A simplified model of the BWR depressurization transient

A simplified model is proposed to evaluate the BWR plant depressurization transient subsequent to the activation of a single safety relief valve. The model is validated with a series of RELAP5 Mod 3 calculations yielding reasonable comparisons. The depressurization behavior of the 26 US BWR plants is analyzed with the model and the relevant parameters controlling the process are identified. Of these, four are plant-specific and their effect on the final outcome of the depressurization transient is quantified. The minimum vessel inventory at the activation of the low pressure emergency core coolant injection is selected as the figure of merit. Core power is the only parameter that significantly affects the outcome of the transient. The role of the low pressure injection and of the discharge port cross-sectional area is discussed in detail. The effect of operator actions on the control rod drive (CRD) injection flow is also discussed.     

A macroscopic cross-section model for BWR pin-by-pin core analysis

A macroscopic cross-section model used in boiling water reactor (BWR) pin-by-pin core analysis is studied. In the pin-by-pin core calculation method, pin-cell averaged cross sections are calculated for many combinations of core state and depletion history variables and are tabulated prior to core calculations. Variations of cross sections in a core simulator are caused by two different phenomena (i.e. instantaneous and history effects). We treat them through the core state variables and the exposure-averaged core state variables, respectively. Furthermore, the cross-term effect among the core state and the depletion history variables is considered. In order to confirm the calculation accuracy and discuss the treatment of the cross-term effect, the k-infinity and the pin-by-pin fission rate distributions in a single fuel assembly geometry are compared. Some cross-term effects could be negligible since the impacts of them are sufficiently small. However, the cross-term effects among the control rod history (or the void history) and other variables have large impacts; thus, the consideration of them is crucial. The present macroscopic cross-section model, which considers such dominant cross-term effects, well reproduces the reference results and can be a candidate in practical applications for BWR pin-by-pin core analysis on the normal operations.     

Gap conductance analysis for BWR rods relocation model

Pellet relocation is estimated as a function of irradiation history.Fuel fracture at BOL causes an ‘initial relocation’, whereby the fragments are displaced towards the canning. If columnar grain growth does not take place, the pellet remains cracked into pie shaped pieces without circumferential fractures; pellet diameter is stably increased by a term independent on linear power.If columnar grain growth occurs, cracks are filled in the restructured zone and, during a shut-down, circumferential cracks appear. The internal void volume is partially filled during up-ramps so that the relocation is an inverse function of linear power. Cracks healing, causing a void volume to be transferred inwards, produces a ‘time dependent relocation’, related to reactor cycling; as exposure proceeds, the pellet approaches a limiting diameter.The semiempirical model was derived from in-pile temperature measurements at low burn-up and BWR Garigliano rods PIE at high burn-up.A proper choice of literature data was also considered in comparing the parameters with experimental points.     

A fast and reliable calculation model for BWR fuel assembly burnup analyses

A code called superb has been developed for the BWR fuel assembly burnup analyses using a supercell model. Each of the characteristic heterogeneities of a BWR fuel assembly like water gap, poisoned pins, control blade etc. is treated by invoking the appropriate supercell concept. The burnup model of superb is so devised as to strike a balance between accuracy and speed. This is achieved by building isotopic densities in each fuel pin separately while the depletion equations are solved only in a few group of pins or burnup zones and the multigroup neutron spectra are differentiated in fewer group of pincell types. Multiple fuel ring burnup is considered only for Gd isotopes. A special empirical formula allows the microscopic cross section of Gd isotopes to be varied even during burnup integration.The supercell model has been tested against Monte-Carlo results for the fresh cold clean Tarapur fuel assembly with two Gd fuel pins. The burnup model of superb has been validated against one of the most sophisticated codes lwr-wims for a benchmark problem involving all the complexities of a BWR fuel assembly.The agreement of superb results with both Monte-Carlo and lwr-wims results is found to be excellent.     

A systematic method to identify nonlinear dynamics of BWR by using the reactor noise

For the identification of the dynamics of the Vermont Yankee BWR with the reactor noise, different parametric models have been tested. The widely used ARMA model is unable to identify the nonlinearity in the noise data. A systematic method by using the NARMA model, which takes advantage of both the ANN and ARMA, is developed. Comparisons are made between the identification results with ARMA and NARMA model. The advantages of identification with NARMA model over ARMA model are demonstrated. The linear-kernels of the identified NARMA models are extracted so that the natural frequency, damping ratio and time constants of the BWR are obtained. The values of those characteristics are well corresponded with the eigenvalues calculated by the differential equations of the Vermont Yankee BWR. The damping ratio with negative value is found to be a criterion for the existence of limit-cycle, which can be seen from the impulse response on the (X_t, X_t−1) plane, in stable nonlinear system.     

