Point Kinetics Method Research Articles

A new surrogate method for the neutron kinetics calculation of nuclear reactor core transients

Reactor core transient calculation is very important for the reactor safety analysis, in which the kernel is neutron kinetics calculation by simulating the variation of neutron density or thermal power over time. Compared with the point kinetics method, the time-space neutron kinetics calculation can provide accurate variation of neutron density in both space and time domain. But it consumes a lot of resources. It is necessary to develop a surrogate model that can quickly obtain the temporal and spatial variation information of neutron density or power with acceptable calculation accuracy. This paper uses the time-varying characteristics of power to construct a time function, parameterizes the time-varying characteristics which contains the information about the spatial change of power. Thereby, the amount of targets to predict in the space domain is compressed. A surrogate method using the machine learning is proposed in this paper. In the construction of a neural network, the input is processed by a convolutional layer, followed by a fully connected layer or a deconvolution layer. For the problem of time sequence disturbance, a structure combining convolutional neural network and recurrent neural network is used. It is verified in the tests of a series of 1D, 2D and 3D reactor models. The predicted values obtained using the constructed neural network models in these tests are in good agreement with the reference values, showing the powerful potential of the surrogate models.

Multi-physics coupling analysis of test heat pipe reactor KRUSTY based on MOOSE framework

The heat pipe reactor utilizes heat pipes for passive heat transfer, eliminating the need for any moving parts. This feature significantly enhances its safety characteristics. Given the intricate nature of the heat pipe reactor system, a comprehensive multi-physics coupling simulation is necessary to study its safety features. In this study, a high-fidelity multi-physics coupling analysis incorporating a neutronic-thermal–mechanical-heat pipe coupling model is conducted. The work is based on the multi-physics coupling framework MOOSE, which integrates the Monte Carlo code OpenMC for neutronic analysis and built-in modules for 3-dimensional thermal–mechanical analysis. Furthermore, a heat pipe simulation method called the Thermal Resistance Grid Method is implemented within the MOOSE framework and employed in the multi-physics coupling analysis. To facilitate transient analysis, the Point Kinetics method is also integrated into the MOOSE framework to account for the time-varying power factor during reactor transients. The various modules and physical fields are coupled together using either loose or tight coupling strategies. These coupling strategies are applied to assess a test heat pipe reactor known as KRUSTY. Steady-state simulations are conducted for both normal operation and single heat pipe failure conditions, enabling the calculation of fission power distribution, temperature distribution, stress and strain profiles, as well as power and temperature redistribution following a heat pipe failure. Moreover, a load-following transient of KRUSTY is simulated, demonstrating its capability for load following without reactivity control. The aforementioned calculations validate the feasibility of the coupling framework utilized in this study and highlight its ability to accurately capture local phenomena within the reactor core.

Adjusted mean generation time parameter in the neutron point kinetics equations

This paper proposes an approximation for the modified point kinetics equations to obtain a mathematically simpler set of equations similar to those of the classic point kinetics. The new method, which is called the adjusted point kinetics method, discards the least important terms in the modified kinetics equations and adjusts the mean generation time parameter to tentatively incorporate the influence of the discarded terms. To validate the proposed model, it is compared to the modified kinetics model in numerical calculations of two very simple reactivity insertion cases.

The application of nodal method for dynamic analysis of TRIGA Mark II

In this paper, Nodal dynamic method is introduced to model the TRIGA Mark II reactor of the University of Pavia as a dynamic system for the total operative power range (i.e. 0–250 kW) using a zero dimensional thermal hydraulic method. Neutronic and thermal hydraulic models are coupled in order to demonstrate reactor dynamic behavior. The reactor is divided into bi-dimensional zones and simulated in Serpent 2 to obtain two group cross sections for each specified zone as well as kinetic parameters. And they are applied in nodal method for the analysis of reactor dynamic behavior. Point kinetic and nodal dynamic methods are utilized for the second core configuration as the neutronic model. Different reactivities (i.e. 190, 104, 78, 40 pcm) are inserted by control rods in different power levels (i.e. 1, 50, 100, 150 kW) for the reactor dynamic analysis. A program is written in MATLAB to couple neutronic and thermal hydraulic models. A system of ordinary differential equations are produced and solved in space state model. The calculated and experimental power excursion results are in good agreement with less than 1% difference. The results between nodal method and point kinetic method are very consistent with less than 0.05% of difference.

