Stability investigation of thermally induced flow oscillations in cryogenic heat exchangers Final report

Analytic model of thermal flow oscillations in heat exchangers for supercritical fluid

Design of Nonlinear PID Controllers and Their Application to a Heat Exchanger System for LNG-fuelled Marine Engines

Excessive use of fossil fuels resources is adding several types of greenhouse gases which make the earth warmer. Emissions from ship's exhausts contribute to global climate change, too. The International Maritime Organization (IMO) has adopted regulations to reduce the emission of air pollutants from international shipping, such as major air pollutants, carbon dioxide (CO2), nitrogen oxides (NOx), and sulphur oxides (SOx) under Annex VI of the 1997 MARPOL protocol. Likewise, as regulations on the emission of major air pollutants have become internationally strict, the development of environmentally friendly vessels and engines is required. One of the globally accepted means of reducing emission gases is the use of more eco-friendly fuel, LNG (Liquefied Natural Gas). LNG as a marine fuel reduces air pollutants as referred compared to traditional heavy fuel oil (HFO). Recently, large engine manufacturers are developing LNG-fuelled marine engines. In order to use this cryogenic LNG as a fuel, it is necessary to change it back to a gaseous state. A heat exchanger is used to regasify LNG. The heat exchange takes place between LNG and glycol on the primary loop, and heat exchange occurs between glycol and steam on the secondary loop. These series of processes are called LNG regasification. To control the temperature of the heat exchanger, it is necessary to model the heat exchanger. However, it is not easy to obtain an accurate mathematical model because the heat exchanger has non-linearity and time-varying characteristics. In addition, a fixed-gain controller is bound to have a limitation in its function if parameters of the heat exchanger are changed. Thus, various techniques have been studied to improve the adaptability and robustness of the controller. Recently, there has been using nonlinear PID (NPID) controller for the controlled system which have highly nonlinear and time-varying characteristics during operation. Therefore, this thesis proposes two types of the nonlinear proportional, integral, derivative (NPID) controllers to control the glycol temperature of the regasification system for LNG-fuelled marine engines. The Fully-Nonlinear PID (F-NPID) controller has a structure that the error between the set-point (or reference input) and output (or the measured output) is scaled nonlinearly, and input into the controller to derive proportional, integral, and derivative controllers. The Partial-Nonlinear PID (P-NPID) controller uses the conventional linear PD controller and only I controller uses the method of F-NPID controller. In this case, the nonlinear functions are implemented by the Fuzzy model of Takagi-Sugeno (T-S) type. In addition, the error is continuously scaled so that outstanding control performance can be maintained even when the operating environment is changed, thereby improving the swiftness and the closeness of responses. Also, the parameters of the two proposed controllers are optimally tuned in terms of minimizing the integral of the absolute error (IAE) objective function based on the genetic algorithm (GA). Meanwhile, it is necessary to examine the stability of overall feedback system that can be caused by introducing nonlinear functions during controller design. For this, the stability of the overall feedback system is analyzed by applying the circle stability theorems, which is often used for stability analysis of nonlinear problems. The proposed controllers are verified their performances which are the set-point tracking, robustness against noise and parameter changes, disturbance rejection performances by comparing with two conventional PID controllers and a conventional NPID controller.Chapter 1. Introduction 1 1.1 Research background and trends 1 1.2 Research content and composition 6 Chapter 2. LNG-fuelled Marine Engines 8 2.1 Changes of LNG-fuelled marine engines 8 2.2 Fuel injection of LNG-fuelled marine engines 10 2.3 Fuel supply system of LNG-fuelled marine engines 13 Chapter 3. Modeling of LNG Regasification System 17 3.1 Heat exchanger 17 3.2 LNG regasification system 18 3.3 Modeling of the secondary loop heat exchanger of LNG regasification system 19 3.3.1 Model of an I/P converter 19 3.3.2 Model of a pneumatic control valve 20 3.3.3 Model of a heat exchanger 23 3.3.4 Model of a disturbance 27 3.3.5 Model of a RTD sensor 28 3.3.6 Model of a time delay 29 3.3.7 Open-loop control system 30 Chapter 4. Surveys of Existing PID Controllers 32 4.1 Linear PID controller 32 4.1.1 Structure of the conventional PID controller 32 4.1.2 Characteristics of control actions 33 4.1.3 Effects of PID controller gains 36 4.2 Gain tuning of the conventional PID controller 37 4.2.1 Ziegler-Nichols tuning method 37 4.2.2 Tyreus-Luyben tuning method 40 4.3 Practical PID controller 41 4.4 Existing nonlinear PID controllers 44 4.4.1 Seraji’s NPID controller 45 4.4.2 Korkmaz’s NPID controller 48 Chapter 5. Suggestion of the Proposed Nonlinear PID Controllers 52 5.1 Fully-nonlinear PID controller 52 5.1.1 Nonlinear P block 53 5.1.2 Nonlinear D block 57 5.1.3 Nonlinear I block 57 5.1.4 Relationship between and 60 5.2 Partially-nonlinear PID controller 62 5.2.1 Linear PD block 63 5.2.2 Nonlinear I block 63 5.3 Feedback control systems 63 5.3.1 Modified F-NPID control system 63 5.3.2 P-NPID control system 66 5.4 Tuning of the controller parameters 68 5.4.1 Genetic algorithm 68 5.4.2 Optimal tuning of the controller parameters 73 Chapter 6. Stability Analysis 75 6.1 System description 75 6.2 Basic definitions and theorems 76 6.3 Stability of the NPID control systems 86 6.3.1 Sector condition of nonlinear block 86 6.3.2 Stability analysis of F-NPID control system 87 6.3.3 Stability analysis of P-NPID control system 88 Chapter 7. Simulation and Discussion of Results 90 7.1 Controller parameter tuning 90 7.2 Reponses to set-point changes 91 7.3 Reponses to noise rejection 94 7.4 Reponses to system parameter changes 95 7.5 Reponses to disturbance changes 97 Chapter 8. Conclusion 99 References 101Docto

