BWR linear stability analysis

A state-of-the-art analytical model has been developed for investigating the linear stability of boiling water nuclear reactors (BWR). This model has been implemented into a computer code named NUFREQ-NP. The NUFREQ-NP code permits an investigation of the stability of a single heated channel, as well as the multi-channel core of a BWR. It accommodates various neutronics models, including point kinetics, one-dimensional, two-dimensional, and three-dimensional neutron kinetics. It is capable of evaluating system stability in terms of any of the following perturbed state variables: inlet flow rate, external reactivity, and system pressure.This paper presents the modeling principles used in NUFREQ-NP to describe the transient two-phase flow and heat transfer phenomena. Special emphasis is placed on those aspects of the model development which are related to variable system pressure effects. Also, the derivation of various transfer functions is given. The results of NUFREQ-NP testing and verification include a parametric study of the effects of various modeling assumptions, and comparisons with both out-of-core and in-core-experimental data. These comparisons indicate very good agreement between the calculated and measured system transfer functions.     

A novel auto-correlation function method for the determination of the decay ratio in BWR stability analysis

A novel auto-correlation function (ACF) method has been investigated for determining the oscillation frequency and the decay ratio in BWR stability analyses. The neutron signals are band-pass filtered to separate the oscillation peak in the power spectral density (PSD) from background. Two linear second-order oscillation models are considered. These models, corrected for signal filtering and including a background term under the peak in the PSD, are then least-squares fitted to the ACF of the previously filtered neutron signal, in order to determine the oscillation frequency and the decay ratio. Our method uses fast Fourier transform techniques with signal segmentation for filtering and ACF estimation. Gliding ‘short-term’ ACF estimates on a record allow the evaluation of uncertainties. Numerical results are given which have been obtained from neutron data of the recent Forsmark I and Forsmark II NEA benchmark project. Our results are compared with those obtained by other participants in the benchmark project.     

Assessment of linear and non-linear autoregressive methods for BWR stability monitoring

A benchmark has been performed to compare the performances of exponential autoregressive (ExpAR) models against linear autoregressive (AR) models with respect to boiling water reactor stability monitoring. The well-known March-Leuba reduced-order model is used to generate the time-series to be analysed, since this model is able to reproduce the most significant non-linear behaviour of boiling water reactors (i.e. converging, diverging and limit-cycle oscillations). In this way the stability characteristics of the signals to be analysed are known a priori. An application to experimental time-traces measured on a thermalhydraulic natural circulation loop is reported as well. All methods perform equally well in determining the stability characteristics of the analysed signals.     

An advanced reduced order model for BWR stability analysis

An advanced reduced order model was developed and qualified in the framework of a novel approach for nonlinear stability analysis of boiling water nuclear reactors (BWRs). This approach is called the RAM-ROM method where RAM is a synonym for system code and ROM stands for reduced order model. In the framework of the RAM-ROM method, integrated BWR (system) codes and reduced order models are used as complementary tools to examine the stability characteristics of fixed points and periodic solutions of the nonlinear differential equations describing the stability behaviour of a BWR loop. This methodology is a novel one in a specific sense: we analyse the highly nonlinear processes of BWR dynamics by applying validated system codes and by the sophisticated methods of nonlinear dynamics, e.g. bifurcation analysis. We claim and we will show that the combined application of independent methodologies to examine nonlinear stability behaviour can increase the reliability of BWR stability analysis.This work is a continuation of previous work at the Paul Scherrer Institute (PSI, Switzerland) of the second author and at the University of Illinois (USA) in this field. In the scope of a PhD work at the Technical University Dresden (Germany), the current ROM was extended to an advanced ROM by adding a recirculation loop model, a quantitative assessment of the necessity for consideration of the effect of sub-cooled boiling and a new calculation methodology for feedback reactivity. A crucial point of ROM qualification is a new calculation procedure for ROM input data based on steady-state RAM (ONA) results. The modified ROM is coupled with the BIFDD bifurcation code which performs a semi-analytical bifurcation analysis (see Appendix C). In this paper, the advanced ROM (TU Dresden ROM, TUD-ROM) is briefly described and the results of a nonlinear BWR stability analysis based on the RAM-ROM method are summarised for NPP Leibstadt, NPP Ringhals and NPP Brunsbüttel. The results show that the TUD-ROM including the new approach for ROM input data calculation is qualified for BWR stability analysis in the framework of the RAM-ROM method.     

