Results for “Reactor Safety” — Page 38

DOE OSTI2020

Strategies for thorium fuel cycle transition in the SD-TMSR

Liquid-fueled Molten Salt Reactor (MSR) systems represent advances in safety, economics, and sustainability. The MSR has been designed to operate with a Th/ 233 U fuel cycle with 233 U used as startup fissile material. Since 233 U does not exist in nature, we must examine other available fissile materials to start up these reactor concepts. This work investigates the fuel cycle and neutronics performance of the Single-fluid Double-zone Thorium-based Molten Salt Reactor (SD-TMSR) with different fissile material loadings at startup: High Assay Low Enriched Uranium (HALEU) (19.79%), Pu mixed with HALEU (19.79%), reactor-grade Pu (a mixture of Pu isotopes chemically extracted from Pressurized Water Reactor (PWR) spent nuclear fuel (SNF) with 33 GW d/tHM burnup), transuranic elements (TRU) from Light Water Reactor (LWR) SNF, and 233 U. The MSR burnup routine provided by SERPENT-2 is used to simulate the online reprocessing and refueling in the SD-TMSR. The effective multiplication factor, fuel salt composition evolution, and net production of 233 U are studied in the present work. Additionally, the neutron spectrum shift during the reactor operation is calculated. The results show that the continuous flow of reactorgrade Pu helps transition to the thorium fuel cycle within a relatively short time (≈ 4.5 years) compared to 26 years for 233 U startup fuel. Finally, using TRU as the initial fuel materials offers the possibility of operating the SD-TMSR for an extended period of time (≈ 40 years) without any external feed of 233 U.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Mechanical Property Assessment of Unirradiated Cladding After Exposure to Time at Temperature

Light water reactors in the United States are operated within inherent safety limits designed to account for anticipated operational occurrences (AOOs). Unlike more severe reactor transients, these events permit the potential reuse of reactor cladding, highlighting the nuanced role of thresholds in influencing reactor efficiency compared to design-basis or beyond-design-basis transient conditions. The threshold designated for AOO peak cladding and fuel temperatures are currently grounded around thermal hydraulic limits such as surpassing the critical heat flux (CHF), rather than in fuel-cladding material performance. This CHF criterion therefore represents a conservative approach to AOO transients during the reactor lifetime. Extending this threshold to higher temperatures than CHF can result in additional operation efficiency gains. Here, a material performance-based approach is assessed to better understand the physical material limits of short time scale exposures to elevated temperatures. This approach, termed time at temperature (t@T), references fuel cladding microstructural and mechanical response to rapid temperature transients in absence of radiation damage. The results of this work are expected to help identify margin for the United States reactor fleet, which could be utilized to increase operational efficiencies through decreased reactor outages.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Kilopower Project: The KRUSTY Fission Power Experiment and Potential Missions

The Kilopower Project was initiated by NASA’s Space Technology Mission Directorate/Game Changing Development Program in fiscal year 2015 to demonstrate subsystem-level technology readiness of small space fission power in a relevant environment (Technology Readiness Level 5) for space science and human exploration power needs. The Kilopower Project centerpiece is the Kilowatt Reactor Using Stirling TechnologY (KRUSTY) test, which consists of the development and testing of a ground technology demonstrator of a 1-kW(electric)–class fission power system (FPS). The technologies to be developed and validated by KRUSTY are extensible to space FPSs from 1 to 10 kW(electric), which can enable modular surface FPSs for human exploration as well as higher-power future potential deep space science missions. The KRUSTY demonstration is cofunded by NASA and the U.S. Department of Energy National Nuclear Security Administration. The KRUSTY demonstration in the National Critical Experiment Research Center’s Device Assembly Facility was completed in the first quarter of 2018.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Nuclear Data for Advanced Reactors and Security Applications [Slides]

Abstract not provided.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Multiscale Thermal-hydraulic analysis of the MARVEL micro-reactor using coupled MOOSE Subchannel (SCM) and SAM

MARVEL is a natural-convection-cooled sodium-potassium microreactor that is anticipated to generate 85 kilowatts of thermal energy. It will operate within Idaho National Laboratory’s Transient Reactor Test Facility and is being developed by the DOE Microreactor Program. MARVEL will be used to test microreactor applications, evaluate systems for remote monitoring, and develop autonomous control technologies. A thermal-hydraulic computational model of this facility is a valuable tool to study important transients and calculate the safety limits of the micro-reactor design. For this purpose, the authors have chosen to use a multiscale coupled simulation: SCM for modeling the reactor core and SAM for the reactor’s primary cooling system. SCM is MOOSE physics module for subchannel analysis, which was designed to model single-phase flows through liquid-metal cooled, wire-wrapped fuel pin sub-assemblies, ordered in a triangular lattice. The SCM code was modified to be able to model MARVEL’s unique geometry. SAM is a systems analysis module based on the MOOSE framework. It aims to provide fast-running, whole-plant transient analyses capability with improved-fidelity for various advanced reactor types. The coupling between the two SCM and SAM for MARVEL modeling is done implementing a domain over-lapping approach. The resulting coupled simulation can model transients such as reactor startup/shutdown and provide an intermediate fidelity picture of the temperature field and other variables, in the core. Results for the steady-state simulations are presented in the article as well as flow blockage transient.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Multiscale Thermal-hydraulic analysis of the MARVEL microreactor using a coupled SAM and SCM simulation. (PPTX)