Investigation of the Stability of a Molten Salt Fast Reactor

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 StudiesIm 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 Studie

Dynamics Modeling of Molten Salt Reactors

The abundance of energy is a necessity for the prosperity of humans. The rise in energy demand has created energy shortages and issues related to energy security. Nuclear energy can produce vast amounts of reliable energy without many of the negative externalities associated with other competing energy sources, such as coal and natural gas. As a result, public interest in nuclear power has increased in the past decade. Many new types of nuclear reactor are proposed. These nuclear reactor designs feature many passive technologies that can operate without external influence. Reactors that feature advanced passive safety features are catagorized as 4$^{th}$ generation advanced reactors. \acp{msr} are a type of advanced reactor that uses molten alkali halide salts as both the coolant and the fuel matrix. \ac{msr} remain as understudied systems with complex dynamic behaviors. Non-linear dynamic simulations allow modeling complex systems such as \acp{msr}. Non-linear modeling as such presented here can be used to understand the unique dynamic behaviors of \acp{msr}. The modeling methodology is implemented in Modelica, an open-source dynamic modeling environment, and is publicly available. Modeling capabilities include 1D thermal hydrolic coupled neutronics, dynamic decay heat production, fission product inventory tracking, and a collection of support utilities. The modeling toolkit \ac{smdmsr} is specifically geared toward modeling the thermal spectrum \ac{msr}. Its modular implementation allows the substitution of various physics modules to capture the specific functional requirements of a specific \ac{msr} system. The publication includes three dynamic models of \ac{msr} systems of varying compexities. They include \ac{msre}, \ac{msdr} and \ac{msrr}. Modeling of each system is discussed, and several transients including both normal and off-normal transients are performed to demonstrate the \ac{smdmsr} toolkit\u27s modeling capabilities

Modélisation dynamique et commande optimale d'un système de réfrigération à base d'éjecteur

