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At least 145 records · Page 8

Creating a Simulation Platform for Research and Development of Advanced Control Methods

Advanced nuclear reactors are essential to meet the changing energy requirements throughout both the United States and the rest of world. In addition to other features, they are designed to enable deployment in remote locations and operate in a fully (or near-fully) autonomous manner, which will require a new control paradigm. To realize autonomously operating reactors, the U.S. Department of Energy’s Nuclear Energy Enabling Technologies Advanced Sensors and Instrumentation (NEET ASI) program conducts research and development into the enabling technologies and methods needed, including digital twins, machine learning, and risk modeling, in addition to various types of control methods. These technologies and methods are the key foundations needed to achieve fully autonomous systems. To develop and evaluate the technologies and methods necessary for achieving autonomous operations, it is critical to identify a software tool capable of integrating all the required elements. In surveying the available solutions, no software platforms were identified that could accomplish what was needed without introducing drawbacks. This challenge was the motivation for the current effort: to develop a software platform that can seamlessly integrate autonomouscontrol-enabling technologies and methods, allowing for accelerated research and development and transfer of ideas. The resulting platform, known as the Control and Optimization Modular Modeling Application for Nuclear Deployment (COMMAND), is Python-based, and leverages open-source tools to provide flexibility and facilitate building upon prior research. It is designed to enable advanced reactor developers to deploy and test advanced control technologies and methods coupled with their own models, solutions, and hardware. Given the substantial undertaking of developing such a platform, the current effort focused on laying down scalable, flexible software foundations and infrastructure, then demonstrating the platform via a use case. These foundations included developing generic modules, which contain the base variable and system blocks (the information and functional building blocks, respectively, that can be used to design a simulation) and the data handling and storage blocks needed to exchange information between the various blocks; as well as enablingtechnology-specific modules. This platform was evaluated via a use case, which was to simulate and control a process for the Microreactor Automated Control System (MACS) test bed. While MACS is not currently directly coupled to any specific microreactor physics, it was initially developed in concert with the Microreactor Applications Research Validation and Evaluation (MARVEL) microreactor, and so the MARVEL physics are used here. As part of this use case, several enabling-technology-specific blocks within COMMAND were integrated, including a proportional integral derivative (PID) control block, a Reactor Excursion and Leak Analysis Program (RELAP5-3D) block, and an anomaly detection block. The COMMAND software platform was successfully demonstrated to achieve the scalability and flexibility objectives of this effort and will be leveraged by the program’s research efforts to advance state of the art control methodologies towards autonomous operations of advanced reactors. As new use cases are created and implemented, it is anticipated that COMMAND will continue to grow and evolve to meet new requirements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Additively Manufactured Strain Sensing for Nuclear Reactor Applications

Real-time monitoring of materials in harsh environments is a crucial technique towards reducing innovation time in nuclear systems. The successful measurement of real time, in-situ strain measurements during nuclear reactor operation requires innovative sensing solutions, including novel sensing strategies as well as advanced sensor design, manufacturing, and materials selection. In this paper, we will discuss two primary strategies for in-situ strain measurement strategies: additively manufactured (AM) capacitive strain gauges (CSGs) and digital image correlation (DIC). Current commercial strain gauges have limited applications in reactors due to the harsh operating conditions and non-trivial attachment strategies (i.e., welding, epoxy-adhesive) that can affect both the sensing performance and the underlying substrate under testing. AM CSGs are a viable solution as they have a low profile, low hysteresis, and wireless sensing integration capabilities that will enhance nuclear sensing technologies. In this work, the mechanical and thermal performance of the AM CSGs were tested up to 300 °C using ASTM standardized testing procedures to simulate the temperatures found in existing light water reactors. The AM CSGs had a similar performance across multiple samples which correlates to analytical models. This work leads towards the development of CSGs designed for higher temperatures and additional environmental factors found in Generation-IV reactors. Non-contact sensors, such as DIC, offer a less destructive way to measure deformation of materials when compared to alternative methods of in-situ strain determination, such as weldable strain gauges. However, DIC requires high contrast surfaces, which often relies on the implementation of artificial patterns. Using traditional splatter techniques to fabricate these patterns have limitations, including poor surface adhesion and reproducibility. In this work, AM fabrication techniques were implemented to avoid such limitations. Accordingly, aerosol jet printing (AJP) was used to print small scale periodic patterns of silver on stainless steel and aluminum tensile specimens. DIC was employed to monitor strain (up to 1100 µe) during temperature cycling from 23-600 °C. The results validated the use of AJP to better control pattern parameters for small fields of view applications at high temperatures.