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.     

Stability analysis of BWR nuclear-coupled thermal-hydraulics using a simple model

A simple mathematical model is developed to describe the dynamics of the nuclear-coupled thermal-hydraulics in a boiling water reactor (BWR) core. The model, which incorporates the essential features of neutron kinetics and single-phase and two-phase thermal-hydraulics, leads to a simple dynamical system comprised of a set of nonlinear ordinary differential equations (ODEs). The stability boundary is determined and plotted in the inlet-subcooling-number (enthalpy)/external-reactivity operating parameter plane. The eigenvalues of the Jacobian matrix of the dynamical system also are calculated at various steady-states (fixed points); the results are consistent with those of the direct stability analysis and indicate that a Hopf bifurcation occurs as the stability boundary in the operating parameter plane is crossed. Numerical simulations of the time-dependent, nonlinear ODEs are carried out for selected points in the operating parameter plane to obtain the actual damped and growing oscillations in the neutron number density, the channel inlet flow velocity, and the other phase variables. These indicate that the Hopf bifurcation is subcritical, hence, density wave oscillations with growing amplitude could result from a finite perturbation of the system even when it is being operated in the parameter region thought to be safe, i.e. where the steady-state is stable. Finally, the power-flow map, frequently used by reactor operators during start-up and shut-down operation of a BWR, is mapped to the inlet-subcooling-number/neutron-density (operating-parameter/phase-variable) plane, and then related to the stability boundaries for different fixed inlet velocities corresponding to selected points on the flow-control line. Also, the stability boundaries for different fixed inlet subcooling numbers corresponding to those selected points, are plotted in the neutron-density/inlet-velocity phase variable plane and then the points on the flow-control line are related to their respective stability boundaries in this plane. The relationship of the operating points on the flow-control line to their respective stability boundaries in these two planes provides insight into the instability observed in BWRs during low-flow/high-power operating conditions. It also shows that the normal operating point of a BWR is very stable in comparison with other possible operating points on the power-flow map.     

A simplified model of steam generators for digital simulation

This paper develops a simplified model of a PWR steam generator. A computer programme for the steady state operation was developed, which will be useful for the dynamic analysis for describing accident situations. The model incorporates all the various flow regimes and heat transfer regimes that are likely to be encountered by the secondary flow of the steam generator. The primary flow is considered as single phase compressed liquid. Given the heat transfer area, pitch and the size of the tubes the computer programme matches the total power generated within five percent accuracy. Detailed pressure and temperature distributions along the length of the preheater and evaporator are also computed.     

A Numerical Analysis for a BWR Fuel Assembly Drop Event

A BWR fuel assembly dropped from the crane hook during outage and clashed against the rack bottom plate of spent fuel pool. The area monitoring system indicated no radiation release, however, damage at the top of fuel channel was found in the following inspection. As fuel integrity is essential for further management, a finite element model was established to evaluate the damage condition. Several component elements including fuel rods, tie plates, and channel were set up and integrated into a full assembly. The analysis results provided the impact force on the fuel assembly and the dynamic response of each component element. The event did result in the damage of fuel channel yet fuel rods fracture was not expected. It's consistent with the inspection observations. There is therefore no concern for future operation such as interim dry storage.     

Identification of an equivalent electrical model to a natural circulation BWR core model

In this work the developing of an electrical model of the natural circulation BWR (NCBWR) from analogies between coolant pressures drops, mass flow rates, and electrical voltages and currents, is presented. The electrical model allows estimating the coolant flows in the core, which is complex in NCBWR. The core processes (nuclear-thermo-hydraulics) are modeled with the reduced model where the reactor power is calculated from a point kinetics model with one group of delay neutrons. The reactivity due to Doppler effect, void fraction and control rod was considered. The predictions in steady state were compared with behavior of the power as a function of an ESBWR core flow, showing excellent agreement. The transient behavior considers positive reactivity due to extraction of the control rods.     

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.     

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.     

Analysis on the mathematical structure of the nonlinear BWR model

The mathematical structure of the point-reactor kinetic equation coupled with several linear void reactivity feedback models has been analyzed with the center manifold method and bifurcation theory. The analysis indicates that whether or not the BWR power oscillation will eventually reach a limit cycle depends on both the order and properties of the feedback reactivity equation. The coefficient of the damping term in the void equation plays an important role in determining the type of limit cycles.     