Signal processing system design for improved shutdown system of CANDU® nuclear reactors in large break LOCA events

For CANDU reactors, several options to improve CANDU nuclear power plant operation safety margin have been investigated in this paper. A particular attention is paid to the response time of CANDU shutdown system number 1 (SDS1) in case of large break loss of coolant accident (LLOCA). Based on point kinetic method, a systematic fundamental analysis is performed to CANDU LLOCA event, and the power transient signal is generated. In order to improve the SDS1 response time during LLOCA events, an innovative power measurement and signal processing system is particularly designed. The new signal processing system is implemented with the input of the LLOCA power transient, and the simulation results of the reactor trip time and signal are compared to those of the existing system in CANDU power plants. It is demonstrated that the new signal processing system can not only achieve a shorter reactor trip time than the existing system, but also accommodate the spurious trip immunity. This will significantly enhance the safety margin for the power plant operation, or bring extra economical benefits to the power plant units.

Qualitative performance comparison of reactivity estimation between the extended Kalman filter technique and the inverse point kinetic method

The Extended Kalman Filtering (EKF) technique has been applied for estimation of subcriticality with a good noise filtering and accuracy. The Inverse Point Kinetic (IPK) method has also been widely used for reactivity estimation. The important parameters for the EKF estimation are the process noise covariance, and the measurement noise covariance. However the optimal selection is quite difficult. On the other hand, there is only one parameter in the IPK method, namely the time constant for the first order delay filter. Thus, the selection of this parameter is quite easy. Thus, it is required to give certain idea for the selection of which method should be selected and how to select the required parameters. From this point of view, a qualitative performance comparison is carried out.

A Hybrid Transport Point-Kinetic method for simulating source transients in subcritical systems

Abstract This paper describes a novel hybrid technique for the solution of the time-dependent neutron transport equation in source switch-on transients. The Hybrid Transport Point Kinetics (HTPK) method is derived from a multi-collision description of the transport equation and is based on the observation that the external source mainly influences the first few neutron generations and, through collisions and multiplications, an ensemble behavior statistically emerges at higher order. The HTPK is designed to separately describe the propagation phenomenon from the ensemble response of the system, using both the rigorous transport equation and simplified kinetic models. Numerical simulations performed on a typical acceleration driven system configuration confirm the basic physical intuition of HTPK and show a significant gain in accuracy when compared to classical point kinetics. The proposed HTPK technique is also shown to be attractive because of its flexibility and competitive computational effort.

Application of Monte Carlo Method to Solve the Neutron Kinetics Equation for a Subcritical Assembly

There is a need to understand the space-dependent kinetics of fast or thermal reactor physics and the Monte Carlo method should be implemented in kinetics codes as well. In a transient accident (for example, control rod ejection accident or loss of coolant accident), changes in the system are much slower than the prompt neutron lifetime. In the present paper, a method is proposed in which the Monte Carlo method is used to solve the neutron kinetics of reactors, such as the case of a subcritical static reactor with an external neutron source. In the proposed method the time derivative of the neutron equation is set to zero, though the time derivative of the delayed neutron precursor equation is treated without any approximation in the time differentiation of delayed neutron precursor equation. Most kinetics calculation methods originate from the point kinetics method, and they require calculation of excess reactivity at each time step, but the present method does not need calculation of excess reactivity. The neutron counts measured with small fission chambers in the subcritical kinetics experiment using the JAEA fast critical assembly are compared with counts calculated by the proposed method and compared with the measured values. The agreement is good, and the excellent performance of the method for space-dependent neutron kinetics is shown.

SMALL AND MEDIUM SIZED LIQUID METAL COOLED SAFETY ANALYSIS USING MULTI LEVEL COMPLEXITY MODEL

SMALL AND MEDIUM SIZED LIQUID METAL COOLED SAFETY ANALYSIS USING MULTI LEVEL COMPLEXITY MODEL Inherent safety characteristics of liquid metal cooled fast reactors is very important capital for next generation nuclear power plants. However inherent safety assessment need appropriate computer code or experiment. Here, a computer code for liquid metal cooled fast reactor accident analysis with various level of complexity has been developed. At the simplest approach, quasi-static method is adopted to get asymptotic condition during UTOP, ULOF, and UTOP-ULOF accident. Here we can get asymptotic power level, asymptotic average coolant temperature, and asymptotic fuel temperature for a certain external reactivity and natural circulation level. In the next grade, the code will simulate transient effect using point kinetic method and quasistatic approach for thermal hidraulic analysis. Here we can get time depedent power change, coolant temperature change and fuel temperature change. Finally in the rigorous analysis, coupled space dependent kinetic and transient thermal hydraulic are coupled and solved to get time depedent information of various process involved in the accident.