36 MATERIALS SCIENCE↗

Diverse Profile of Fermentation Byproducts From Thin Stillage

The economy of biorefineries is influenced not only by biofuel production from carbohydrates but also by the production of valuable compounds from largely underutilized industrial residues. Currently, the demand for many chemicals that could be made in a biorefinery, such as succinic acid (SA), medium-chain fatty acids (MCFAs), and lactic acid (LA), is fulfilled using petroleum, palm oil, or pure carbohydrates as raw materials, respectively. Thin stillage (TS), the residual liquid material following distillation of ethanol, is an underutilized coproduct from the starch biofuel industry. This carbon-rich material has the potential for chemical upgrading by microorganisms. Here, we explored the formation of different fermentation products by microbial communities grown on TS using different bioreactor conditions. At the baseline operational condition (6-day retention time, pH 5.5, 35°C), we observed a mixture of MCFAs as the principal fermentation products. Operation of a bioreactor with a 1-day retention time induced an increase in SA production, and a temperature increase to 55°C resulted in the accumulation of lactic and propionic acids. In addition, a reactor operated with a 1-day retention time at 55°C conditions resulted in LA accumulation as the main fermentation product. The prominent members of the microbial community in each reactor were assessed by 16S rRNA gene amplicon sequencing and phylogenetic analysis. Under all operating conditions, members of the Lactobacillaceae family within Firmicutes and the Acetobacteraceae family within Proteobacteria were ubiquitous. Members of the Prevotellaceae family within Bacteroidetes and Lachnospiraceae family within the Clostridiales order of Firmicutes were mostly abundant at 35°C and not abundant in the microbial communities of the TS reactors incubated at 55°C. The ability to adjust bioreactor operating conditions to select for microbial communities with different fermentation product profiles offers new strategies to explore and compare potentially valuable fermentation products from TS and allows industries the flexibility to adapt and switch chemical production based on market prices and demands.

59 BASIC BIOLOGICAL SCIENCES↗

Monte Carlo Perturbation Analysis of Fuel Temperature Variations in the MCNP Model of the Annular Core Research Reactor

The Annular Core Research Reactor (ACRR) Monte Carlo N-Particle (MCNP) model is used by ACRR reactor operators and experiment designers at Sandia National Laboratories for a variety of computational calculations ranging from reactor kinetics parameter estimates and safety analyses to experimental planning. To understand the dominant source of uncertainty within the MCNP model, perturbations in temperature were applied to individual ACRR MCNP fuel rods. Fuel rod temperatures were randomly sampled from a uniform distribution from operational temperatures to quantify temperature-related uncertainty effects. Stochastic mixing was used to blend the cross sections of the desired temperatures using the MCNP continuous and Thermal Neutron Scattering Treatment [S(α,β)] libraries in ENDF/B-VII.1. Furthermore, this uncertainty analysis produced a 640 row × 640 column correlation and covariance matrix of the neutron energy spectra. Positive covariance was produced around the 1-MeV region and the 0.2-eV region. Correlation was found in the thermal and fast energy regions, but no correlation was observed in the slowing-down energy region because interactions in this region are not dominated by fuel.

