An Analytical Study of Nonlinear Reactor Dynamics Based on Bifurcation Theory with Reference to BWR Power Oscillation

A nonlinear reactor dynamics model of reduced order is derived and an analytical study on BWR power oscillation is made using this model. It provides some essential features which are not given by numerical studies, such as the explicit expressions of the linear stability condition and the weak stability condition which is related to the periodic motion. In addition, the relation between the reactivity feedback and these conditions is obtained. The application of the analytical results to the qualitative analysis of BWR dynamics is easy and quick in comparison with numerical approaches.     

Approach to Improvement of Thermal Efficiency in BWR Plant Based on Exergy Analysis

This paper presents finite element analytical results of the thermal and irradiation induced stresses occurred in the target plate of the divertor structures which are exposed to neutron irradiation at 0-1 dpa with high heat flux up to 15MW/m². Three types of target plate models are studied in the present work, e.g., flat plate, saddle and mono-block type models which have bonded structures of one-dimensional high thermal conductivity Carbon-Carbon (C/C) composite material and Oxygen-Free-High Conductivity Copper (OFHC). With these results, it is concluded that flat model exhibits the longer life-time up to 1 dpa under 15 MW/m², whereas serious troubles, such as fracture in bonded interface or drop-off of armor tile from bonded substrate, are expected in saddle and mono-block type models before 1 dpa. Design change with reduction of the volume of armor region in the model is also effective to prolong the life-time by the reduction of sublimation of armor material.     

Irradiated Fuel Behavior under Power Oscillation Conditions

In order to examine high burnup fuel performance under power oscillation conditions, two tests of irradiated fuels under simulated power oscillation conditions were conducted in the Nuclear Safety Research Reactor (NSRR). Irradiated fuels at burnups of 56 and 25 GWd/tU were subjected to four to seven power oscillations, which peaked at 50 to 95 kW/m with intervals of 2 s. The power oscillations were caused by quick withdrawal and insertion of six regulating rods of the NSRR with a computerized control. Impacts of cyclic loads on the fuel performance under hypothetical unstable power oscillations arising during an anticipated transient without scram (ATWS) in boiling water reactors (BWRs) were examined in the tests. Deformation of the fuel cladding of the test rods was comparable to those observed in shorter transient tests, which simulated reactivity-initiated accidents (RIAs), at the same fuel enthalpy level up to 368 J/g. The fuel deformation was mainly caused by pellet-cladding mechanical interaction (PCMI) and was roughly proportional to the fuel enthalpy. Enhanced cladding deformation due to ratcheting by the cyclic load was not observed. Fission gas release, on the other hand, was considerably smaller than in the RIA tests, suggesting different release mechanisms in the two types of transients.     

Multi-Channel Thermal Hydraulic Model for LOCA Analysis of Heterogeneous BWR Core

A multi-channel thermal hydraulic model for LOCA analysis of a heterogeneous core such as a HCBWR has been developed. This model solves integral formulations for basic equations based on a one-dimensional drift flux model. The core region is divided into several fuel channel groups which differ in their thermal power or geometry. The various flow patterns in the core are determined by calculating the redistribution of vapor generated in the lower plenum into the fuel channel groups. In order to verify the multi-channel model, a computer program FLORA was developed based on the multi-channel model and large and small break LOCA experiments conducted in the Two Bundle Loop (TBL) facility were analyzed by the FLORA program. As a result, the difference in thermal hydraulic behavior between two bundles with different power in the various break LOCA experiments were well simulated.     

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.     

Modeling for Void Reactivity Effect by Subcooled Boiling under Reactivity Initiated Accident Condition of BWR

A simple mechanistic model is presented to evaluate the subcooled void reactivity effect under a Reactivity Initiated Accident (RIA) at cold critical condition of BWR. This model consists of a drift flux model for vapor velocity and a vapor mass conservation model with a term of vapor source on a heated wall, and it was incorporated into a homogeneous and equilibrium thermal-hydraulic code EUREKA-JINS. A sample analysis by this model showed that the subcooled void reactivity effect leads to reduction of the maximum fuel enthalpy by about 20 cal/g UO₂ in the case of RIA at cold critical condition. Though the reduced value is dependent on the reactor core condition, this result indicates the significance of subcooled void reactivity effect in the accident, while the effect can be neglected in the hot stand-by case where, at most, only 4 cal/g UO₂ is reduced for the maximum fuel enthalpy.     