Comments on the application of bifurcation analysis in BWR stability analysis

Currently, BWR stability analysis is most often performed by the application of system codes which provide the time evolution of the neutron flux or thermal power at a defined operational point (OP) after imposing a system parameter perturbation. However, in general it is impossible to understand the real stability state of the BWR at a specific OP by the application of system code analysis alone. Hence, we are exploring methods developed in the nonlinear dynamics field in order to reveal the nature of the BWR stability states when power oscillations are observed. A powerful method is bifurcation analysis. In order to motivate this “nonlinear thinking” versus “linear thinking”, in this paper we will demonstrate some examples of phenomena which can only be understood in nonlinear terms by application of bifurcation theory and where linear interpretation leads to incorrect conclusions.     

Simplified distributed parameters BWR dynamic model for transient and stability analysis

This paper describes a simplified model to perform transient and linear stability analysis for a typical boiling water reactor (BWR). The simplified transient model was based in lumped and distributed parameters approximations, which includes vessel dome and the downcomer, recirculation loops, neutron process, fuel pin temperature distribution, lower and upper plenums reactor core and pressure and level controls. The stability was determined by studying the linearized versions of the equations representing the BWR system in the frequency domain. Numerical examples are used to illustrate the wide application of the simplified BWR model. We concluded that this simplified model describes properly the dynamic of a BWR and can be used for safety analysis or as a first approach in the design of an advanced BWR.     

Application of TRACE/PARCS to BWR stability analysis

The work described here is the validation of TRACE/PARCS for Boiling Water Reactor stability analysis. A stability methodology was previously developed, verified, and validated using data from the OECD Ringhals stability benchmark. The work performed here describes the application of TRACE/PARCS to all the stability test points from cycle 14 of the Ringhals benchmark. The benchmark points from cycle 14 were performed using a half-core symmetric, 325 channel TRACE model. Several parametric studies are performed on test point 10 of cycle 14. Two temporal difference methods, Semi-Implicit method (SI) and Stability Enhanced Two Step (SETS) method are applied to three different mesh sizes in heated channels with series of time step sizes. The results show that the SI method has a smaller numerical damping than the SETS method. When applying the SI method with adjusted mesh and Courant time step sizes (the largest time step size under the Courant limit), the numerical damping is minimized, and the predicted Decay Ratio (DR) agrees well with the reference values which were obtained from the measured noise signal. The SI method with adjusted mesh and Courant time step size is then applied to all test points of cycle 14 with three types of initiating perturbations, control rod (CR), pressure perturbation, and noise simulation (NS). There is good agreement between the decay ratios and frequencies predicted by TRACE/PARCS and those from the plant measurements. Sensitivities were also performed to investigate the impact on the decay ratio and natural frequency of the heat conductivity of the gap between fuel and clad, as well as the impact of the pressure loss coefficient of spacers.     

BWR stability boundary surveillance

Neutron noise analysis can make great contributions in order to prevent the power instability event during the reactor starting up process. There is not reason to suppose that the stability boundary in the operation map, cannot drift away getting closer to the real operation point. Noise analysis can perform a double eye boundary drift surveillance by fitting the noise time series to an autoregressive model, and calculating the complex and the real pole. The complex pole accounts for the Decay Ratio and the real pole confirms this accounting. The real pole has a hidden relation with the chaotic behavior of the power, and it is related with the bubble residence time. In case of instability, the real pole vanishes.     