ACRR↗

Proceedings of the international conference on physics of reactors - Physor 2022

The theme for this year's conference is 'Making Virtual a Reality: Advancements in Reactor Physics to Leap Forward Reactor Operation and Deployment'. As we leap forward to the future of nuclear technology, micro-reactors, small modular reactors, advanced reactors, and high energy LWR fuel are at the forefront of the topics.The Physor 2022 will cover a broad range of topics in thirty standard and special sessions tracks, and ten panel sessions gathering more than 350 papers.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Thermal-Hydraulic-Mechanical Modeling and Simulation of Sodium-Potassium–Cooled MARVEL Microreactor Core

The U.S. Department of Energy's Microreactor Program, with Idaho National Laboratory's development of a nuclear microreactor applications test bed named MARVEL, aims to support R&D for the deployment of small, transportable reactors across civilian, industrial, and defense sectors. The MARVEL microreactor, an 85-kWth thermal fission reactor, incorporates TRIGA nuclear fuel and a sodium-potassium eutectic as its primary coolant, designed for safety and efficiency, with natural circulation eliminating the risk of critical heat flux conditions. The reliance on natural circulation for primary cooling means the reactor avoids using fuel spacers to minimize core pressure drop, which could disrupt the primary coolant's natural flow. However, the reactor core’s tight P/D ratio of 1.05, in the absence of fuel spacers, could pose a risk of fuel rod contact and increased peak cladding temperatures. To ensure the reactor safety, this study conducted computational modeling and simulations to investigate the reactor's thermal-hydraulic-mechanical characteristics, including the reactor core heat transfer coefficients, the potential for rod-to-rod contact, and assessed its impact on peak cladding temperature and overall reactor safety. The computational analyses of the MARVEL microreactor core revealed that the thermal deformation of fuel rods under worst-case scenario may lead to the fuel rod contact, but the peak cladding temperatures will remain significantly lower than the safety criteria, ensuring the safety operation reactor without fuel spacers under normal operating conditions.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

Performance of U 3 Si 2 in an LWR following a cladding breach during normal operation

High-density fuels have been proposed as a possible replacement for uranium-dioxide as a fuel for light water reactors (LWRs) due to their increased loading of fissionable material. The objectives of this proposal are (1) to increase reactor cycle length and reactor power, and (2) to offset any neutronic penalty associated with advanced cladding systems. Of the high-density fuels under consideration, there is particular interest in triuranium disilicide (U 3 Si 2 ) due to its increased metal density and favorable thermal properties as compared to UO 2 . However, there are concerns regarding the chemical compatibility of U 3 Si 2 with water and steam as used for LWR coolant.This paper summarizes research on fuel-coolant chemical compatibility for UO 2 LWR fuel during a cladding breach and highlights that generally, because of its chemical inertness, UO 2 -coolant reactions are of little consequence to reactor operation. However, the volumetric expansion associated with the reaction of UO 2 and oxygen is a concern for possible conditions encountered during air ingress of dry storage. These same concerns arise for U 3 Si 2 , which exhibits greater volumetric expansion than UO 2 when exposed to water or steam. These reactions ultimately result in increased fuel volume that the cladding must accommodate, as well as additional heat generated as the fuel reacts.The BISON fuel performance code was used to perform a comparative analysis on the behavior of UO 2 and U 3 Si 2 under normal operation. Silicide fuel simulations were then extended to demonstrate how varying thermodynamic and chemical kinetics influence fuel expansion and subsequent cladding performance during a cladding breach. These simulations were further extended to a 3D subsection of a fuel rod to demonstrate the characteristics of the resulting cladding crack.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Impacts of LEU+ and ATF on Fresh Fuel Storage Criticality Safety

The use of increased fuel enrichment, which is still in the realm of low-enriched uranium (LEU) fuel, has been of interest to commercial light water reactor operators as part of the next iteration in fuel cycle technological advances and research and development. Using increased enrichment fuel, or high-assay LEU (HALEU), in power plants has clear benefits for being able to load cores with additional power-producing fuel. Although HALEU enrichments can range up to 20%, the more guarded approach of investigating enrichments above current fuels within 10% enrichment is referred to as LEU plus (LEU+) to reflect the less drastic change in operating conditions and requirements and similarity to current fuel cycles. Of additional interest and increasing maturity is the incorporation of accident-tolerant fuel (ATF) concepts, which are also applicable to the current fleet. This class of technologies involves changes such as cladding (e.g., chromium coating or FeCrAl) and fuel composition (e.g., chromia dopant) alterations to demonstrate improved fuel performance under accident scenarios. The ability to properly store fuel before and after residence time in the reactor is crucial to plant operation. Typically, this is done in either a new fuel vault (NFV) or spent fuel pool (SFP). Storing, loading, and unloading dozens of fuel assemblies within the same general area provides opportunities for obvious criticality concerns. These concerns are addressed with regulations to the subcriticality margin that the NFV and SFP must maintain in certain conditions. Adopting LEU+ fuel results in inherent reactivity increases, which are extremely relevant for safe fuel storage. Therefore, a clear understanding of the effects of LEU+ fuel and ATF on criticality safety margins to regulatory limits is required, as well as an understanding of the degree of absorber crediting under normal and accident conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Modeling of the TRIGA IPR-R1 research reactor with the Serpent2/RINNOVO Nodal core analysis package

