Simulation of an hypothetical out-of-phase instability case in boiling water reactor by RELAP5/PARCS coupled codes

A very complex type of power instability occurring in boiling water reactor (BWR) consists of out-of-phase regional oscillations, in which normally subcritical neutronic modes are excited by thermal-hydraulic feedback mechanisms. The out-of-phase mode of oscillation is a very challenging type of instability and its study is relevant because of the safety implications related to the capability to promptly detect any such inadvertent occurrence by in-core neutron detectors, thus triggering the necessary countermeasures in terms of selected rod insertion or even reactor shutdown. In this work, simulations of out-of-phase instabilities in a BWR obtained by assuming an hypothetical continuous control rod bank withdrawal are being presented. The RELAP5/Mod3.3 thermal-hydraulic system code coupled with the PARCS/2.4 3D neutron kinetic code has been used to simulate the instability phenomenon. Data from a real BWR nuclear power plant (NPP) have been used as reference conditions and reactor parameters. Simulated neutronic power signals from local power range monitors (LPRM) have been used to detect and study the local power oscillations. The decay ratio (DR) and the natural frequency (NF) of the power oscillations (typical parameters used to evaluate the instabilities) have been used in the analysis. The results are discussed also making use of two-dimensional plots depicting relative core power distribution during the transient, in order to clearly illustrate the out-of-phase behavior.     

Development of SIRIUS-N facility with simulated void-reactivity feedback to investigate regional and core-wide stability of natural circulation BWRs

The SIRIUS-N facility was designed and constructed for highly accurate simulation of core-wide and regional instabilities of a natural circulation BWR. A real-time simulation was performed in the digital controller for modal point kinetics of reactor neutronics and fuel-rod conduction on the basis of measured void fractions in reactor core sections of the thermal-hydraulic loop. Stability experiments were conducted for a wide range of thermal-hydraulic conditions, power distributions, and fuel rod time constants, including the nominal operating conditions of a typical natural circulation BWR. The results show that there is a sufficiently wide stability margin under nominal operating conditions, even when void-reactivity feedback is taken into account. The stability experiments were extended to include a hypothetical parameter range (double-void reactivity coefficient and inlet core subcooling increased by a factor of 3.6) in order to identify instability phenomena. The regional instability was clearly demonstrated with the SIRIUS-N facility, when the fuel rod time constant matches the oscillation period of density wave oscillations.     

Flashing-induced density wave oscillations in a natural circulation BWR—mechanism of instability and stability map

The SIRIUS-N facility was designed and constructed for highly accurate simulation of core-wide and regional instabilities of a natural circulation BWR. A real-time simulation was performed in the digital controller for modal point kinetics of reactor neutronics and fuel-rod conduction on the basis of measured void fractions in reactor core sections of the thermal-hydraulic loop. Stability experiments were conducted for a wide range of thermal-hydraulic conditions, power distributions, and fuel rod time constants, including the nominal operating conditions of a typical natural circulation BWR. The results show that there is a sufficiently wide stability margin under nominal operating conditions, even when void-reactivity feedback is taken into account. The stability experiments were extended to include a hypothetical parameter range (double-void reactivity coefficient and inlet core subcooling increased by a factor of 3.6) in order to identify instability phenomena. The regional instability was clearly demonstrated with the SIRIUS-N facility, when the fuel rod time constant matches the oscillation period of density wave oscillations.     

Mutual Shielding Effect in 238U-239Pu Mixture

A three-dimensional time-domain core analysis code was applied to numerical simulations for an actual regional neutron flux oscillation observed in a commercial BWR core, in order to investigate potential nonlinear behavior in its coupled neutronic and thermohydraulic system. The present study shows existence of the nonlinear reactivity interaction between the fundamental and first azimuthal spatial harmonics modes of neutron flux distribution under the regional event. The spectrum analysis of the simulated data provides a unique result, that is, temporal harmonics peaks are excited at the even- and odd-order multiples of the characteristic resonance frequency in the fundamental and first spatial harmonics responses, respectively. The numerical simulation also shows that the strong nonlinearity of the coupled neutronic and thermohydraulic dynamics locally appears where the power unstably oscillates with large amplitudes, inducing the power shift and reactivity bias which are shown in the core-wide situation under the global oscillations. This contributes to suppression of the divergence of the local power oscillation, and also to development of the saturated self-limited cycles under the regional oscillations.     

