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.     

Nodal methods for three-dimensional simulators

For the successful operation of power and research reactors, a three-dimensional simulator plays a key role. This paper deals with the neutronic part of such a simulator. The neutronic calculations for thermal reactors are usually performed in three stages. The first two stages are respectively the cell and box homogenization, and the final stage corresponds to core calculations. Here we restrict ourselves to the last stage only. At this stage the fine-mesh finite difference method is not suited because of the large number of mesh points needed, and hence more computational time. The nodal coupling method is found to be very successful for such core calculations. The status of the nodal coupling method from its initial stages to the present stage is reviewed. The first simulator based on the above method is the code FLARE. The equations of FLARE are derived and the salient features of later simulators like COMET-G, PRESTO, MOGS, TRILUX, SANLUX, COSMOS-2, SIMULATE etc. are discussed. Also the analytical methods for the treatment of relflector and optimized iteration strategies for Boiling Water Reactors are discussed.     

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.     

Transient and stability analysis of a BWR core with thorium–uranium fuel

The kinetic response of a boiling water reactor (BWR) equilibrium core using thorium as a nuclear material, in an integrated blanket–seed assembly, is presented in this work. Additionally an in-house code was developed to evaluate this core under steady state and transient conditions including a stability analysis. The code has two modules: (a) the time domain module for transient analysis and (b) the frequency domain module for stability analysis. The thermal–hydraulic process is modeled by a set of five equations, considering no homogeneous flow with drift-flux approximation and non-equilibrium thermodynamic. The neutronic process is calculated with a point kinetics model. Typical BWR reactivity effects are considered: void fraction, fuel temperature, moderator temperature and control rod density. Collapsed parameters were included in the code to represent the core using an average fuel channel. For the stability analysis, in the frequency domain, the transfer function is determined by applying Laplace-transforming to the calculated pressure drop perturbations in each of the considered regions where a constant total pressure drop was considered. The transfer function was used to study the system response in the frequency domain when an inlet flow perturbation is applied. The results show that the neutronic behavior of the core with thorium uranium fuel is similar to a UO₂ core, even during transient conditions. The stability and transient analysis show that the thorium–uranium fuel can be operated safely in current BWRs.     

Nonlinear analysis of nuclear coupled density wave instability in time domain for a boiling water reactor core undergoing core-wide and regional modes of oscillations

The objective of the paper is to develop a nuclear coupled thermal-hydraulic model in order to simulate core-wide (in-phase) and regional (out-of-phase) stability analysis in time domain within the limitation of desktop research facility for a boiling water reactor subjected to operational transients. The integrated numerical tool, which is a combination of thermal-hydraulic, neutronic and fuel heat conduction models, is used to analyze a complete boiling water reactor core taking into account the strong nonlinear coupling between the core neutron dynamics and primary circuit thermal-hydraulics via the void-temperature reactivity feedback effects. The integrated model is validated against standard benchmark and published results. Finally, the model is used for various parametric studies and a number of numerical simulations are carried out to investigate core-wide and regional instabilities of the boiling water reactor core with and without the neutronic feedback effects. Results show that the inclusion of neutronic feedback effects has an adverse effect on boiling water reactor core by augmenting the instability at lower power for same inlet subcooling during core-wide mode of oscillations, whereas the instability is being suppressed during regional mode of oscillations in presence of the neutronic feedback. Dominance of core-wide instability over regional mode of oscillations is established for the present case of simulations which indicates that the preclusion of the former will automatically prevent the latter at the existing working condition.     

On the stability of the point reactor kinetics equations

As the basic neutronic problem is unstable by nature, maintaining a reactor critical is a task that requires a lot of effort. This work presents and discusses some aspects related to the stability of the basic physics behind a nuclear reactor core based on the well-known point reactor kinetics equations. First, the linear non-feedback case is studied where differences between Lyapunov and BIBO stability are found. These differences are shown both numerically and analytically, and explained using a reactor physics based reasoning. Finally, a simple model is used to analyse the intrinsic stability of the point reactor equations when reactivity feedbacks are taken into account. A method for constructing conceptual stability design maps is proposed and a basic interpretation of the simple results obtained is given.     

