, não excedendo em muito o valor crítico do número de Reynolds. Argumentos são expostos para justificar esta afirmação e possíveis maneiras de modificar a teoria para estender esta faixa são apresentadas. São reportados, ainda, teoria e resultados sobre um novo tipo de condição de contorno,denominado impedância fluida, que permite reduzir o tamanho do domínio de cálculo necessário para simulação de escoamentos externos, comparativamente à comumente utilizada condição de outflow. Neste caso, abordou-se a faixa 20 <= Re <= 600. / This work adresses the incompressible flow around a circular cylinder. What we want to prove, based on numerical experiments, reads: The Landau equation can be derived from the Navier-Stokes equations by means of a global nonlinear stability analysis. The theory leads to a procedure for calculating numerically the coefficients of these equation, thus permitting their interpretation as a simplified model - reduced Navier-Stokes equation - for the prediction of the forces applied by the fluid on the cylindrical structure, which can be compared against experimental data. The nonlinear model is based on an asymptotic theory which, as is known, has its validity range in the parameter space determined a posteriori. The focus lies in the range 46 <= Re <= 80. It was found that the theorys applicability range as presented here is restricted to a small neighborhood of Rec. This affirmation in justified and possible means of modifying the theory in order to enlarge this range are proposed. Theory and results concerning a new type of boundary condition called fluid impedance are also reported, permitting the reduction of the domain size necessary for simulating external flows, comparatively to the commonly used outflow condition. In this case, the range 20 <= Re <= 600 was considered.

Este trabalho aborda o escoamento incompressível ao redor de um cilindro circular. A tese que se quer defender, com base em experimentos numéricos, é: A equação de Landau pode ser obtida a partir das equações de Navier-Stokes por uma análise de estabilidade não-linear global. A teoria produz um procedimento bem-definido para determinação dos coeficientes da equação de Landau, permitindo assim a sua interpretação como um modelo simplificado (equações reduzidas de Navier-Stokes) para a predição das forças aplicadas pelo fluido ao cilindro, que podem ser comparados com resultados experimentais. O modelo não-linear se baseia em uma teoria assintótica que, como se sabe, tem sua faixa de validade no espaço de parâmetros determinada a posteriori, por meio da própria comparação com dados de laboratório. Resultados na faixa 46 <= Re <= 80 são apresentados. Descobriu-se, que a faixa de aplicabilidade da teoria como aqui exposta é restrita, não excedendo em muito o valor crítico do número de Reynolds. Argumentos são expostos para justificar esta afirmação e possíveis maneiras de modificar a teoria para estender esta faixa são apresentadas. São reportados, ainda, teoria e resultados sobre um novo tipo de condição de contorno,denominado impedância fluida, que permite reduzir o tamanho do domínio de cálculo necessário para simulação de escoamentos externos, comparativamente à comumente utilizada condição de outflow. Neste caso, abordou-se a faixa 20 <= Re <= 600. / This work adresses the incompressible flow around a circular cylinder. What we want to prove, based on numerical experiments, reads: The Landau equation can be derived from the Navier-Stokes equations by means of a global nonlinear stability analysis. The theory leads to a procedure for calculating numerically the coefficients of these equation, thus permitting their interpretation as a simplified model - reduced Navier-Stokes equation - for the prediction of the forces applied by the fluid on the cylindrical structure, which can be compared against experimental data. The nonlinear model is based on an asymptotic theory which, as is known, has its validity range in the parameter space determined a posteriori. The focus lies in the range 46 <= Re <= 80. It was found that the theorys applicability range as presented here is restricted to a small neighborhood of Rec. This affirmation in justified and possible means of modifying the theory in order to enlarge this range are proposed. Theory and results concerning a new type of boundary condition called fluid impedance are also reported, permitting the reduction of the domain size necessary for simulating external flows, comparatively to the commonly used outflow condition. In this case, the range 20 <= Re <= 600 was considered.