BWR core-wide stability analysis with respect to dominant feedback mechanisms and characteristic poles

BWR core-wide stability is studied from the viewpoint of linear dynamic stability treated via poles of a closed-loop transfer function. The quantitative study is performed using a BWR noise model describing neutronic and thermal-hydraulic core dynamics. Transfer functions of neutron power to reactivity and core inlet flow are derived in explicit forms and their poles are evaluated both numerically and analytically. It is shown that the characteristic poles may be classed into three groups relating to neutronic process, fuel heat transfer and core void dynamics. In particular, the poles for the void dynamics take complex values and hence give rise to core-wide damped oscillation of neutron power. Furthermore, the study of characteristic poles serves for the stability analysis of the Ringhals-1 benchmark test data. It is shown and clarified that two stability indexes, decay ratio and resonance frequency, have clear dependence on reactor power and core inlet flow.     

A sensitivity study of BWR instability over global and regional modes at different exposures

Boiling water reactors have unique mechanisms coupling between neutronic and two-phase flow thermalhydraulic behaviors, and may exhibit in-phase (global mode) instability and out-of-phase (regional mode) instability. In some observation modes, the regional mode instability is associated with an increase in power in one half of the core and a simultaneous decrease in power in the other half, such that the average power remains essentially constant. Yet in practice, sometimes the real situation is hidden, the neutron flux may oscillate more vigorously than expected. To investigate the stability behavior at the stability boundary from BOC (beginning of cycle) to EOC (end of cycle), fractional changes of the decay ratio are used to evaluate the parametric sensitivity of the global mode and the regional mode at different exposures. Decay ratios for regional mode oscillations are much less than those under core-wide conditions. Current studies demonstrated that for some of the parameters under particular conditions, the variation in the regional mode decay ratio exceeded that in the global mode. In this work, the thermalhydraulic parameters (such as flow rate and system pressure) exhibit a more sensitive regional variation than global. Moreover, some parameters (density reactivity coefficient and delayed-neutron fraction, for example) depend on the shape of the axial power shape; for the bottom peak axial power shape, the regional mode decay ratio variation is more sensitive than global; for the top peak axial power shape, the opposite is true.     

Investigation of chaotic oscillations in boiling-water reactors

The chaotic dynamics of boiling-water reactors is investigated on the basis of a one-dimensional integral model of momentum for the boiling-water channel and point equation of kinetics. It is shown that chaotic oscillations during which the sign of the coolant velocity in the boiling channel changes occur in the case of strong feedback on steam content with the parameters of the boiling channel deep in the region of instability occur in boiling-water reactors with natural and forced circulation of the coolant. It is determined that such oscillations can occur with the standard reactor arrangement when the core entrance is open for water to enter the core and for back circulation of the coolant as well as with an arrangement where the entrance is half open – closed for back circulation of the coolant. A numerical calculation of the chaotic oscillations is performed. The mechanism of pulsed chaos is described. Regions of stability and stochasticity are separated in the plane of the parameters characterizing the underheating of water to the saturation temperature at the entrance to the reactor and stationary average steam content in the core. One-dimensional point mappings determining the chaotic dynamics of the boiling water reactor are constructed. The properties of the mappings and the bifurcation of their stationary points are investigated.     

核反馈对并联双通道自然循环系统流动不稳定性的影响

将热工水力系统分析程序RELAP5与三维物理瞬态输运程序TDOT T采用并行方式耦合,对并联双通道自然循环系统内核热耦合不稳定性进行分析,得到系统的不稳定边界。分别以燃料时间常数差异较大的板型元件及棒型元件为对象,讨论了核反馈对系统稳定性的影响。对于板型元件,核反馈作用对低含汽率区的第1类密度波振荡（DWO）有明显的抑制作用,而对高含汽率区的第2类DWO基本无影响。对于棒型元件,计算分析结果表明核反馈对系统稳定性几乎无影响。     

Influence of subcooled boiling on out-of-phase oscillations in boiling water reactors