采用FFT方法对横摇条件下堆芯核热耦合流动不稳定性的分析

基于开发的海洋条件下堆芯核热耦合流动不稳定性分析程序,利用快速傅里叶变换（FFT）方法对堆芯通道的流量振荡曲线进行分析,获得了静止和横摇条件下堆芯发生核热耦合流动不稳定性时通道的频谱特性。研究表明,静止条件下堆芯发生流动不稳定性时仅具有1个频率峰值,其对应固有频率;在横摇条件下堆芯发生流动不稳定性时,堆芯所有通道均受到横摇条件和核热耦合效应影响,但只有最高功率通道中固有频率处于支配地位,该类功率通道首先发生流动不稳定性。FFT方法可精确地分析复杂流量振荡曲线的特性,进而判定横摇下堆芯核热耦合系统是否发生流动不稳定性。     

Spatial neutronic coupling aspects in nuclear reactors

In this paper, an effort is made to gain insights about neutronic coupling and decoupling phenomena of nuclear reactors and its consequences on their safety and stability. The neutronic coupling and decoupling aspects are investigated using eigenvalue separation (EVS) methodology. Higher harmonic eigenvalues are calculated by the method of mode subtraction. The eigenvalue separation for a typical 1000 MWe PWR is calculated and its relations with reactor core shape and size and consequent effects on spatial stability are investigated. It is demonstrated quantitatively that it is necessary to optimize height to diameter (H/D) ratio to suppress the susceptibility to multimode oscillations and to enable ease in designing spatial control algorithm. Consequences of extreme H/D ratio are also addressed. Optimum shape of the reactor core is investigated and the evaluation of upper limit of about 1.3 for H/D ratio has been carried out for large PWR cores. Safety implications of neutronic loose coupling on departure from nucleate boiling ratio (DNBR) are also addressed.     

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。     

Power-reactor performance evaluation using nodal/modal analysis

An analytical procedure for calculating the 3-D power distribution in LWRs based on two-group coarse-mesh nodal analysis is described. The use of source-sink analysis of the fast-neutron source distribution yields a very efficient eigenvalue equation. Neutron coupling between nodes is evaluated using a modal analysis of the neutron-source shape within each node based on the multiplication and transport properties of the source node and its immediate neighbors. Both the core and fuel-assembly geometry and the neutronic characteristics of LWRs are particularly well suited to this type of analysis.     

First 3-D calculation of core disruptive accident in a large-scale sodium-cooled fast reactor

The SIMMER-IV computer code is a three-dimensional fluid-dynamics code coupled with a fuel-pin model and a space- and energy-dependent neutron transport kinetics model. The present study has attempted the first application of SIMMER-IV to a core disruptive accident in a large-scale sodium-cooled fast reactor. A principal point of this study was to investigate reactivity effects with fuel relocation under three-dimensional core representation including control rods. The calculation has indicated that the fuel discharge from the core was disturbed by a significant flow resistance at the entrance nozzle in the current design. Additional static neutronic calculations have been performed to compare basic neutronic characteristics between different scale cores. The static neutronic calculations have clarified that the outward fuel compaction within the inner core increased the reactivity in the large-scale core unlike the small-scale core.     

Dynamic analysis of multiple nuclear-coupled boiling channels based on a multi-point reactor model