The Serpent2/RINNOVO nodal core analysis code system, a dedicated tool for modeling research reactors, has the capability to accurately predict important core physics parameters involved in the safety of reactor operation, such as various reactivity coefficients, control rod and bank worths including the shutdown margin, power distributions as well as local neutron flux predictions at various core locations of high importance, e.g., at irradiation rigs. In this work, a hexagonal model of the unrodded initial core of the Brazilian IPR-R1 Mark I type TRIGA nuclear reactor has been created using the Serpent2/RINNOVO code system. The choice of employing a hexagonal core geometry representation has mainly been made to facilitate subsequent fuel shuffling operations and core follow calculations of this reactor. Numerical results in terms of the core eigenvalue and the assembly power distribution have then been compared against corresponding full core Serpent2 results to prove feasibility of using the Serpent2/RINNOVO code system for modeling small and highly heterogeneous TRIGA reactors. Overall, RINNOVO predicts the power distribution very accurately but the eigenvalue error still remains quite large. In light of being the very first evaluation of a TRIGA reactor with the RINNOVO nodal core simulator, these results are also considered to be very preliminary. Improved accuracy is expected by incorporating a proper methodology in the current code system for computing discontinuity factors for multi-assembly configurations. Furthermore, improved results are expected by increasing the number of energy groups used by RINNOVO in these core calculations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A simulation study of the ability to detect power distribution perturbations in the texas A&M TRIGA reactor with self-powered neutron detectors

Given the variety of ways that nuclear reactor core power may be perturbed, reactor operators and developers are keen on understanding the accuracy and convergence time during which perturbations in reactor power distribution may be synthesized (i.e., inferred) from an array of in-core radiation detectors. A simulation study was conducted as described herein using a highly detailed model of the Texas A&M Training, Research, Isotopes, General Atomics Reactor, in which an array of self-powered neutron detectors (SPNDs) was considered for input to the power synthesis methodology. The core power synthesis is conducted using a point-based iterative method with an iterative loop built in to ensure working equation consistency. The forward problem of SPND response to simulated perturbations in reactor power was solved for Gaussian peak-type perturbations in the reactor power distribution. These perturbations varied in variance, amplitude, and core location to assess their impact on synthesis error and to determine the number of iterations required for convergence. A relation between the unique resolvability limit and perturbation width was identified such that the maximum synthesis error increased rapidly when the peak width went beneath this limit (a width approximating half the reactor’s fuel pin-to-pin pitch); this resolvability limit is specific to the SPND configuration and fuel segmentation considered herein. The synthesis error increased linearly with perturbation peak amplitude, whereas the convergence time increased nonlinearly. Perturbations located closer to the center of the core were synthesized more accurately, albeit with a higher number of required iterations. These findings provide a qualitative and quantitative understanding of the accuracy and speed at which different types of spatial power perturbations can be resolved in light-water reactors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

A compact furnace to support in situ neutron imaging of hydrogen dynamics in yttrium hydride moderators

A compact, nuclear microreactor that utilizes low-enriched uranium fuel is a promising solution to meet U.S. energy demands in nonconventional nuclear markets such as remote and decentralized energy grids. Yttrium hydride (YHx) is a potential moderator material for a microreactor design that reduces the amount of required fuel and provides superior retention of hydrogen at high reactor operating temperatures. Hydrogen diffusion properties in YHx are highly sought after for computer model validation and reactor prototyping. To characterize hydrogen diffusion, a compact dual-zone furnace was developed at Los Alamos National Laboratory and analyzed via neutron imaging at the Los Alamos Neutron Science Center (LANSCE). The goal of these measurements is to assess hydrogen diffusion in YHx samples as a function of applied temperature gradients. Included herein is recent progress in technique and furnace developments as well as initial results from concentration- and temperature-gradient measurements at LANSCE.