In this paper, we develop a reduced order model with modal kinetics for the study of the dynamic behavior of boiling water reactors. This model includes the subcooled boiling in the lower part of the reactor channels. New additional equations have been obtained for the following dynamics magnitudes: the effective inception length for subcooled boiling, the average void fraction in the subcooled boiling region, the average void fraction in the bulk-boiling region, the mass fluxes at the boiling boundary and the channel exit, respectively, and so on. Each channel has three nodes, one of liquid, one with subcooled boiling, and one with bulk boiling. The reduced order model includes also a modal kinetics with the fundamental mode and the first subcritical one, and two channels representing both halves of the reactor core. Also, in this paper, we perform a detailed study of the way to calculate the feedback reactivity parameters. The model displays out-of-phase oscillations when enough feedback gain is provided. The feedback gain that is necessary to self-sustain these oscillations is approximately one-half the gain that is needed when the subcooled boiling node is not included.     

A coupled analysis of system thermal-hydraulics and three-dimensional reactor kinetics for a 12-finger control element assembly drop event in a PWR plant

A coupled system thermal-hydraulics (T-H) and three-dimensional reactor kinetics code, MARS/MASTER, was developed to attain more accurate predictions for nuclear system transients that involve strong interactions between neutronic and T-H phenomena. In this paper, a 12-finger control element assembly (CEA) drop event in a two-loop pressurized water reactor (PWR) plant under a full power condition was analyzed, where the 12-finger CEA that is nearest to the hot leg of Loop 2 is assumed to incidentally drop. This instantaneously results in an asymmetric radial power distribution and, in turn, asymmetric loop behavior, which may lead to a reactor trip due to a low departure from nucleate boiling (DNB) ratio at the intact side of the core or an excessive difference between the cold leg coolant temperatures. This event clearly requires a coupled calculation of system T-H and three-dimensional reactor kinetics to realistically investigate the thermal-hydraulic behavior of the reactor core. A simple theoretical modeling is also devised to evaluate the cold leg temperature difference under a quasi-steady state.     

Experimental study of the coupled thermo-hydraulic–neutronic stability of a natural circulation HPLWR

The HPLWR (high performance light water reactor) is the European concept design for a SCWR (supercritical water reactor). This unique reactor design consists of a three pass core with intermediate mixing plena. As the supercritical water passes through the core, it experiences a significant density reduction. This large change in density could be used as the driving force for natural circulation of the coolant, adding an inherent safety feature to this concept design. The idea of natural circulation has been explored in the past for boiling water reactors (BWR). From those studies, it is known that the different feedback mechanisms can trigger flow instabilities. These can be purely thermo-hydraulic (driven by the friction – mass flow rate or gravity – mass flow rate feedback of the system), or they can be coupled thermo-hydraulic–neutronic (driven by the coupling between friction, mass flow rate and power production). The goal of this study is to explore the stability of a natural circulation HPLWR considering the thermo-hydraulic–neutronic feedback. This was done through a unique experimental facility, DeLight, which is a scaled model of the HPLWR using Freon R23 as a scaling fluid. An artificial neutronic feedback was incorporated into the system based on the average measured density. To model the heat transfer dynamics in the rods, a simple first order model was used with a fixed time constant of 6 s. The results include the measurements of the varying decay ratio (DR) and frequency over a wide range of operating conditions. A clear instability zone was found within the stability plane, which seems to be similar to that of a BWR. Experimental data on the stability of a supercritical loop is rare in open literature, and these data could serve as an important benchmark tool for existing codes and models.     

Linear modal analysis of out-of-phase instability in boiling water reactor cores

An eigenvalue problem governing BWR core nuclear thermal-hydraulic modes which result in out-of-phase power oscillations is formulated. This formulation is based on the linearization approximation to nonlinear feedback terms and the very simple models for neutronics and thermal-hydraulics. The eigenvalue problem in 5 × 5 matrix formulation can be easily solved without using a computer. A series of the calculations are carried out, at a high-power and low-core-flow condition, to investigate the dependence of the eigenvalues and eigenfunctions on the void reactivity coefficient and the subcriticality of spatial neutronic modes, where the latter parameter is identical to the eigenvalue separation of the higher-harmonic neutronic mode. These results show that the threshold value of the void coefficient for initiating the unstable out-of-phase oscillation strongly depends on the subcriticality. The oscillation mode becomes more unstable with an increase in the absolute value of the negative void coefficient, whereas the mode becomes more stable, almost linearly, with increasing subcriticality. The resonant frequency of the oscillation and the phase shifts between the nuclear thermal-hydraulic variables are consistent with previous measured or calculated values.     