Recently, the ejector-based refrigeration system (ERS) has been widely used in the cooling industry as an appropriate alternative to the compressor-based cooling systems. However, the advantages of ERS such as the reliable operation and low operation and maintenance costs are overshadowed by its low efficiency and design complexity. In this context, this thesis presents the efforts to develop a control model enabling the ERS to operate in its optimal operational conditions. The extensive experimental studies of ERS revealed that at a fixed condenser inlet condition, there exists an optimal primary stream mass flow rate (generating pressure) that simultaneously maximizes the compression ratio (Cr) and exergy efficiency and minimizes the evaporating pressure. Then, the steady state models of the heat exchangers were developed and used to investigate the influence of the increase in generating pressure on the coefficient of performance (COP) of the system and it showed that increasing the generating pressure reduces the COP, linearly. In order to predict the choking regime of the ejector and explain the reasons of observed physical phenomenon, the 1D model of a fixed geometry ejector installed within an R245fa ERS was developed. The developed model demonstrated that the ejector operates in the subcritical mode when the generating pressure is below the Cr optimum point, while it operates in critical mode at or above the optimum generating pressure. Next, a dynamic model of the ERS was built to evaluate the ERS transient response to an increase in the primary stream mass flow rate. Since the ERS dynamics is mainly dominated by the thermal dynamics of the heat exchangers, the dynamic models of the heat exchangers were developed using the moving boundary approach and connected to the developed models of the ejector and steady state models of the pump and expansion valve to build a single dynamic model of the system. The built dynamic model of an ERS was used to estimate the time response of the system in the absence of accurate experimental data of the system’s dynamics. Finally, a control model was designed to drive an ERS towards its optimal operation condition. A self-optimizing, model-free control strategy known as Extremum seeking control (ESC) was adopted to minimize evaporating pressure in a fixed condenser thermal fluid inlet condition. The innovative ESC model named batch phasor ESC (BPESC) was proposed based on estimating the gradient by evaluating the phasor of the output, in batch time. The simulation results indicated that the designed BPESC model can seek and find the optimum evaporating pressure with good performance in terms of predicting the steady state optimal values and the convergence rates.Récemment, le système de réfrigération à éjecteur (SRE) a été largement utilisé dans l'industrie du refroidissement en tant que solution de remplacement appropriée aux systèmes de refroidissement à compresseur. Cependant, les avantages du SRE, tels que le fonctionnement fiable et les faibles couts d'exploitation et de maintenance, sont éclipsés par son faible rendement et sa complexité de conception. Dans ce contexte, ce projet de recherche de doctorat a détaillé les efforts déployés pour développer une stratégie de commande permettant au système de fonctionner dans ses conditions opérationnelles optimales. Les études expérimentales approfondies du SRE ont révélé que, dans une condition d'entrée de condensateur constante, il existe un débit massique optimal du flux primaire (générant une pression) qui maximise simultanément le taux de compression (Cr) et l'efficacité exergétique, et minimise la pression d’évaporation. Ensuite, les modèles à l’état d’équilibre des échangeurs de chaleur ont été développés et utilisés pour étudier l’influence de l’augmentation de la pression générée sur le coefficient de performance (COP) du système et il en ressort que l'augmentation de la pression génératrice réduit le COP de manière linéaire. Afin de prédire le régime d'étouffement de l'éjecteur et d'expliquer les raisons du phénomène physique observé, le modèle 1D d'un éjecteur à géométrie fixe installé dans un système SRE R245fa a été développé. Le modèle développé a démontré que l'éjecteur fonctionne en mode sous-critique lorsque la pression génératrice est inférieure au point optimal de Cr, alors qu'il fonctionne en mode critique à une pression égale ou supérieure à la pression génératrice optimale. Ensuite, un modèle dynamique du SRE a été développé pour étudier la réponse transitoire du SRE lors d’une augmentation du débit massique du flux primaire. Puisque la dynamique du SRE est principalement dominée par la dynamique thermique des échangeurs de chaleur, les modèles dynamiques des échangeurs de chaleur ont été développés à l'aide de l'approche des limites mobiles et connectés aux modèles développés de l'éjecteur et des modèles à l'état stationnaire de la pompe et de la vanne un seul modèle dynamique du système. En l’absence de données expérimentales précises sur la dynamique d’un système SRE, le modèle dynamique développé du SRE a été simulé numériquement pour étudier sa réponse temporelle. Enfin, une stratégie de commande extrêmale (ESC) a été élaboré pour régler automatiquement le SRE à ses conditions de fonctionnement optimales, c’est-à-dire pour trouver la vitesse de la pompe qui minimise la pression dans des conditions d'entrée de condenseur fixes. Afin de proposer une ESC implémentable en temps discret sur une installation réelle sujette à un bruit de mesure important et un traitement hors-ligne par trame, une nouvelle commande extrémale basée sur une approche par phaseur avec une procédure de traitement de signal par trame (BPESC) a été développée et simulée avec le modèle numérique. Les résultats de la simulation ont indiqué que le modèle BPESC peut trouver la vitesse optimale de la pompe avec de bonnes performances en termes de précision et de vitesse de convergence