Nuclear Reactor Model Research Articles

Estimation of resonance self-shielding effect in PWR pin cell for different fuel types

The most important factors in any code used for nuclear reactor modeling are the time and precision of the results. In principle, deterministic codes are used in calculations due to the long computational time required by stochastic codes to achieve reliable results. The accuracy of deterministic codes is related to the method used in treating the resonance self-shielding behavior of the cross-sections; hence it is essential to select the best self-shielding method. Both the equivalence in dilution, and the subgroup approaches are used to represent the self-shielding effect in PWR pin cell. The calculations are performed using three classes of subgroup approaches based on physical and mathematical (Ribon extended model and subgroup projection method) probability tables. In the present paper, various cross-section library formats are considered to assess the performance of three PWR fuel types: UO2, PuO2–UO2, and ThO2–UO2, using DRAGON4 and WIMS-D5 codes. The accuracy of the calculations is determined by comparison with the stochastic MCNP6 code. The results obtained indicate that the radial sub-divisions and proper resonance treatment are required to treat the rim effect. This is demonstrated in DRAGON code that can accurately calculate the radial distributions for all reaction rates.

CALCULATION OF NEUTRON-CAPTURE REACTIONS CONTRIBUTION TO ENERGY RELEASE IN VVER-1000 USING SERPENT CODE

Calculating the energy release in fuel elements is an important aspect of the modeling and design of nuclear reactors. Most of the energy is produced by fission, but a non-negligible percentage is coming from neutron capture reactions, such as (n, γ) or (n, α). We implement a previously developed method for the calculation of effective energy release using Serpent Monte Carlo code. We investigate the percentage of capture component in effective energy release for various models of VVER-1000 fuel: firstly, an equivalent cell, then fresh fuel assemblies of different compositions, differing in fuel enrichment and the presence of burnable absorbers. The results are compared to similar calculations previously done in MCNP 4 and MCU 5.

Robustness of proper dynamic output feedback for discrete-time singularly perturbed systems

In this paper, the dynamic output feedback control problem of discrete-time singularly perturbed systems is considered based on the reduced-order technique. We first show that a proper but not strictly proper dynamic output feedback controller designed for the reduced-order model generally is not a stabilizing compensator for the original system, even though the fast subsystem is stable. To obtain the robustness of the dynamic output feedback controller, an auxiliary system is designed. Based on this, the design of the dynamic output feedback for the reduced-order subsystem is reduced to the simultaneous design of a static output feedback controller for the fast subsystem and a strictly proper dynamic output feedback controller for the auxiliary system, respectively. Based on the obtained results, we confirm that it is possible to generate the robustness for the proposed dynamic output feedback control. Thus, the restriction on the strict properness can be alleviated. Finally, a realistic practical example for the nuclear reactor model is provided to show the effectiveness of the obtained theoretical results.

Robust observer based control for axial offset in pressurized-water nuclear reactors based on the multipoint reactor model using Lyapunov approach

Abstract In nuclear reactor imbalance of axial power distribution induces xenon oscillations. These fluctuations must be maintained bounded within allowable limits. Otherwise, the nuclear power plant could become unstable. Therefore, bounded these oscillations is considered to be a restriction for the load following operation. Also, in order to design the nuclear reactor control systems, poisons concentrations, especially xenon must be accessible. But, physical measurement of these parameters is impossible. In this paper, for the first time, in order to estimate the axial xenon oscillations and ensures these oscillations are kept bounded within allowable limits during load-following operation, a robust observer based nonlinear control based on multipoint kinetics reactor model for pressurized-water nuclear reactors is presented. The reactor core is simulated based on the multi-point nuclear reactor model (neutronic and thermal-hydraulic). Simulation results are presented to demonstrate the effectiveness of the proposed observer based controller for the load-following operation.

Estimation of the poisons reactivity in the P.W.R Nuclear Reactors using modified higher order sliding mode observer based on the multi-point nuclear reactor model

Reactor power control is one of the most important problems in a nuclear power plant. Considering the importance of the negative feedback reactivity from neutron absorber poisons such as xenon and samarium in the design of the nuclear reactor control system and regarding the limitations of the xenon and samarium reactivity measurement, in this paper, for the first time, a modified higher-order sliding mode observer is presented to estimate the xenon and samarium reactivity in the P.W.R Nuclear Reactors. The reactor core is simulated based on the multi-point nuclear reactor model (neutronic and Thermal-hydraulic) and three delayed neutrons groups. Traditional sliding mode technique has intrinsic problem of chattering. To cope with this problem, Higher Order Sliding Mode (HOSM) is used. The employed method is easy to implement in practical applications and moreover, the higher order sliding mode control exhibits the desired dynamic behavior during the entire output-tracking process. Simulation results are presented to demonstrate the effectiveness of the proposed observer in terms of performance, robustness and stability and show that the HOSM observer follows the actual system variables accurately and is satisfactory in the presence of the parameters uncertainties and disturbances.