This work investigates the non-linear dynamics and stabilities of a multiple nuclear-coupled boiling channel system based on a multi-point reactor model using the Galerkin nodal approximation method. The nodal approximation method for the multiple boiling channels developed by Lee and Pan [Lee, J.D., Pan, C., 1999. Dynamics of multiple parallel boiling channel systems with forced flows. Nucl. Eng. Des. 192, 31–44] is extended to address the two-phase flow dynamics in the present study. The multi-point reactor model, modified from Uehiro et al. [Uehiro, M., Rao, Y.F., Fukuda, K., 1996. Linear stability analysis on instabilities of in-phase and out-of-phase modes in boiling water reactors. J. Nucl. Sci. Technol. 33, 628–635], is employed to study a multiple-channel system with unequal steady-state neutron density distribution. Stability maps, non-linear dynamics and effects of major parameters on the multiple nuclear-coupled boiling channel system subject to a constant total flow rate are examined. This study finds that the void-reactivity feedback and neutron interactions among subcores are coupled and their competing effects may influence the system stability under different operating conditions. For those cases with strong neutron interaction conditions, by strengthening the void-reactivity feedback, the nuclear-coupled effect on the non-linear dynamics may induce two unstable oscillation modes, the supercritical Hopf bifurcation and the subcritical Hopf bifurcation. Moreover, for those cases with weak neutron interactions, by quadrupling the void-reactivity feedback coefficient, period-doubling and complex chaotic oscillations may appear in a three-channel system under some specific operating conditions. A unique type of complex chaotic attractor may evolve from the Rossler attractor because of the coupled channel-to-channel thermal-hydraulic and subcore-to-subcore neutron interactions. Such a complex chaotic attractor has the imbedding dimension of 5 and the fractal dimension ranging from 1.26 to 1.35.     

Development of Ignalina NPP RBMK-1500 reactor RELAP5-3D model

This paper deals with the development of an integrated thermal-hydraulics–neutronics model for RBMK-1500 reactors for the analysis of specific plant transients in which the neutronic response of the core is important. A successful best estimate coupled RELAP5-3D model of Ignalina nuclear power plant (NPP) has been developed. The validation of the thermal-hydraulic model has been performed using operational transients from Ignalina NPP. The results of the calculations obtained with the RELAP5-3D model compare reasonably with the real plant data. The RELAP5-3D nodal kinetics model provides reasonable agreement with Ignalina NPP reactor power and coolant density profiles. The eigenvalue is close to unity, indicating that reasonable values are calculated for the neutron fluxes.     

Two mathematical expressions for the pulse decay in a two-point reactor

The mathematical equivalence of two solutions, both expressing the pulse decay in a two-point reactor, is illustrated. The first is a series superposing time eigenfunctions of two-point kinetic equations, while the second is a series summing the effects of groups of neutrons, each group having undergone a specified number of trips between the two cores after the initial pulse. The two expressions are alternative representations of a single solution. Taking a symmetric coupled-core system, numerical examples are given, and the relevant time range for the truncated solution of each is examined. The possibility of damped oscillation is investigated using the second solution. The concept of equivalence applies to the propagation of a neutronic disturbance within a large reactor core, provided the nodal model is feasible.     

Asymptotic stability for delayed differential systems with nonnegative coupling in reactor dynamics

We present in this paper two families, V^±(p^±), of nonquadratic, non positive definite Lyapunov functionals depending on several parameters, that are suited to handle nonlinear stability problems for ordinary or functional (delayed) differential equations. The approach is based on the property of essential positivity of the Jacobian matrix A+B of the nondelayed system, which physically corresponds to nonnegative coupling among state variables, such as powers and precursor populations in a nodal dynamics model of a coupled core reactor. Positive power coefficients in some nodes are compatible with stability provided the remaining ones are sufficiently negative to ensure that A+B is a stable matrix, independently of the magnitude of the delays. In this case the combined use of functionals from the V^±(p^±) families, p^±>1, yields a better estimate (which of course reduces with increasing the magnitude of the delays) of the domain of attraction of the null solution of the system equations than would be allowed by a single and/or more conventional (e.g. quadratic) functional.     

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.     

A methodology for the coupling of RAMONA-3B neutron kinetics and TRAC-BF1 thermal-hydraulics

The initial objective of this project was to directly couple the RAMONA and TRAC codes running on different PCs. The idea was to use the best part of each one and eliminate some of their limitations and widen the applicability of these codes to simulate different BWR and system components. It was required to try to minimize the amount of changes to present code subroutines and calculation procedures. If possible, just substitute values obtained in the parallel code. Preliminary results indicated that using a CHAN component of TRAC to model thermal-hydraulic phenomena for each neutronic channel modeled in RAMONA is rather difficult. Large amounts of CPU time consumption are obtained and lots of PCs would make this solution difficult, besides considerable large transients are introduced by the differences in thermal-hydraulic results of these codes. The substitution of the thermal-hydraulics of RAMONA, by the TRAC channel calculations, is possible but simulation of a null transient on both codes must be planed and a gradual change must be controlled by an additional supervisory subroutine. An indirect coupling of these codes, it is therefore proposed, in order to eliminate most of these limitations. In this indirect coupling, a thermal-hydraulic model of the average tube in a bundle and the global channel cooling fluid dynamics is programmed for each neutronic channel while the global reactor vessel and core is modeled by TRAC with just four channels and four rings. Results are more reliable, coupling is simpler and faster simulations are possible.     