Torres, James↗

Establishing Isotopic Measurement Capabilities using Laser-Induced Breakdown Spectroscopy for the Molten Salt Reactor Campaign

Proof-of-principle H isotope ratios of aqueous aerosol systems and liquid droplets on filter paper have been measured using laser-induced breakdown spectroscopy (LIBS) with root mean square error of prediction values down to 1.9%. Molten salt reactors (MSRs) will consist of a complex chemical and radiological system consistently producing new fission products as the reactor operates. Some of these fission products and/or their daughter species will leave the salt in the reactor off-gas. Monitoring the composition of the off-gas, as well as the salt itself, is important for monitoring reactor performance, including burnup, corrosion, and the concentration of impurities. Tritium is of concern for MSRs because it will be produced from the irradiation of key salt constituents, including Li and Be. LIBS offers an avenue for in situ salt and off-gas monitoring by firing a laser onto or into the sample stream to generate a plasma. The plasma light can be monitored to measure an elemental fingerprint of the sample. Extending this analysis to include isotopic ratios offers a critical expansion of the in situ monitoring capabilities being developed. This study demonstrates the expansion of Oak Ridge National Laboratory’s LIBS capabilities to monitor isotopes and shows how simple calibrations may provide rapid semiquantitative models.

07 ISOTOPE AND RADIATION SOURCES↗

Transition core modeling for extended enrichment, accident tolerant fuel using PARCS/Polaris

Current plans and efforts from reactor operators and vendors to include extended enrichment (EE) and accident-tolerant fuel (ATF) in current reactor fleets motivate the study of these changes in reactor physics analysis. This work uses the US Nuclear Regulatory Commission core simulator PARCS to do the core calculation and SCALE Polaris lattice physics code to generate the required homogenized, few-group constants. The lattice model used is based on the GE-14 10x10 assemblies with UO{sub 2} fuels. Both nominal core and transition core are studied in this work, and both cores use GE-14 10x10 assemblies with UO{sub 2} fuel. The nominal core uses regular UO{sub 2} fuel with a maximum enrichment of 5 wt % and ZIRC-2 cladding. The ATF transition core uses FeCrAl cladding and regular UO{sub 2} fuel, while the EE-ATF transition core uses FeCrAl cladding with UO{sub 2} fuel with 8 max wt % enrichment. The accuracy presented in the colorset models verified the capability of the PARCS/Polaris procedures for the transition core analysis. For the whole core calculation, the ATF and EE-ATF transition core models were made in addition to the nominal core model. The core parameters to study are the core power distribution and power peaking factor, doppler temperature coefficients, and control rod worth at cold zero power and hot full power. Comparing the core parameters of the transition cores with the nominal core in PARCS, the results suggest that there is no unexpected outcome for the implementation of ATF and EE fuels. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Markov Decision Processes for Intelligent, Risk-Informed Asset-Management Decision-Making

Advanced nuclear reactors are a promising option for aiding the world in achieving its net-zero carbon emission goals, however, there are significant challenges to attaining and maintaining economic competitiveness with other sources of electricity. To improve the economic competitiveness of advanced reactor designs, a project was initiated to explore the use of Markov Decision Processes (MDPs) to guide asset-management decision-making during advanced reactor operation. MDPs are a powerful tool for optimizing decision-making in complex environments and their application to advanced reactors can aid in planning maintenance and repair activities to minimize downtime and maximize generation. The described approach expands on previous work regarding the use of MDPs for operational decision-making through the direct incorporation of real-time plant information. The integral MDP analysis includes information from online component diagnostic tools and the plant’s real-time generation risk assessment (GRA) and probabilistic risk assessment (PRA), which evaluate plant risk from both an economic and safety perspective. The result is an asset-management optimization framework that is based on real-time data regarding plant component status and the current best-estimate of plant risk. The paper presents an overview of the theoretical framework to incorporate the different information pathways into an integral MDP analysis, along with example analyses.

