This thesis is concerned with nonlinear analyses of BWR stability behaviour, contributing to a deeper understanding in this field. Despite negative feedback-coefficients of a BWR, there are operational points (OP) at which oscillatory instabilities occur. So far, a comprehensive and an in-depth understanding of the nonlinear BWR stability behaviour are missing, even though the impact of the significant physical parameters is well known. In particular, this concerns parameter regions in which linear stability indicators, like the asymptotic decay ratio, lose their meaning. Nonlinear stability analyses are usually carried out using integral (system) codes, describing the dynamical system by a system of nonlinear partial differential equations (PDE). One aspect of nonlinear BWR stability analyses is to get an overview about different types of nonlinear stability behaviour and to examine the conditions of their occurrence. For these studies the application of system codes alone is inappropriate. Hence, in the context of this thesis, a novel approach to nonlinear BWR stability analyses, called RAM-ROM method, is developed. In the framework of this approach, system codes and reduced order models (ROM) are used as complementary tools to examine the stability characteristics of fixed points and periodic solutions of the system of nonlinear differential equations, describing the stability behaviour of a BWR loop. The main advantage of a ROM, which is a system of ordinary differential equations (ODE), is the possible coupling with specific methods of the nonlinear dynamics. This method reveals nonlinear phenomena in certain regions of system parameters without the need for solving the system of ROM equations. The stability properties of limit cycles generated in Hopf bifurcation points and the conditions of their occurrence are of particular interest. Finally, the nonlinear phenomena predicted by the ROM will be analysed in more details by the system code. Hence, the thesis i.

Linear and Non-Linear Stability Analysis in Boiling Water Reactors: The Design of Real-Time Stability Monitors presents a thorough analysis of the most innovative BWR reactors and stability phenomena in one accessible resource. The book presents a summary of existing literature on BWRs to give early career engineers and researchers a solid background in the field, as well as the latest research on stability phenomena (propagation phenomena in BWRs), nuclear power monitors, and advanced computer systems used to for the prediction of stability. It also emphasizes the importance of BWR technology and embedded neutron monitoring systems (APRMs and LPRMs), and introduces non-linear stability parameters that can be used for the onset detection of instabilities in BWRs. Additionally, the book details the scope, advantages, and disadvantages of multiple advanced linear and non linear signal processing methods, and includes analytical case studies of existing plants. This combination makes Linear and Non-Linear Stability Analysis in Boiling Water Reactors a valuable resource for nuclear engineering students focusing on linear and non-linear analysis, as well as for those working and researching in a nuclear power capacity looking to implement stability methods and estimate decay ratios using non-linear techniques. Explores the nuclear stability of Boiling Water Reactors based on linear and non-linear models Evaluates linear signal processing methods such as autoregressive models, Fourier-based methods, and wavelets to calculate decay ratios Proposes novel non-linear signal analysis techniques linked to non-linear stability indicators Includes case studies of various existing nuclear power plants as well as mathematical models and simulations

Contents of this Doctoral Dissertation include: Understanding the linear stability characteristics of BWRs, Experiments on the stability of the Desire facility, Applications of the reducer-order model, Numerical analysis of the nonlinear dynamics of BWRs, Experiments on the nonlinear dynamics of natural-circulation two-phase flows, Experiments on the neutronic-thermalhydraulic stability, Conclusions and Discussion

Abstract: A study of a Boiling Water Reactor (BWR) dynamics is presented with the objective of determining the attractors, domains of attraction and change in system stability with fluctuations in the system parameters. A reduced order model of the system was used for the investigations. The cell to cell mapping technique (CCMT) is used to determine the attractors and the domains of attraction for the system. The CCMT is a numerical technique for the global analysis of non-linear dynamics of systems and models system evolution as a Markov chain in time. The probabilistic modeling of the system dynamics and no differentiability requirements on the governing equations makes CCMT naturally suited for analysis of systems with stochastic parameters. This method, however, runs into performance problems with increasing number of state variables (degrees of freedom) of the system under investigation. Two methods are proposed to improve the performance of the CCMT for higher order systems. One of them is based on choosing different mapping time steps for different initial conditions for the system. The second method restricts the source cell region and gives a conditional probability of the system location. MATLAB v7.0 was used to set up the system and the simulations were run using the Ohio Supercomputing Center's distributed computing facilities. It is shown that these proposed methods lead to significant reduction in computational time compared to conventional CCMT. The results obtained are also generally better compared to the conventional approach. Using these proposed techniques it is determined that the BWR system has only one attractor and the only way to keep the reactor stable is to control the values of the system parameters. The parametric analysis was conducted using Taguchi methods, which are based on design of experiment techniques and the application of the signal-to-noise ratios. The experiment design was done using MINITAB v14. The experiments were used to determine the effects of parameter variation on the stability of the system as well as the interactions amongst the parameters. The parametric studies reveal that the heat transfer coefficient (k), the heat generation coefficient (Q), the Doppler's coefficient of reactivity ([gamma]1), delayed neutron precursor concentration ([beta]) and fitting parameters a1 and a2 have a notably larger effect on the response. Out of these parameters k, a, Q and [gamma]1 tend to destabilize the system at higher values while [beta], a1 and a2 have a stabilizing effect at higher values. Further, cross effects between a, k and Q were also found to be negligible compared to the main effects of the control factors.