Prediction of Transient Boiling Transition in BWR Fuel Rod Bundles by Subchannel Analysis Program MENUETT

Transient CHF (critical heat flux) tests of a 4 X 4 rod bundle were analyzed by the subchannel analysis program MENUETT. MENUETT is based on a non-equilibrium, five equation, two-phase flow model and is available both for steady state and transient analyses. Turbulent mixing and void drift effects are taken into account to calculate cross flows in fuel rod bundles. The tendency of calculated subchannel mass fluxes and qualities agreed with experimental data. By using a critical quality correlation obtained from steady state CHF data, the position of the earliest boiling transition could be predicted regardless of non-uniform axial heat flux distributions. This transition occurrence time was predicted within a difference of 0.1～0.3 s from the experimental time. MENUETT applicability was confirmed for transient calculations predicting thermalhydraulic behavior in bundles.     

Fission Product Model for BWR Lattice Calculation Code

A benchmark calculation of full fission product was performed for thermal reactor application using an isotope transmutation code DCHAIN based on 185 nuclides with revised nuclear data library. The fission product model for BWR lattice calculation was studied and tested with the benchmark results, and a model containing 45 explicit nuclides and one pseudo nuclide was selected as a reasonably best model to predict the burn up reactivity with high precision for practically all types of fuel and reactor operating conditions. The evaluated thermal cross section and resonance integral for the pseudo nuclide are σ_2,200 = 2.6b and.RI = 10.6b, combined with the pseudo fission yield values of 1.3898, 1.3233, 1.3675 and 1.2773 for fissions from ²³⁵U, ²³⁸U, ²³⁹Pu and ²⁴¹Pu, respectively. The present results are believed as equally applicable to PWR lattice calculation.     

Evaluation of Dynamic Loads Induced by Chugging

A dynamic load evaluation method has been proposed for chugging phenomena which are assumed to occur and produce relatively large amplitude pressure spikes in the pressure suppression pool of a BWR containment, in case of a postulated loss of coolant accident. The proposed method is based on the analysis code developed by the authors and on theseven vent full scale tests performed at Japan Atomic Energy Research Institute (JAERI CRT), considering random nature of chugging phenomena. The dynamic loads are obtained by applying the design source functions of impulsive nature to the vent pipe exists in each BWR containment analysis model. The design source functions are defined to produce dynamic pressures which reasonably envelope the design spectrum based on JAERI CRT data in frequency domain.

As an application example, the dynamic loads induced by chugging have been assessed based on the proposed method and on the reported JAERI CRT data from the view point of conservative load evaluation.

The applicability of the analysis code has also been confirmed, since the simulated dynamic pressures have shown features and magnitudes similar to those observed in JAERI CRT.     

RELAP4 Modeling for Reverse Flow Property of BWR Jet Pump under Large Break LOCA Condition

It is very important to identify the reverse loss coefficient of BWR jet pump in the evaluation of core inlet flow at the beginning phase of BWR LBLOCA (Large Break Loss-of-Coolant Accident) analyses. Hence, the reverse flow property of jet pump was investigated in relation between the momentum equation, pressure loss coefficient and RELAP4 noding, and a new modeling has been proposed. In the proposed modeling, an equivalent pressure loss coefficient is used to take into account of the effect of accellerating pressure loss by the continuous flow area reduction from the tale pipe to the throat. The effectiveness of this model was studied by analyses for the LOFT 1/6 scale jet pump experiment and typical BWR LBLOCA. It has been, consequently, shown that this proposed model gives better jet pump property than a previous model which is used in the WREM sample problem and which gives very conservative result in core inlet flow and in the peak cladding temperature through whole transient.     