A simplified model for concrete at low confining pressures

The paper describes a model for the response of concrete that is subjected to essentially monotonic straining at low confining pressures. We assume that, under these conditions, the response of the concrete is dominated by cracking when the stress state is predominantly tensile, and by gross inelastic deformation under compressive stress. The model uses a “crack detection surface” in stress space to determine when cracking takes place and the orientation of the cracking at a point, together with a damaged elasticity approach to describe the post-failure behavior of the concrete with open cracks. A yield/flow surface (associated flow) model is used to define the concrete's response in compressive states of stress. The model is simple enough that it can be implemented so as to operate effectively in an implicit finite element code: modeling accuracy is sacrificed for this purpose. Preliminary studies with the model indicate that it can give useful predictions in cases of interest.     

Identification of BWR dynamics from autoregressive analysis of multivariable experiments

A method of time series analysis was applied to study dynamics of a boiling water reactor. The main aim of this work is to examine the usefulness of a multivariable autoregressive modelling technique for identifying a complicated reactor dynamics. Two kinds of experimental data were treated by this method; one from a perturbation experiment, and the other from a measurement of fluctuations of variables under normal operation conditions. Several open loop dynamics and closed loop dynamics were successfully identified from the perturbation experiment, and some specific open loop dynamics were also obtained from the measurement of fluctuations. The identified models were compared with each other in order to clarify the difference in identifiability of the reactor dynamics under these experimental conditions. An attempt was made to validate a theoretical model, and some uncertain parameters in the model were estimated by using the identified model. These results suggest that the present method is useful not only for study of dynamics but also for diagnosis and surveillance of nuclear power plants.     

A simplified two-fluid model of a steam generator for digital simulation of operational transients

A two-fluid model with 1-D flow was developed for solving the transient conservation equations to simulate the transients of the steam generator used in a PWR plant. Two separate phases were assumed to exist on the secondary side and a single phase on the primary side. Five conservation equations for the secondary side and three for the primary side were solved numerically using finite difference for the spatial variable with an explicit scheme for the temporal variable. The transients modelled as disturbances in the secondary-inlet parameters were analysed using the code developed. The performance after introducing disturbances of 10% in the parameters showed acceptable variations. There were no numerical instabilities. The CPU time for a 4 s transient was 9.58 min.     

BWR 90-the advanced BWR of the 1990s

The future global role of nuclear power will be determined by its ability to provide economical and safe energy. Nuclear power, like any other substantial contributor to the world's energy needs, must be generated at an acceptable cost and with negligible environmental effects. Besides, it must achieve and maintain a socially reasonable level of public acceptance, which in turn is not necessarily governed by rational assessments of the true safety and environmental impact of nuclear power. The ABB Atom approach to this situation can best be characterized as a ‘cautious evolution'; for the next decade the company will largely base its offerings to the market on its ‘evolutionary' light water reactor design, the BWR 90. This design builds closely on the experience from successful construction and operation of its predecessor, the BWR 75 design. In 1995 and 1996, plants of this design achieved an average load factor greater than the 87% set by EUR; the two BWR units at Olkiluoto in Finland are among the very best performing plants in the world, with an average load factor of 94% over the last 7 years. The continued LWR design development focuses on meeting requirements from utilities as well as new regulatory requirements. A particular emphasis is put on the consequences of severe accidents; there shall be no large releases to the environment. Other design improvements involve: all-digital I and C systems and enhanced human factors engineering to improve work environment for operators, optimization of buildings and containment design to decrease construction time and costs, and selection of materials as well as maintenance and operating procedures to even further reduce occupational radiation exposures. Probabilistic safety assessments and life-cycle cost evaluations have become major tools in the design optimization work. The BWR 90 was offered to Finland in the early 1990s, and will now as the first BWR design be reviewed by a number of European utilities with respect to its conformance to the European Utility Requirements (EUR); a specific EUR Volume 3 for the BWR 90 will be the final result. The paper describes some of the unique characteristics of the BWR 90, with emphasis on the features that are most important for achieving improved economy and enhanced safety.     

A Transient Modal Analysis of a BWR Instability Event

To solve the time dependent neutron diffusion equation a modal method, based on the expansion of the neutronic flux in terms of the dominant Lambda modes of a static configuration of the reactor is presented. This method is used to analyse transients of a nuclear power reactor where an instability event can be developed. A simulation of a transient with the same conditions given for the case 9 of Ringhals stability benchmark has been analysed. It is shown that with these conditions an out of phase oscillation associated with the two first azimuthal modes can be developed. These results are corroborated using a power modal decomposition, using the local power distribution provided by RAMONA code. To complete the analysis, the modal feedback reactivities have been calculated to study the coupling mechanism among modes.     

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.