A spatial kinetic model for simulating VVER-1000 start-up transient

An accurate prediction of reactor core behavior in transients depends on how much it could be possible to exactly determine the thermal feedbacks of the core elements such as fuel, clad and coolant. In short time transients, results of these feedbacks directly affect the reactor power and determine the reactor response. Such transients are commonly happened during the start-up process which makes it necessary to carefully evaluate the detail of process. Hence this research evaluates a short time transient occurring during the start up of VVER-1000 reactor. The reactor power was tracked using the point kinetic equations from HZP state (100 W) to 612 kW. Final power (612 kW) was achieved by withdrawing control rods and resultant excess reactivity was set into dynamic equations to calculate the reactor power. Since reactivity is the most important part in the point kinetic equations, using a Lumped Parameter (LP) approximation, energy balance equations were solved in different zones of the core. After determining temperature and total reactivity related to feedbacks in each time step, the exact value of reactivity is obtained and is inserted into point kinetic equations. In reactor core each zone has a specific temperature and its corresponding thermal feedback. To decrease the effects of point kinetic approximations, these partial feedbacks in different zones are superposed to show an accurate model of reactor core dynamics. In this manner the reactor point kinetic can be extended to the whole reactor core which means “Reactor spatial kinetic”. All required group constants in calculations are prepared using the WIMS code. In addition CITATION code was used to calculate the flux, power distribution and core reactivity inside the core. To update the last change in group constants and resultant reactivity in point kinetic equations, these neutronic codes were coupled with a developed dynamic program. This study is applied on a typical VVER-1000 reactor core to show the reactor response in short time transients caused during start-up procedure.     

Global physical and numerical stability of a nuclear reactor core

Low order models are used to investigate the influence of integration methods on observed power oscillations of some nuclear reactor simulators. The zero-power point reactor kinetics with six-delayed neutron precursor groups are time discretized using explicit, implicit and Crank–Nicholson methods, and the stability limit of the time mesh spacing is exactly obtained by locating their characteristic poles in the z-transform plane. These poles are the s to z mappings of the inhour equation roots and, except for one of them, they show little or no dependence on the integration method. Conditions for stable power oscillations can be also obtained by tracking when steady state output signals resulting from reactivity oscillations in the s-Laplace plane cross the imaginary axis. The dynamics of a BWR core operating at power conditions is represented by a reduced order model obtained by adding three ordinary differential equations, which can model void and Doppler reactivity feedback effects on power, and collapsing all delayed neutron precursors in one group. Void dynamics are modeled as a second order system and fuel heat transfer as a first order system. This model shows rich characteristics in terms of indicating the relative importance of different core parameters and conditions on both numerical and physical oscillations observed by large computer code simulations. A brief discussion of the influence of actual core and coolant conditions on the reduced order model is presented.     

Analytical modeling of flashing-induced instabilities in a natural circulation cooled boiling water reactor

A dynamic model for natural circulation boiling water reactors (BWRs) under low-pressure conditions is developed. The motivation for this theoretical research is the concern about the stability of natural circulation BWRs during the low-pressure reactor start-up phase. There is experimental and theoretical evidence for the occurrence of void flashing in the unheated riser under these conditions. This flashing effect is included in the differential (homogeneous equilibrium) equations for two-phase flow. The differential equations were integrated over axial two-phase nodes, to derive a nodal time-domain model. The dynamic behavior of the interface between the one and two-phase regions is approximated with a linearized model. All model equations are presented in a dimensionless form. As an example the stability characteristics of the Dutch Dodewaard reactor at low pressure are determined.