This is .pptx document presenting a summary of the paper of the same name that has been submitted and accepted to NURETH-21: MARVEL is a natural-convection-cooled sodium-potassium microreactor that is anticipated to generate 85 kilowatts of thermal energy. It will operate within Idaho National Laboratory Transient Reactor Test Facility and is being developed by the DOE Microreactor Program. MARVEL will be used to test microreactor applications, evaluate systems for remote monitoring, and develop autonomous control technologies. A thermal-hydraulic computational model of this facility is a valuable tool to study important transients and calculate the safety limits of the micro-reactor design. For this purpose, the authors have chosen to use a multiscale coupled simulation: SCM for modeling the reactor core and SAM for the reactor's primary cooling system. SCM is MOOSE physics module for subchannel analysis, which was designed to model single-phase flows through liquid-metal cooled, wire-wrapped fuel pin sub-assemblies, ordered in a triangular lattice. The SCM code was modified to be able to model MARVEL?s unique geometry. SAM is a systems analysis module based on the MOOSE framework. It aims to provide fast-running, whole-plant transient analyses capability with improved-fidelity for various advanced reactor types. The coupling between the two SCM and SAM for MARVEL modeling is done implementing a domain over-lapping approach. The resulting coupled simulation can model transients such as reactor startup/shutdown and provide an intermediate fidelity picture of the temperature field and other variables, in the core. Results for the steady-state simulations are presented in the article as well as flow blockage transient.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

DOE OSTI2023

Exploring the speciation of actinide salts in the presence of contaminants related to molten salt reactors

Molten salt reactors (MSR) are up-and-coming Generation IV nuclear reactors with either coolant and/or radioactive fuel in molten salt form. Due to their improved safety, efficiency, affordability and convenient waste processing system, these reactors are considered a superior alternative to conventional ones. However, prior to commercial implementation, it is necessary to have an extensive understanding of the reactions occurring in the MSR. The safety parameters of the MSR are determined by the rheological properties such as density and viscosity of the molten salt and these properties are governed by the local structure of the molten salts. Due to the high operational temperatures of MSR's, corrosion plays an important role. Because of their influence, the container corrosion products become part of the fuel salt matrix. In this work, we are investigating how these corrosion products, e.g., Mo, Ni, Cr, would impact the speciation of the actinide metal centers. For the initial studies, lanthanides are used as a surrogate for actinides. Lanthanide chloride salts (LnCl3) are mixed with transition metals and excess of alkali or alkali earth metal salts or salt mixtures (LiCl, NaCl, KCl). These are added to an alumina crucible, placed in a quartz tube, and sealed under a vacuum. This is heated up to around 1000 °C and slowly cooled to a temperature above the melting point of the salt and at that temperature, the reaction is taken out of the furnace. The excess salt is removed, and the resulting product is analyzed using X-ray diffraction techniques, scanning electron microscopy, and spectroscopic methods such as Raman, UV-Visible, and FTIR spectroscopy.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗

DOE OSTI2025

Employing MACS/ViBRANT as a Surrogate MARVEL Reactor for Startup Reactivity Tuning and Supervisory Control Processes

Advanced nuclear reactors are a key part of the future of nuclear energy both in the United States and globally. They offer unique benefits for various energy-demanding applications, including use in remote locations, compact size, modular manufacturing, remote monitoring, low and/or variable power rating operation, and reliance on novel technologies to enhance operational safety. To achieve economic feasibility, advanced reactors must significantly reduce their workforces in comparison with the current fleet. Achieving this reduction will occur through reducing staff workloads using technology to achieve autonomous or semi-autonomous operations, demonstrated by comprehensive testing and validation activities. These operations will require both software and hardware platforms during the design and testing phases. While simulations are useful during the design phase, their performance can significantly deviate during actual deployment on hardware. This report presents the outcomes of a collaborative technical initiative between the U.S. Department of Energy (DOE) Microreactor Program (MRP) and Advanced Sensors and Instrumentation (ASI) Program. The collaboration utilized the Microreactor Automated Control System (MACS) hardware platform to bridge the gap between theoretical reactor design and actual startup and control operations. Two key use cases were investigated: facilitating the startup testing period and demonstrating supervisory control. The first use case details the key Microreactor Applications Research Validation and Evaluation (MARVEL) reactor startup physics testing activities conducted using the MACS platform. These activities included drum worth measurements, shutdown margin assessment, temperature feedback analysis, and scram time evaluation, as well as unique testing that would apply to the MARVEL reactor to demonstrate the testing methodologies in a low-risk environment. The MACS platform, serving as a surrogate representation of the MARVEL reactor, proved instrumental in performing these tests. The exercise revealed aspects that led to optimized processes, refined hardware design, and enhanced base software capabilities. By maturing methods and technologies in this manner, the initiative promises to reduce wasted time in the actual on-site reactor deployment effort, thereby saving significant time and resources. The second use case focuses on the development and implementation of supervisory control methods aimed at managing core tilt, which can result from asymmetrical operations or manufacturing imperfections in fuel rods or reactivity control devices. A key objective was to assess and compare the use of artificial intelligence (AI) for supervisory control. The effort aimed to define the role of supervisory control to enhance performance without risking control instability. This effort explored three distinct approaches: rules-based (RB) methods, optimization techniques, and reinforcement learning (RL) algorithms. Each approach was evaluated for its ease of implementation, its usability, and its effectiveness in responding to asymmetries in neutron flux. Comparative analysis of these approaches provided valuable insights into their applicability and effectiveness, offering a robust framework for advanced reactor operations. Together, these two use cases highlight the potential of hardware test beds to help streamline the design, operation, and control of advanced nuclear reactors. This collaborative effort underscores the importance of continued innovation and experimentation in achieving the next generation of safe, reliable, and economically viable nuclear energy solutions.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI1995