Application of the response matrix method to BWR lattice analysis

A lattice calculation code RESPLA has been developed for light-water reactor lattices on the basis of the response matrix method treating the heterogeneity in pin cells. The spatial dependency of neutron flux distribution along each cell boundary is taken into account by dividing the cell boundary into several subsurfaces and the anisotropy of neutron angular distribution is considered up to the P₁ component by using a relation between the P₀ and P₁ components. The RESPLA code has been applied to BWR lattice calculations and the calculational results have been compared with those obtained by the S_n method and the collision probability method. It has been found that the present response matrix method has the same accuracy as the collision probability method with fine spatial meshes and the error caused by the use of coarse meshes is much smaller than that by the collision probability method. Furthermore, the required computing time is smaller by about a factor of five than that in the collision probability method.     

Kuosheng BWR/6 stability analysis with LAPUR5 code

Unstable power/flow oscillation of a nuclear power reactor core is one of the main reasons that cause minor core damage. Stability analysis to determine system’s decay ratio needs to be performed at each core reload design to prevent core instability events from happening. Making use of LAPUR5 and SIMULATE-3 codes, we have established a methodology to conduct such analysis. Comparisons made with vendor’s STAIF results indicated close agreements, within acceptable ±0.2 in decay ratios, for Kuosheng NPP Unit2 Cycle 17 reloads design. Sensitivity studies have shown that density reactivity coefficient, delayed-neutron fractions (β) and decay constants (λ), total core flow, and core power axial shape are the most important parameters that might affect the accuracy of decay ratios. We have also found that core conditions at EOC result in larger decay ratios than those at BOC.     

Spatial and model-order based reactor signal analysis methodology for BWR core stability evaluation

A new methodology for the boiling water reactor core stability evaluation from measured noise signals has been recently developed and adopted at the Paul Scherrer Institut (PSI). This methodology consists in a general reactor noise analysis where as much as possible information recorded during the tests is investigated prior to determining core representative stability parameters, i.e. the decay ratio (DR) and the resonance frequency, along with an associated estimate of the uncertainty range. A central part in this approach is that the evaluation of the core stability parameters is performed not only for a few but for ALL recorded neutron flux signals, allowing thereby the assessment of signal-related uncertainties. In addition, for each signal, three different model-order optimization methods are systematically employed to take into account the sensitivity upon the model-order.     

Application of a reduced order model to BWR corewide stability analysis

The determination of system stability parameters from power readings is a problem usually solved by time series techniques such as autoregressive modeling. These techniques are capable of determining the system stability, but ignore the physics of the process and focus on the determination of a nth order linear model. A nonlinear reduced order system is used in conjunction with estimation techniques to present a different approach for stability determination. The simulation of the reduced order model shows the importance of the feedback reactivity imposed by the thermal-hydraulics; the dominant contribution to this feedback is provided by the void reactivity, being a function of power, burnup, power distribution, and in general of the operating conditions of the system. The feedback reactivity is estimated from power measurements and used in conjunction with a reduced order model to determine the system stability properties in terms of the decay ratio.     

Reactivity calculation in the frequency domain for BWR stability codes

This paper deals with the problem of computing the feedback reactivity in the frequency domain codes as the LAPUR code. First, we explain how to calculate the feedback reactivity in the frequency domain using slab-geometry (1D) kinetics, also we show how to perform the coupling of the 1D kinetics with the thermal–hydraulic part of the LAPUR code in order to obtain the density to reactivity feedback coefficients, the power to reactivity feedback coefficients and the inlet temperature to reactivity feedback coefficients for the different channels.     

Assessment of the interchannel mixing model with a subchannel analysis code for BWR and PWR conditions

The influence of the interchannel mixing model employed in a traditional subchannel analysis code was investigated in this study, specifically on the analysis of the enthalpy distribution and critical heat flux (CHF) in rod bundles in BWR and PWR conditions. The equal-volume-exchange turbulent mixing and void drift model (EVVD) was embodied to the COBRA-IV-I code. An optimized model of the void drift coefficient has been devised in this study as the result of the assessment with the two-phase flow distribution data for the general electric (GE) 9-rod and Ispra 16-rod test bundles. The influence of the subchannel analysis model on the analysis of CHF was examined by evaluating the CHF test data in rod bundles representing PWR and BWR conditions. The CHFR margins of typical light water nuclear reactor (LWR) cores were evaluated by considering the influence on the local parameter CHF correlation and the hot channel analysis result. It appeared that the interchannel mixing model has an important effect upon the analysis of CHFR margin for BWR conditions.     