Wavelet based iterative methods for a class of 2D-partial integro differential equations

In this paper, an iterative method based on quasilinearization is presented to solve a class of two dimensional partial integro differential equations that arise in nuclear reactor models and population models. Two different approaches based on Haar and Legendre wavelets are studied to develop numerical methods. In the first approach, time domain is approximated with the help of forward finite difference approach. In the second approach, both time as well as space domains are approximated by wavelets. Appropriate examples are solved using these methods and the obtained results are compared with the methods available in the recent literature.

Fractional order PID controller for power control in perturbed pressurized heavy water reactor

This paper presents an interval fractional-order proportional integral derivative (INFOPID) controller design for the power control of a highly nonlinear Pressurized Heavy Water Reactor (PHWR) under step-back condition. A single robust INFOPID controller is designed utilizing stability boundary locus method for eight nuclear reactor models considering eight interval conditions for each reactor model of the PHWR. The interval models have been obtained using Edge theorem. Simulation results show that the proposed INFOPID controller applied for active step-back in the reactor gives an efficient set point tracking performance, defined for variation in initial power level or control rod drop. The performance of the proposed INFOPID controller is evaluated using different integral error criterion by comparing its performance with existing methods in the literature. The proposed controller is found to give better results than the existing techniques.

Optimal Run Strategies in Monte Carlo Iterated Fission Source Simulations

The method of successive generations used in Monte Carlo simulations of nuclear reactor models is known to suffer from intergenerational correlation between the spatial locations of fission sites. One consequence of the spatial correlation is that the convergence rate of the variance of the mean for a tally becomes worse than O(N–1). In this work, we consider how the true variance can be minimized given a total amount of work available as a function of the number of source particles per generation, the number of active/discarded generations, and the number of independent simulations. We demonstrate through both analysis and simulation that under certain conditions the solution time for highly correlated reactor problems may be significantly reduced either by running an ensemble of multiple independent simulations or simply by increasing the generation size to the extent that it is practical. However, if too many simulations or too large a generation size is used, the large fraction of source particles discarded can result in an increase in variance. We also show that there is a strong incentive to reduce the number of generations discarded through some source convergence acceleration technique. Furthermore, we discuss the efficient execution of large simulations on a parallel computer; we argue that several practical considerations favor using an ensemble of independent simulations over a single simulation with very large generation size.

Seismic Response Analysis of Nuclear Island Buildings on Non-rock Foundation

A key technical problem of seismic response analysis of nuclear island buildings under the condition of non-rock foundation is the effective simulation of soil-structural interaction (SSI) and the nonlinear characteristics of soil. A seismic response analysis calculation model of nuclear island buildings on non-rock foundation is established on the basis of software platform of SuperFLUSH, which adopts equivalent linear method to describe the nonlinear dynamic characteristics of the near field ground, by setting viscous artificial boundary in the limited area of foundation to simulate the impact of radiation damping, and takes advantage of one-dimensional finite element method to make a response analysis of free field for the ground motion input. At last, by taking calculation model of CPR1000 nuclear reactor on the non-rock foundation as the object of study, the numerical examples verify the reliability and engineering application of the established model. Furthermore, the results of study can provide reference for seismic analysis of adaptability of inland nuclear power plant foundation and optimization design of foundation treatment scheme under the condition of non-rock foundation.

Adaptive robust control for axial offset in the P.W.R nuclear reactors based on the multipoint reactor model during load-following operation

Control of the nuclear reactors during load-following operation is the most important problem in nuclear power plants due to safety reasons. In the nuclear reactor, imbalance of axial power distribution induces xenon oscillations. These fluctuations must be maintained bounded within allowable limits. Otherwise, the nuclear power plant could become unstable. Therefore, bounded these oscillations is considered to be a restriction for the load following operation. In this paper, for the first time, in order to ensure these oscillations are kept bounded within allowable limits during load-following operation, an adaptive robust control based on the multipoint kinetics reactor model is presented for P.W.R nuclear reactors. The reactor core is simulated based on the multi-point nuclear reactor model (neutronic and thermal-hydraulic) and three delayed neutrons groups. The adaptation laws for updating the reactor parameters are generated using the Lyapunov approach. The stability analysis is given by means Lyapunov approach, then the control system is guaranteed to be stable within a large range.Simulation results are presented to demonstrate the effectiveness of the proposed adaptive control in terms of performance, robustness and stability and show that the adaptive parameters are bounded and stable in the presence of the parameters uncertainties and disturbances.

