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
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:72464 |
| Date | 30 October 2020 |
| Creators | Kraus, Maximilian |
| Contributors | Lange, Carsten, Viebach, Marco, Lippmann, Wolfgang, Technische Universität Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:masterThesis, info:eu-repo/semantics/masterThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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