Density Wave Oscillations (DWOs) are known to be possible when a coolant undergoes considerable density reduction while passing through a heated channel. In the development of boiling water reactors (BWRs), there has been considerable concern about the effects of such oscillations when coupled with neutronic feedback. The current trend of increasing reactor power density and relying more extensively on natural circulation for core cooling may have consequences for the stability characteristics of new BWR designs. This work addresses a wide range of issues associated with the BWR stability: 1) flashing-induced instability and natural circulation BWR startup; 2) stability of the BWRs with advanced designs involving high power :densities; 3) modeling assumptions in stability analysis methods; and 4) the fuel clad performance during power and flow oscillations. To capture the effect of flashing on density wave oscillations during low pressure startup conditions, a code named FISTAB has been developed in the frequency domain. The code is based on a single channel thermal-hydraulic model of the balance of the water/steam circulation loop, and incorporates the pressure dependent water/steam thermodynamic properties, from which the evaporation due to flashing is captured. The functionality of the FISTAB code is confirmed by testing the experimental results at SIRIUS-N facility. Both stationary and perturbation results agree well with the experimental results. The proposed ESBWR start-up procedure under natural convection conditions has been examined by the FISTAB code. It is confirmed that the examined operating points along the ESBWR start-up trajectory from TRACG simulation will be stable. To avoid the instability resulting from the transition from single-phase natural circulation to two-phase circulation, a simple criterion is proposed for the natural convection BWR start-up when the steam dome pressure is still low. Using the frequency domain code STAB developed at MIT, stability analyses of some proposed advanced BWRs have been conducted, including the high power density BWR core designs using the Large Assembly with Small Pins (LASP) or Cross Shape Twisted (CST) fuel designs developed at MIT, and the Hitachi's RBWR cores utilizing a hard neutron spectrum and even higher power density cores. The STAB code is the predecessor of the FISTAB code, and thermodynamic properties of the coolant are only dependent on system pressure in STAB. It is concluded that good stability performance of the LASP core and the CST core can be maintained at nominal conditions, even though they have 20% higher reactor thermal power than the reference core. Power uprate does not seem to have significant effects on thermal-hydraulic stability performance when the power-to-flow ratio is maintained. Also, both the RBWR-AC and RBWR-TB2 designs are found viable from a stability performance point of view, even though the core exit qualities are almost 3 times those of a traditional BWR. The stability of the RBWRs is enhanced through the fast transient response of the shorter core, more flat power and power-to-flow ratio distributions, less negative void feedback coefficient, and the core inlet orifice design. To examine the capability of coupled 3D thermal-hydraulics and neutronics codes for stability analysis, USNRC's latest system analysis code, TRACE, is chosen in this work. Its validation for stability analysis and comparison with the frequency domain approach, have been performed against the Ringhals 1 stability tests. Comprehensive assessment of modeling choices on TRACE stability analysis has been made, including effects of timespatial discretization, numerical schemes, thermal-hydraulic channel grouping, neutronics modeling, and control system modeling. The predictions from both the TRACE and STAB codes are found in reasonably good agreement with the Ringhals 1 test results. The biases for the predicted global decay ratio are about 0.07 in TRACE results, and -0.04 in STAB results. However, the standard deviations of decay ratios are both large, around 0.1, indicating large uncertainties in both analyses. Although the TRACE code uses more sophisticated neutronic and thermal hydraulic models, the modeling uncertainty is not less than that of the STAB code. The benchmark results of both codes for the Ringhals stability test are at the same level of accuracy. The fuel cladding integrity during power oscillations without reactor scram is examined by using the FRAPTRAN code, with consideration of both the stress-strain criterion and thermal fatigue. Under the assumed power oscillation conditions for high burn-up fuel, the cladding can satisfy the stress-strain criteria in the ASME Code. Also, the equivalent alternating stress is below the fatigue threshold stress, thus the fatigue limit is not violated. It can be concluded that under a large amount of the undamped power oscillation cycles, the cladding would not fail, and the fuel integrity is not compromised.