Robust observer-based non-linear control for PWR nuclear reactors with bounded xenon oscillations during load-following operation using two-point nuclear reactor model

Robust observer-based non-linear control for PWR nuclear reactors with bounded xenon oscillations during load-following operation using two-point nuclear reactor model

Robust observer-based non-linear control for PWR nuclear reactors with bounded xenon oscillations during load-following operation using two-point nuclear reactor model

In this paper, Sliding Mode Control (SMC) which is a robust nonlinear controller is designed to control the pressurised-water nuclear reactor power for the load-following operation problem that ensures xenon oscillations are kept bounded within acceptable limits. Considering neutron absorber poisons and regarding the limitations of the xenon concentration and delayed neutrons precursors densities measurement, a sliding mode observer is designed to estimate their values and finally an SMC based on the sliding mode observer is presented to control the reactor core power. The reactor core is simulated based on the two-point nuclear reactor model and three delayed neutrons groups. The stability analysis is given by means of the Lyapunov approach, thus the control system is guaranteed to be stable within a large range. Simulation results are presented to demonstrate the effectiveness of the proposed controller in terms of performance, robustness and stability.

Multi-objective optimization of a compact pressurized water nuclear reactor computational model for biological shielding design using innovative materials

The aim of the present work is to develop a computational model of a compact pressurized water nuclear reactor (PWR) to investigate the use of innovative materials to enhance the biological shielding effectiveness. Two radiation transport codes were used: the first one – MCNP – for the PWR design and the GEM/EVENT to simulate (in a 1D slab) the behavior of several materials and shielding thickness on gamma and neutron radiation. Additionally MATLAB Optimization Toolbox was used to provide new geometric configurations of the slab aiming at reducing the volume and weight of the walls by means of a cost/objective function. It is demonstrated in the reactor model that the dose rate outside biological shielding has been reduced by one order of magnitude for the optimized model compared with the initial configuration. Volume and weight of the shielding walls were also reduced. The results indicated that one-dimensional deterministic code to reach an optimized geometry and test materials, combined with a three-dimensional model of a compact nuclear reactor in a stochastic code, is a fast and efficient procedure to test shielding performance and optimization before the experimental assessment. A major outcome of this research is that composite materials (ECOMASS 2150TU96) may replace (with advantages) traditional shielding materials without jeopardizing the nuclear power plant safety assurance.

Towards a Consolidated Approach for the Assessment of Evaluation Models of Nuclear Power Reactors

The STARS project at the Paul Scherrer Institut (PSI) has adopted the TRACE thermal-hydraulic code. For analyses involving interactions between system and core, a coupling of TRACE with the SIMULATE-3K (S3K) light water reactor (LWR) core simulator has been developed. In this configuration, the codes and associated simulation models play a central role to achieve a comprehensive safety analysis capability. Therefore, efforts have now been undertaken to consolidate the validation strategy by implementing a more rigorous and structured assessment approach for TRACE applications. The principle is to systematically track the evolution of a given set of predicted physical quantities of interest (QoIs) over a multidimensional parametric space. If properly set up, such environment should provide code developers and code users with persistent (less affected by user effect) and quantified information (sensitivity of QoIs) on the applicability of a simulation scheme (codes, methodology, and input models) for steady-state and transient analysis of full LWR systems. Through this, for each given transient/accident, critical paths of the validation process can be identified that could then translate into defining reference schemes to be applied for downstream predictive simulations. To illustrate this approach, this validation strategy is applied to an inadvertent blowdown event that occurred in a Swiss BWR/6. The transient was initiated by the spurious actuation of the automatic depressurization system. Here, the validation approach progresses through a number of dimensions: (a) different versions of the TRACE code; (b) the methodology dimension—in this case imposed power and updated TRACE core models are investigated; and (c) the nodalization dimension, where changes to the input model are assessed. For each step in each validation dimension, a common set of QoIs is investigated. For the steady-state results, these include fuel temperature distributions. For the transient part of the present study, the evaluated QoIs include the system pressure evolution and water carryover into the steam line. It has been seen that the improvements to the model predictions resulted in a small impact on the system pressure gradient, thus confirming a persistency of the downstream mechanical stress estimate, whereas the water carryover could vary by up to 150% as a function of the adopted simulation methodology.

The Virtual Environment for Reactor Applications (VERA): Design and architecture

VERA, the Virtual Environment for Reactor Applications, is the system of physics capabilities being developed and deployed by the Consortium for Advanced Simulation of Light Water Reactors (CASL). CASL was established for the modeling and simulation of commercial nuclear reactors. VERA consists of integrating and interfacing software together with a suite of physics components adapted and/or refactored to simulate relevant physical phenomena in a coupled manner. VERA also includes the software development environment and computational infrastructure needed for these components to be effectively used. We describe the architecture of VERA from both software and numerical perspectives, along with the goals and constraints that drove major design decisions, and their implications. We explain why VERA is an environment rather than a framework or toolkit, why these distinctions are relevant (particularly for coupled physics applications), and provide an overview of results that demonstrate the use of VERA tools for a variety of challenging applications within the nuclear industry.