The present thesis studies transition to turbulence in a spatially developing bound-ary layer for subcritical Reynolds numbers. A fully nonlinear iterative direct-adjoint optimisation technique is employed to identify finite amplitude perturbations triggering transition in an energy efficient way. The study explores two approaches to find the Reynolds number scaling of the subcritical transition energy threshold Ec(Re) and the corresponding nonlinear optimum which is the minimal seed for subcritical transition to turbulence. The first approach focuses on shortened optimisation time horizons T compared to a reference case with T = 400. It is shown that the transition energy threshold Ec increases for T = 200/300 when compared to the reference value Ec,T =400. This is linked to the existence of local optima which maximise the objective functional for short transient times. These local optima are fully localised and feature the Orr and liftup energy growth mechanisms as observed for the reference case. However, their long-time evolution is suboptimal since it leads to a stable streak configuration which is found to relaminarise also for initial amplitudes of E0 &gt; Ec,T =400. The second approach of using an inflow Reynolds number increased by factor 3/2 but non-shortened T is shown to be suitable to identify the scaling Ec(Re). Exploratory optimisation runs suggest a decrease in the transition energy threshold of at leastEc(3/2 · Re)/Ec(Re) &lt; 0.47. / Denna avhandling studerar turbulensöverång i ett rumsligt-utvecklande gränsskikt vid subkritiska Reynolds tal. En icke-linjär iterativ direkt-adjoint optimeringsteknik implimenteras för att indentifiera perturbationer med ändlig amplitud som leder till övergång på ett energieffektivt sätt. Studien utforskar två metoder för att hitta skalningen av Reynolds numret till den subkritiska energytröskeln Ec(Re) för övergång och det tillhörande icke-linjära optimum minimal seed som leder till subkritisk turbulensövergång. Den första metoden fokuserar på förkortade optimeringstidshorisonter T jämfört med referensfallet med T = 400. Det visar sig att energitröskeln Ec ökar för T = 200/300 jämfört med referensvärdet Ec,T =400. Detta är kopplat till förekomsten av lokala optima som maximerar the objective functional för korta transienta tidsho-risonter. Dessa lokala optima är helt lokala i rummet och uppvisar samma Orr och liftup energitillväxtmekanismer som referensfallet. Utvärderingen på lång sikt visar sig dock vara suboptimal då den leder till en stabil streak konfiguration som återför även initiella perturbationsamplituder E0 &gt; Ec,T =400 till ett laminärt tillstånd. Den andra metoden, som använder sig av Reynolds tal ökade med en faktor 3/2 men icke-förkortade tidshorisonter T , visar sig lämplig för att identifiera skalningen Ec(Re). Utforskande optimering antyder att en minskning i energitröskeln för övergång medminst Ec(3/2 · Re)/Ec(Re) &lt; 0.47.

This diploma thesis describes the design and assessment of steel structural design of the steel aggregate bins including roofing. The construction has a ground plan of about 33 x 9 m and it is divided into 8 cells bins. Main material is steel, grade S355 and S235. There is developed a static analysis of the main load-bearing parts of the structure, including joints and selected details.

This work focusses on analysing the stability of the MSFR – a molten salt reactor with a fast neutron spectrum. The investigations are based on a model, which was published and studied by the Politecnico di Milano using a linear approach. Since linear methods can only provide stability information to a limited extent, this work continues the conducted investigations by applying nonlinear methods. In order to examine the specified reactor model, the system equations were implemented, adjusted and verified using MATLAB code. With the help of the computational tool MatCont, a so-called fixed-point solution was tracked and its stability monitored during the variation of selected control parameters. It was found that the considered fixed point does not change its stability state and remains stable. Coexisting fixed points or periodic solutions could not be detected. Therefore, the analysed MSFR model is considered to be a stable system, in which the solutions always tend towards a steady state.:1. Introduction 2. Molten Salt Reactor Technology 2.1. Introduction 2.2. Historical Development 2.3. Working Principle of Molten Salt Reactors 2.4. Molten Salt