Heat Removal Performance Evaluation of Several Passive Containment Cooling Systems during Loss of Coolant Accident

As a passive containment cooling system (PCCS), which is adopted in simplified BWRs, several concepts, differing in cooling location and method, such as the suppression chamber water wall, the drywell water wall, the isolation condenser (I/C) and the drywell cooler, have been considered. This paper summarizes the characteristics of each PCCS concept, and the analysis results of the performance for several PCCSs during a main steam line break LOCA for a reference simplified BWR plant, obtained by the newly developed containment thermalhydraulic response analysis code TOSPAC.

The performance comparison suggests that I/C and drywell cooler have good heat removal capability with regard to the smallest heat transfer area among PCCS concepts evaluated in the present analysis. I/C removes decay heat efficiently, since it absorbs steam directly from the reactor pressure vessel, which is the hottest portion inside the containment. The suppression chamber water wall is ineffective, mainly due to high non-condensable gas partial pressure in the suppression chamber, and low suppression pool temperature.

Calculations of other pipe breaks were also implemented for the reference plant adopting I/C as PCCS. The results show the effectiveness of the I/C cooling over a wide range of break spectra.     

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.     

Comparisons of HELIOS,ORIGEN2, and Monteburns Calculated 241 Am and 243 Am Concentrations to Measured Values for PWR,BWR, and VVER Spent Fuel

A study was performed at Los Alamos National Laboratory to explore the accuracy of several reactor analysis codes in calculating ²⁴¹ Am and ²⁴³Am concentrations in light water reactor spent fuel. Calculated higher-actinide concentrations were compared to measured values from the literature for three reactor fuels. The fuel samples were taken from the Mihama Unit 3 pressurized water reactor, the Garigliano boiling water reactor, and a VVER-440. The ²⁴¹Am and ²⁴³Am concentrations were calculated using the HELIOS-1.4 lattice-physics code, the ORIGEN2 burnup code, and a linked MCNP/ORIGEN2 code named Monteburns 3.01. Comparisons were made between the calculated and measured values. It was determined that all codes performed consistently well for the Mihama Unit 3 measurements (within ±5% for ²⁴¹Am and ±20% for ²⁴³Am) and the Garigliano measurements (within ±12% for ²⁴¹ Am and ±20% for ²⁴³Am). It was determined that the ORIGEN2 pressurized water reactor libraries are insufficient for the VVER-440 measurements. The HELIOS and MONTEBURNS codes both demonstrated good ability to calculate these isotopes for VVER-440 fuel (±10% for ²⁴¹Am and ±12% for ²⁴³Am). The accuracies of these codes and the associated radiochemical measurements of these higher-actinide isotopes may be insufficient for safeguards and fuel management purposes; thus, development of new methods and modification to existing data libraries may be necessary in order to enable cost-effective safeguarding of these higher-actinide materials.     

Stability Analysis of BWRs Using Bifurcation Theory

Abstract

This paper presents a new approach using the bifurcation theory for the stability analysis of BWRs. In this approach, the dependencies of the equilibrium states on the parameters that have a large influence on the stability are investigated topological over a wide range of phase space. The stability information can be derived from the analysis of the bifurcation phenomena on the equilibrium states. This investigation enabled us to obtain qualitative and global information on the stability of a nonlinear system. The new approach was applied to the analysis of the stability associated with in-phase power oscillation (core reactivity stability). The loss of linear stability took place at a lower reactor power as the coolant flow rate decreased, and this instability occurs at the Hopf bifurcation point. The sensitivity analysis of the stability boundary for the various parameters revealed that the channel hydrodynamics heavily play a significant role in the stability. The Hopf bifurcation analysis proved that the periodic state bifurcating at the Hopf bifurcation point was orbitally unstable and a limit cycle attractor did not exist in the vicinity of the bifurcation point. This fact led to the conclusion that a limit cycle in-phase power oscillation observed in BWR instability was not excited directly by the bifurcation of the orbitally unstable periodic state.     