Feedback control for the nuclear reactors

ABSTRACTThe paper considers the standard nuclear reactor model with pointwise active zone dynamics together with the dynamics of the external circuits of the reactor in the linearised version. There are presented some Lyapunov functions and the corresponding stability theorems. These Lyapunov functions can be used in synthesising feedback controllers for the reactor power. Two cases – the control Lyapunov function and the sliding mode control – are considered. It is shown that the same Lyapunov functions used in synthesis can be used to obtain stability of the closed-loop reactor-controller.

Neutronics and thermal hydraulics analysis of a low-enriched uranium cermet fuel core for a Mars surface power reactor

A fission reactor utilizing low-enriched uranium cermet fuel and supercritical carbon dioxide as coolant was designed to provide electrical power for a manned Mars base. The reactor was designed to generate 1.67MWth for a fifteen year operational lifetime, with an electric output of 333kWe. The core has alternating rows of fuel elements and a breeder blanket, with nineteen coolant channels in the fuel element and a single coolant channel in the breeder blanket. The design uses 15% isotopic enriched U-235 based cermet fuel, and uranium dioxide fuelled blankets. S-CO2 is used as a coolant, which converts the heat generated by the reactor to electricity using a closed Brayton cycle. Cermet fuel is used in the form of hexagonal shaped elements with 19 coolant channels and a zirconium hydride neutron moderator. The reactor uses B4C based control drums for control and safety. ZrC is used as thermal insulator, and ensures that the ZrH moderator does not reach an unacceptably high temperature. The coolant channels have a cladding of tungsten to prevent the release of fission gas from the fuel into the coolant. Beryllium reflectors are used to moderate and reflect neutrons back into the active core. The active core has a bull’s eye configuration, in which there are alternate fuel and blanket circular rows. Nuclear reactor modeling, neutronics, and depletion analysis were done using MCNP6. The neutronics analysis found the maximum peaking factor that would occur in the core. This was used to determine the greatest amount of thermal power that the core’s fuel elements and breeder blanket would experience. This provided the basis for the thermal hydraulics, which sought to determine the maximum inlet and outlet temperatures of the S-CO2 that could be obtained while also keeping all of the reactor materials within an acceptable temperature range. Maximizing these temperatures would provide the highest performance for a power conversion system. Finding the coolant conditions that kept this section of the core below the maximum permissible temperature would ensure that the rest of the core would also remain within an acceptable temperature limit. Simulations were conducted at the different power levels the fuel element and breeder blanket would generate throughout the reactor’s fifteen-year lifecycle. The thermal hydraulics which was done using COMSOL Multiphysics. This research presents a very viable reactor design that uses materials currently tested on other types of reactors.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

Uniform Tally Density–Based Strategy for Efficient Global Tallying in Monte Carlo Criticality Calculation

Based on the inspiration of the uniform fission site (UFS) algorithm, we propose a strategy for biasing fission secondary neutrons using tally density obtained from past cycles in a Monte Carlo criticality calculation when the purpose is to seek high-performance global tallying. Using this strategy for global volume-averaged cell flux and energy deposition tallies when performing criticality calculations on a pin-by-pin model of the Dayawan nuclear power station nuclear reactor yields better performance. All the strategies (including the original UFS algorithm) are implemented in a parallel Monte Carlo particle transport code JMCT (J Monte Carlo Transport), which is recently developed software constructed on the framework of JCOGIN (J COmbinatorial Geometry Monte Carlo transport INfrastructure).

Algorithm researches for efficient global tallying in criticality calculation of Monte Carlo method

Based on the research of the uniform fission site algorithm, the uniform tally density algorithm and the uniform track number density algorithm are proposed and compared with the original uniform fission site algorithm in this paper for seeking high performance of global tallying in Monte Carlo criticality calculation. Because reducing the largest uncertainties to an acceptable level simply by running a large number of neutron histories is often prohibitively expensive, the researches are indispensable for the calculation to reach the goal of practical application (the so called 95/95 standard). Using the global volume-averaged cell flux tally and energy deposition tally of the pin-by-pin model of Dayawan nuclear reactor as two examples, these new algorithms show better results. Although the uniform tally density algorithm has the best performance, the uniform track number density algorithm still has the advantage of being applicable to any type of tally, which is based on the track length estimator without any modification. All the algorithms are realized in a recently developed parallel Monte Carlo particle transport code JMCT.