Analysis of Core Stability Measurement Data of Advanced 9×9 Fuel Assembly in a BWR Core

The core stability measurements were taken during the cycle-9 startup of the 1,300MWe BWR, Kernkraftwerk Kruemmel (KKK). The core contained advanced 9×9 type high burn-up design reload fuel with a higher enrichment than current 8x8 fuel. A design feature of the advanced 9x9 fuel assembly (FA) is a large square water channel for enhanced neutron moderation. The measurement data as a function of core flow and power showed almost the same stability characteristics as those of the past measurement during the cycle-3 startup of the KKK core with the 8×8 FA. The local power range monitors (LPRM) detected neutron flux oscillations in both core-wide in-phase and half-core out-of-phase modes.

The frequency-domain stability analysis using the STAIF-PK code well reproduced the measurement result that the onset of unstable operation in KKK first occurs when about half of the reactor internal pumps are operating and the other half are stopped. The stability performance of the advanced 9×9 FA in the core was compared with the 8×8 FA by a design parameter analysis with respect to thermal-hydraulic and neutronic design. It has been demonstrated by the analysis that the stability performance of the advanced 9×9 FA is comparable with current 8×8 FA.     

Introducing and validating a new method for coupling neutronic and thermal-hydraulic calculations

In this study, a new and innovative method is introduced for analyzing neutronic and thermal-hydraulic calculation. For this aim, VVR-S research reactor was selected, and the calculation procedure was performed for it. WIMS, CITATION and COBRA-EN codes were used for investigation. Calculation model consists of two sub-models: neutronic and thermo-hydraulic. The neutronic model uses WIMS and CITATION codes for neutronic simulation of the reactor core and calculating flux and power distribution over it. WIMS code simulates the fuel assemblies and CITATION models the core. The thermal-hydraulic model uses COBRA-EN code for performing the relative calculation. In this study, FORTRAN 90 program is used for linking two sub-models and performing the calculation. The proposed procedure is performed for VVR-S analysis and finally, the obtained results are compared with the experimental results that show good agreement with it.     

物理-热工耦合对超临界水堆系统特性的影响分析

物理-热工耦合是超临界水堆系统分析的关键问题之一。以日本超临界水冷热堆Super LWR的堆芯设计为例,借助Dragon编制中子截面数据库,建立双群中子扩散方程计算模块,联系同时建立的热工计算模块,得到超临界水堆的物理-热工耦合计算模型。通过对比稳态与瞬态工况下耦合前、后的热工工况,分析物理-热工耦合条件下的超临界水堆系统热工特性。结果表明：在稳态工况下,物理-热工耦合将导致内、外组件堆芯功率峰值沿轴向发生明显偏移,使得部分节点的包壳温度升高,但包壳最高温度降低;在瞬态工况下,物理-热工耦合将导致堆芯包壳最高温度的发生位置有所改变。发生给水加热丧失瞬态后,在某一时刻,外部组件的包壳最高温度将转而超过内部组件的包壳最高温度。可见,物理-热工耦合对包壳最高温度的大小和发生位置均可能产生明显影响。计算分析可为超临界水堆瞬态及安全分析提供相应理论参考。     

Thermal and Stability Considerations of Super LWR during Sliding Pressure Startup

The feasibility of the sliding pressure startup of a high-temperature supercritical-pressure light water reactor (super LWR, SCLWR-H) is assessed from both thermal and stability considerations. In the sliding pressure startup, nuclear heating starts at subcritical pressure and the reactor is pressurized to supercritical pressure at a low power and high enough flow rate. The reactor power and flow rate are then raised gradually to the rated normal values at constant supercritical operating pressure. During startup, the maximum cladding surface temperature must not exceed 620°C. For two-phase flow at subcritical pressures, the homogeneous equilibrium model is used. The thermal-hydraulic and coupled neutronic thermal-hydraulic stabilities during pressurization and power-raising are investigated by a frequency-domain linear analysis for both supercritical-pressure and subcritical-pressure operating conditions. The same stability criteria as those of BWRs are used. From the analysis results, a sliding pressure startup procedure is proposed for super LWR. The thermal criteria are satisfied by keeping the core power between the maximum allowable limit and minimum limit required for turbine startup and operation. The thermal-hydraulic stability and coupled neutronic thermal-hydraulic stability can be maintained by applying an orifice pressure drop coefficient at the inlet of fuel assembly and by controlling the power and flow rate during startup.     