Development of Evaluation Code for Long-Term Cooling of Containment with Passive Safety Feature

Simplified BWRs are characterized as an adoption of a passive ECCS and a passive containment cooling system (PCCS). While a passive ECCS has a short term core cooling function, a PCCS has a long-term decay heat removal function. As a PCCS, several concepts, differing in cooling location and method employed, have been considered. From the containment thermal- hydraulic response analysis viewpoint, simplified BWRs are essentially different from the current BWRs. For evaluating and comparing the performance of several PCCSs over full break spectra, the new containment safety evaluation code TOSPAC was developed as a preliminary design tool for PCCS. This paper summarizes the thermal-hydraulic modelings of the TOSPAC code and the validity evaluation of the TOSPAC code, compared with TRAC-BF1 calculation.

From the validity evaluation concerning a main steam line break (MSLB) accident analysis for an isolation condenser (I/C) as a PCCS, it was found that the TOSPAC calculation result shows reasonable agreement with that for TRAC, even though the TOSPAC consists of simpler modelings.     

Sensitivity Study of Fuel Cost in Extended Burnup BWR Core

A sensitivity study on the fuel cost of an extended burnup BWR core has been carried out on the basis of a realistic model of discharge burnup extension. Full power operating length in months in a refueling cycle and the number of refueling batches are chosen as independent variables in the model to describe extended burnup cores of various types. The reference core for the sensitivity study adopts 9-month full power operation and 4-batch refueling scheme. The difference in the plant cost between the extended burnup core and the reference core, which is referred to as plant capacity factor (PCF) credit, is estimated and combined with the fuel cost to calculate the fuel cost with PCF credit.

The results show that the fuel cost with PCF credit decreases for the extended burnup core with stretched operating length as the burnup extends in cases of constant non-operating length in a cycle, and that it may increase for the extended burnup core with decreased batch number in cases of constant plant capacity factor. It is also suggested that the cost minimum combination of the independent variables can be found to a given discharge burnup for the extended burnup core with decreased batch number in an intermediate case between these two extreme cases. Extended burnup cores with fixed batch number tend to have a lower natural uranium requirement, but larger separative work requirement.

The economic break-even condition for the extended burnup core with decreased batch number is discussed based on the fraction of fixed part in the non-operating length, which is insensitive to the cycle length stretch-out.     

Pin Power Reconstruction Methods of the Few-Group BWR Core Simulator NEREUS

An improved pin power reconstruction method has been incorporated in the few-group nodal BWR core simulator NEREUS, which is based on the analytic polynomial nodal method. With the analytic polynomial nodal method, accurate node surface fluxes are available, which are used later to reconstruct pin powers. The intranodal homogeneous thermal flux is corrected using a semi-empirical proportional relation between surface transition components of the homogeneous and heterogeneous fluxes. This correction method is effective for BWR calculations, especially for controlled assemblies or mixed loading of off-set assemblies. A unified model accounting for effects of spectral histories, caused by spectral interactions between fuel assemblies and the control blade insertion, was also developed for intranodal burnup correction. The change in pin powers due to the control blade history can be predicted well, without laborious assembly depletion calculations with control blade insertion. R-factors used in critical power ratio calculations are also reconstructed from the pin powers. The NEREUS pin power reconstruction method was verified against heterogeneous multi-assembly depletion calculations.     

Evaluation of Reactivity and Xe Behavior during Daily Load Following Operation

A boiling water reactor (BWR) has an excellent load following capability provided by a core flow control, which is used for changing a reactor power level and for compensating the subsequent Xe concentration change.

The core characteristics during load following operations are investigated in detail, using our reactor core simulator. Comparisons of changes of the Doppler reactivity, the void reactivity and the Xe reactivity during transients are performed. Also the features of Xe transient during load following operations are shown.

It has been shown that the core flow change required to compensate the Xe reactivity change produces much greater change of the void reactivity than that required for power level changes, and that the resulting local power change in the lower part of the core is greater than that in the upper part, because the Xe concentration change in the lower part is hardly compensated by the core flow control. Also the effects of power level changes, cycle patterns, and initial concentration of Xe and I on the Xe transient behavior have been investigated.