Coolants 2.5. Advantages and Drawbacks 2.6. Classification 2.7. Molten Salt Fast Reactor Design 3. Stability Characteristics of Dynamical Systems 3.1. Introduction 3.2. Dynamical Systems 3.3. Stability Concepts 3.3.1. Introduction 3.3.2. Lagrange Stability (Bounded Stability) 3.3.3. Lyapunov Stability 3.3.4. Poincaré Stability (Orbital Stability) 3.4. Fixed-Point Solutions 3.4.1. Stability Analysis of Fixed-Point Solutions 3.4.2. Bifurcations of Fixed-Point Solutions 3.5. Periodic Solutions 3.5.1. Stability Analysis of Periodic Solutions 3.5.2. Bifurcations of Periodic Solutions 4. Analysed Reactor System 4.1. Introduction 4.2. Specified Reactor Model 4.3. Implementation and Verification of the Linearised System of Equations 4.3.1. Linearised System of Delayed Differential Equations 4.3.2. Comparison with Reference Plots 4.3.3. Adaptation of Parameter Values 4.4. Implementation and Verification of the Nonlinear System of Equations 4.4.1. Nonlinear System of Delayed Differential Equations 4.4.2. Delayed Neutron Precursor Equation Adjustments 4.4.3. Salt Temperature Equation Adjustments 4.4.4. Nonlinear System of Ordinary Differential Equations 4.4.5. Verification of the Nonlinear System of Ordinary Differential Equations 5. Conducted Stability Analyses 5.1. Introduction 5.2. Nonlinear Stability Analysis 5.2.1. Implementation 5.2.2. Results 5.2.3. Interpretation 5.3. Linear Stability Analysis 5.3.1. Comparison Between the Linearised and Nonlinearised MSFR System of Equations 5.3.2. Stability Investigations Using a Linear Criterion 5.4. MatCont Reliability Test Using an MSBR Model 6. Conclusions and Recommendations for Future Studies / Im Fokus dieser Arbeit steht die Stabilitätsanalyse des MSFR – eines Flüssigsalzreaktors mit schnellem Neutronenspektrum. Als Grundlage wurde ein Modell verwendet, das am Politecnico di Milano erstellt und dort mittels linearer Methoden untersucht wurde. Da lineare Betrachtungen nur eingeschränkte Stabilitätsaussagen treffen können, erweitert diese Arbeit die Untersuchungen um die nichtlineare Stabilitätsanalyse. Zur Untersuchung des vorgegebenen Reaktormodells wurden die Systemgleichungen in MATLAB übertragen und verifiziert. Mithilfe der Rechensoftware MatCont wurde eine sogenannten Fixpunkt-Lösung des Modells unter der Variation ausgewählter Parameter verfolgt und deren Stabilität überprüft. Es hat sich gezeigt, dass der betrachtete Fixpunkt seinen Stabilitätszustand dabei nicht verändert und stabil bleibt. Koexistierende Fixpunkte oder periodische Lösungen konnten nicht nachgewiesen werden. Daher gilt das betrachtete MSFR-Modell als ein stabiles System, dessen Lösungen immer auf einen stationären Zustand zulaufen.:1. Introduction 2. Molten Salt Reactor Technology 2.1. Introduction 2.2. Historical Development 2.3. Working Principle of Molten Salt Reactors 2.4. Molten Salt Coolants 2.5. Advantages and Drawbacks 2.6. Classification 2.7. Molten Salt Fast Reactor Design 3. Stability Characteristics of Dynamical Systems 3.1. Introduction 3.2. Dynamical Systems 3.3. Stability Concepts 3.3.1. Introduction 3.3.2. Lagrange Stability (Bounded Stability) 3.3.3. Lyapunov Stability 3.3.4. Poincaré Stability (Orbital Stability) 3.4. Fixed-Point Solutions 3.4.1. Stability Analysis of Fixed-Point Solutions 3.4.2. Bifurcations of Fixed-Point Solutions 3.5. Periodic Solutions 3.5.1. Stability Analysis of Periodic Solutions 3.5.2. Bifurcations of Periodic Solutions 4. Analysed Reactor System 4.1. Introduction 4.2. Specified Reactor Model 4.3. Implementation and Verification of the Linearised System of Equations 4.3.1. Linearised System of Delayed Differential Equations 4.3.2. Comparison with Reference Plots 4.3.3. Adaptation of Parameter Values 4.4. Implementation and Verification of the Nonlinear System of Equations 4.4.1. Nonlinear System of Delayed Differential Equations 4.4.2. Delayed Neutron Precursor Equation Adjustments 4.4.3. Salt Temperature Equation Adjustments 4.4.4. Nonlinear System of Ordinary Differential Equations 4.4.5. Verification of the Nonlinear System of Ordinary Differential Equations 5. Conducted Stability Analyses 5.1. Introduction 5.2. Nonlinear Stability Analysis 5.2.1. Implementation 5.2.2. Results 5.2.3. Interpretation 5.3. Linear Stability Analysis 5.3.1. Comparison Between the Linearised and Nonlinearised MSFR System of Equations 5.3.2. Stability Investigations Using a Linear Criterion 5.4. MatCont Reliability Test Using an MSBR Model 6. Conclusions and Recommendations for Future Studies