Numerical investigations on power ramping procedure for a natural circulation boiling water reactor

Startup of a natural circulation boiling water reactor (NCBWR) is studied numerically, using a thermal-hydraulic system code RELAP5. A number of numerical experiments are carried out using various power ramps, and a suitable heat-up rate is identified to pressurize the reactor to the desired operating conditions in a reasonable time without considerable void generation in the core. It is observed that the occurrence of flashing in the riser section is unavoidable. Although flashing helps in steam production, the amplitude of flow oscillations induced by flashing is the event of concern, as in the case of the pressure tube type NCBWR studied here. Therefore, the feasibility of a complete single-phase startup is also examined and found not attractive. A new startup procedure, which completely bypasses the unstable two-phase region, is conceptualized, and the method to take the system to the operating condition without encountering flow oscillations is numerically investigated.     

Thermal-hydraulic transient analysis of light water reactors using moving boundaries

This paper examines the applicability of a mathematical dynamic model developed here for the simulation of the thermal-hydraulic transient analysis for light water reactors (LWRs). The thermal-hydraulic dynamic modeling of the fuel pin and adjacent coolant channel in LWRs is based on the moving boundary concept. The fuel pin model (FUELPIN) with moving boundaries is developed to accommodate the core thermal-hydraulic model, with detailed thermal conduction in fuel elements. Some results from transient calculations are examined for the first application of the thermal-hydraulic model and the fuel pin model with moving boundaries in a boiling water reactor (BWR). An accurate minimum departure from nucleate boiling ratio (MDNBR) and its axial MDNBR boundary versus time within the fuel channel are predicted during transients. Transient analysis using a known thermal-hydraulic code, COBRA and FUELPIN linked with a PWR systems analysis code show that the thermal margin gains more by a transient MDNBR approach than the traditional quasi-steady methodology for a pressurized water reactor (PWR). The studies of the overall nuclear reactor system show that moving boundary formulation provides an efficient and suitable tool for thermal transient analysis of LWRs.     

Estimation of sensitivity coefficients of core characteristics based on reduced-order modeling using sensitivity matrix of assembly characteristics

We propose an estimation method of sensitivity coefficients of core neutronics parameters based on a multi-level reduced-order modeling approach. The idea is to use lower-level models to identify the dominant input parameter variations, constrained to the so-called active subspace, which are employed to determine the sensitivity coefficients of the core neutronic parameters. In our implementation, the lower-level model is represented by two-dimensional assembly calculations, which are employed in the preparation of the few-group cross-sections for core-wide calculations. The active subspace basis is estimated using the singular value decomposition of sensitivity matrices of assembly neutronics parameters. In numerical verification calculation, sensitivity coefficients of core characteristics for a typical three-loop PWR equilibrium-cycle are estimated using the proposed method and the direct method. Comparison of these two results shows that the proposed method well reproduces the results obtained by the direct method with lower calculation costs. Through the verification calculations, applicability of the proposed method to practical light water reactor analysis is confirmed.     

Numerical simulation and artificial neural network modeling of natural circulation boiling water reactor

Numerical simulation of natural circulation boiling water reactor is important in order to study its performance for different designs and under various off-design conditions. Numerical simulations can be performed by using thermal-hydraulic codes. Very fast numerical simulations, useful for extensive parametric studies and for solving design optimization problems, can be achieved by using an artificial neural network (ANN) model of the system. In the present work, numerical simulations of natural circulation boiling water reactor have been performed with RELAP5 code for different values of design parameters and operational conditions. Parametric trends observed have been discussed. The data obtained from these simulations have been used to train artificial neural networks, which in turn have been used for further parametric studies and design optimization. The ANN models showed error within ±5% for all the simulated data. Two most popular methods, multilayer perceptron (MLP) and radial basis function (RBF) networks, have been used for the training of ANN model. Sequential quadratic programming (SQP) has been used for optimization.