Grabaskas, David↗

Study of effect of PWR cold leg temperature gradient on reactor core condition

Effects of temperature and flow gradients in Westinghouse designed three-loop Pressurized Water Reactor (PWR) cold legs, the piping between the main coolant pump and the reactor vessel, were evaluated using Computational Fluid Dynamics (CFD) code STAR CCM+ and coupled neutronic and thermal-hydraulic (T/H) code system VERA. In the parametric study, several symmetric and asymmetric temperature gradients that were significantly larger than those observed from plant measurements were applied to the cold leg inlets for comparison with the base case without any temperature gradient. A CFD model using the STAR-CCM+ code was developed for a portion of the RCS region between the Reactor Coolant Pump (RCP) and the core inlet based on previously validated modeling approach. The CFD simulation results were processed for the temperature and flow rate distributions at the core inlet as input to the VERA calculations. The VERA code system consists of COBRA-TF (CTF) for thermal-hydraulics, MPACT for reactor physics and neutron transport, and ORIGEN for isotopic depletion. The VERA model was for depletion calculations of a high-burnup loading pattern with the reactor core in pin-by-pin and subchannel resolution. The results of the study indicate that the postulated temperature gradients within the PWR cold legs do not result in any significant changes in the core inlet temperature distributions and the core power distributions during the reactor operation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Postirradiation examination of HFIR-irradiated yttrium hydrides

The U.S. Department of Energy’s (DOE) Microreactor Program (MRP) is advancing key technologies to enable the deployment of truck-transportable, plug-and-play microreactors that operate at low power levels (< 20 MW th ), but at high temperatures (> 600 °C), while ensuring inherently safe reactor operation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Numerical Simulation and Experimental Comparison of System Analysis Module 1D Mixing Model for Cold Shock Transients in the Gallium Thermal-Hydraulic Mixing Facility

Abstract Liquid metals are being investigated as coolants in many advanced reactor designs because of their high thermal conductivity and effectiveness at high temperatures. However, they often pose challenges to reactor operation and safety because of the complex thermal mixing and stratification in the plenum of pool-type reactor designs. The advanced system analysis code System Analysis Module (SAM) currently under development at Argonne National Laboratory aims to develop and implement thermal mixing models to accurately capture these complex thermal fluid behaviors. In this study, the SAM thermal mixing model was compared against experimental data from the Gallium Thermal-Hydraulic Experiment facility, a scaled liquid metal test facility that uses gallium as a surrogate fluid to investigate the stratification and thermal mixing of low-Prandtl-number fluids in the upper plenum of a liquid metal-cooled reactor. Two cold shock transient cases were used: one with stable stratified flow (Ri = 32) and one with stronger thermal mixing (Ri = 0.5). The resultant temperatures were then compared with the experimental temperatures over the entire plenum to assess the ability of the mixing models to capture the thermal behavior and to better correspond mixing parameters to various flow scenarios. Generally, the zero-dimensional mixing model was more capable of capturing the bulk temperature of the component modeled assuming that an accurate mass flow rate was provided, but it was inherently unable to capture thermal gradients in space. The one-dimensional mixing model was capable of capturing that the thermal gradients provided accurate selection of the mixing coefficients. Further, the temperature at the outlet junction was compared over time for each of the mixing models with the recorded experimental temperature. The implemented mixing models demonstrated the ability to effectively capture the overall thermal behavior for stronger mixing scenarios but struggled with more stably stratified flows. It was found that a system analysis code's covering of the entire range of different operating conditions still remains a challenging task, and it is suggested that further model and closure improvements are necessary to accurately capture complex thermal mixing and stratification phenomena.

stratification↗

POLCA8 - modelling of cross section variations inside hexagonal assemblies

This paper presents the POLCA8 approach for modelling non-constant cross section distributions inside hexagonal fuel assemblies. The multigroup diffusion equation is modified to account for intranodal cross section variations. The obtained equation is solved in a node-wise manner based on the Fourier expansion method. As a result of varying cross sections, the solution includes a particular part additionally to the homogeneous one. A method for obtaining the particular solution is derived. Numerical tests on a VVER-1000 core are presented showing the impact of cross-section variations to some key parameters for reactor operation. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