Detecting long-range correlation with detrended fluctuation analysis: Application to BWR stability

The aim of this paper is to explore the application of detrended fluctuation analysis (DFA) to study boiling water reactor stability. DFA is a scaling method commonly used for detecting long-range correlations in non-stationary time series. This method is based on the random walk theory and was applied to neutronic power signal of Forsmark stability benchmark. Our results shows that the scaling properties breakdown during unstable oscillations.     

Surveillance of nuclear-thermohydraulic stability in BWR operation

A concept of a survey of the nuclear-thermohydraulic stability during operation of large modern boiling water reactors is presented. The concept incorporates detailed measurements of the stability boundary as well as accompanying evaluations of the stability margin during the operating reactor cycle. An automatic system to avoid unstable power flow conditions by immediate control rod insertion is an additional element of the concept. The proper functioning of this system in a practical event was demonstrated. Thus, inadvertent unstable reactor operating conditions could be avoided in all completed cycles by means of reactor and core loading design together with the enforced surveillance concept.     

Assessment of two BWR accident management strategies

Candidate mitigative strategies for the management of in-vessel events during the late phase (after-core degradation has occurred) of postulated boiling water reactor (BWR) severe accidents were considered at Oak Ridge National Laboratory (ORNL) during 1990. The identification of new strategies was subject to the constraint that they should, to the maximum extent possible, make use of the existing equipment and water resources of the BWR facilities, and not require major equipment modifications or additions. As a result of this effort, two of these candidate strategies were recommended for further assessment. The first was a strategy for containment flooding to maintain the core and structural debris within the reactor vessel in the event that vessel injection cannot be restored to terminate a severe accident sequence. The second strategy pertained to the opposite case, for which vessel injection would be restored after control blade melting had begun; its purpose was to provide an injection source of borated water at the concentration necessary to preclude criticality upon recovering a damaged BWR core. Assessments of these two strategies were performed during 1991 and this paper provides a discussion of the motivation for and purpose of these strategies, and the potential for their success.     

A nodal modal method for the neutron diffusion equation. Application to BWR instabilities analysis

Fast codes, capable of dealing with three-dimensional geometries, are needed to be able to simulate spatially complicated transients in a nuclear power reactor. In this paper, we propose a modal method to integrate the neutron diffusion equation in which the spatial part has been previously dicretized using a nodal collocation method. For the time integration of the resulting system of differential equations it is supposed that the solution can be expanded as a linear combination of the dominant Lambda modes associated with a static configuration of the reactor core and, using the eigenfunctions of the adjoint problem, a system of differential equations of lower dimension is obtained. This system is integrated using a variable time step implicit method. Furthermore, for realistic transients, it would be necessary to calculate a large amount of modes. To avoid this, the modal method has been implemented making use of an updating process for the modes at each certain time step. Five transients have been studied: a homogeneous reactor, a non-homogeneous reactor, the 3D Langenbuch reactor and two transients related with in-phase and out-of-phase oscillations of Leibstadt NPP. The obtained results have been compared with the ones provided by a method based on a one-step backward discretization formula.     

Core stability tracking of the KKB BWR in recent years

The core inventories of a number of BWRs are currently experiencing gradual transitions from 8 × 8 lattice fuel to SVEA fuel. One of them is the KKB (Brunsbüttel) BWR. In this reactor, as in many others in Germany, core stability tests have been conducted on a regular basis for many years, following an established and well-defined procedure.The test experience which has been acquired from the KKB core over recent years shows that, as its inventory of 8 × 8 lattice fuel was gradually replaced by SVEA fuel, the core stability improved progressively.The paper comments on the stability tests which were conducted in the KKB plant over the time period concerned, and discusses the observed stability trend in the light of the operational characteristics of the core on the various test occasions.