On the Performance of Point Kinetics for the Analysis of Accelerator-Driven Systems

The ability of point kinetics to describe dynamic processes in accelerator-driven systems (ADSs) is investigated. Full three-dimensional energy-space-time-dependent calculations, coupled with thermal and hydraulic feedback effects, are performed and used as a standard of comparison. Various transient accident sequences are studied. Calculations are performed in the range of keff = 0.9594 to 0.9987 to provide insight into the dependence of the performance on the subcritical level. Numerical experiments are carried out on a minor-actinide–loaded and lead-bismuth–cooled ADS. It is shown that the point kinetics approximation is capable of providing highly accurate calculations in such systems. The results suggest better precision at lower keff levels. It is found that subcritical operation provides features that are favorable from a point kinetics view of application. For example, reduced sensitivity to system reactivity perturbations effectively mitigates any spatial distortions. If a subcritical reactor is subject to a change in the strength of the external source, or a change in reactivity within the subcritical range, the neutron population will adjust to a new stationary level. Therefore, within the normal range of operation, the power predicted by the point kinetics method and the associated error in comparison with the exact solution tends to approach an essentially bounded value. It was found that the point kinetics model is likely to underestimate the power rise following a positive reactivity insertion in an ADS, which is similar to the behavior in critical systems. However, the effect is characteristically lowered in subcritical versus critical or near-critical reactor operation.

Multidimensional TMI-1 Main-Steam-Line-Break Analysis Methodology Using TRAC-PF/NEM

A comparison of a point-kinetics calculation and a full three-dimensional thermal-hydraulic/kinetics calculation using TRAC-PF1/NEM is presented. The coupled TRAC-PF1/NEM methodology uses version 5.4 of the TRAC-PF1/MOD2 code, developed by the Los Alamos National Laboratory, and a special kinetics module, developed at The Pennsylvania State University and based on the nodal expansion method. Cross sections are obtained from two-dimensional tables generated using CASMO-3.The results of the analysis show that the point-kinetics calculation is conservative and predicts a return to power. The three-dimensional analysis shows no return to power despite an extended overfeeding of the affected generator with feedwater. The difference is believed to be caused by the inability of the standard point-kinetics method to properly account for the moderator density feedback, local effects, and flux redistribution, which occur during the transient.

Measurement of large negative reactivity in WWER-440. Sources of uncertainty

The sources of uncertainty in measurement of large negative reactivity in WWER-440 by the inverse point kinetics method, are evaluated quantitatively on the example of measurement of the reactivity worth of the shutdown control rod system of WWER-440 at zero power. Considering the specific features of the control rod system of WWER-440, it is demonstrated that using an appropriate formulation of the inverse solution of the equations of point kinetics, the uncertainty of measured reactivity ρ/ β introduced by the assumption of constancy of the parameters of kinetics can be reduced to <3–5% for the case of the discussed rod-drop test at zero power. Based on an analysis of both numerically simulated and actual rod-drop transients, it is shown that the uncertainty of measured reactivity ρ/ β can be quite considerable due to the underlying delayed neutron data set—the values of ρ/ β obtained using different data sets can differ by ∼15%. Inexact accounting of the share of 239Pu in the fission neutron source is estimated to contribute to the total uncertainty of measured ρ/ β of ∼1%, whereas possible spatial effects are expected to result in a relative error in ρ/ β of ∼5%.

Fast Power Excursions in Pebble-Bed Reactors—Methods and Results

The DYN and COSTANZA program systems for kinetics analysis are compared using sample calculations for pebble-bed high-temperature reactors. The DYN point kinetics method appears to be successful even where reactivity changes exceed ..beta...

An Early-Time Analysis of Space-Dependent Nuclear Reactor Transients

An analytical procedure is described for the early-time asymptotic solution of a partial-differential integral equation of the parabolic type. Several applications to the analysis of the early stages of space-dependent nuclear reactor transients are presented. The one-energy-group diffusion model with a ''Newton law of cooling'' linear feedback is employed. Physical interpretations of the results are given. Comparisons with results obtained by different formulations of the point-kinetic method are performed.

On the Use of Point Kinetics for the Analysis of Rod-Ejection Accidents

The results of a numerical study as to the adequacy of the point kinetics method for analyzing rod-ejection accidents are presented. Two-group slab representations of three different seed-blanket r...