Nuclear Safety [Vol. 36, No. 2, July-December 1995]

Nuclear Safety is a journal that covers significant issues in the field of nuclear safety. Its primary scope is safety in the design, construction, operation, and decommissioning of nuclear power reactors worldwide and the research and analysis activities that promote this goal, but it also encompasses the safety aspects of the entire nuclear fuel cycle, including fuel fabrication, spent-fuel processing and handling, and nuclear waste disposal, the handling of fissionable materials and radioisotopes, and the environmental effects of all these activities. Table of Contents for this issue follows. THE CHORNOBYL ACCIDENT: 195 The Chornobyl Accident Revisited, Part III: Chernobyl Source Term Release Dynamics and Reconstruction of Events During the Active Phase, A. R. Sich; GENERAL SAFETY CONSIDERATIONS: 218 Second ANS Workshop on the Safety of Soviet-Designed Nuclear Power Plants, R. A. Bari; 234 Elements of a Nuclear Criticality Safety Program, C. M. Hopper; 243 Rickover, Excellence, and Criticality Safety Programs, R. E. Wilson; ACCIDENT ANALYSIS: 249 Transient Analysis of the PIUS Advanced Reactor Design with the TRAC-PF1/MOD2 Code, B. E. Boyack, J. L Steiner, S. C. Harmony, H. J. Stumpf, and J. F. Lime; 278 The Hierarchy-By-Interval Approach to Identifying Important Models that Need Improvement in Severe-Accident Simulation Codes, T. J. Heames, M. Khatib-Rahbar, J. E. Kelly, R. P. Jenks-Johnson, and Y.-S. Chen; 290 RELAP5/MOD3 Code Coupling Model, R. P. Martin; 299 Missiles Caused by Severe Pressurized-Water Reactor Accidents, R. Krieg; DESIGN FEATURES: 310 Validation of COMMIX with Westinghouse AP-600 PCCS Test Data, J. G. Sun, T. H. Chien, J. Ding, and W T. Sha; ENVIRONMENTAL EFFECTS: 321 Spent Nuclear Fuel Characterization for a Bounding Reference Assembly for the Receiving Basin for Off-Site Fuel, S. D. Kahook, R. L. Garrett, L. R. Canas, and M J. Beckum; OPERATING EXPERIENCES: 332 Reactor Shutdown Experience, Compiled by J. W. Cletcher; U.S. NUCLEAR REGULATORY COMMISSION INFORMATION AND ANALYSES: 335 Reactor Coolant System Blowdown at Wolf Creek on September 17, 1994, J. V. Kauffman and S. L. Israel; RECENT DEVELOPMENTS: 344 Reports, Standards, and Safety Guides, D. S. Oueener; 349 Proposed Rule Changes as of June 30, 1995; ANNOUNCEMENTS: 320 Symposium on Acceptability of Risk From Radiation—Application to Manned Space Flight; 320 24th DOE/NRC Nuclear Air Cleaning and Treatment Conference; 361 Radiation Biology and Radiation Protection— Modern Developments and Tendencies in Radiation Biology; 362 1997 IEEE Sixth Conference on Human Factors and Power Plants; 354 The Authors; 360 Reviewers of Nuclear Safety, Vol. 36.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Technical Assessment of Off-Gas System Technologies for Potential Use in Molten Salt Reactors

Molten salt reactors (MSRs) are a class of Generation IV advanced reactor technologies aimed to enhance and improve the safety, fuel utilization and cost-effectiveness of nuclear power generation. MSR concepts are based on using a molten salt mixture as a primary nuclear reactor coolant, while the fuel can be either directly dissolved in the coolant (i.e., fluid-fueled) or can be in a separate solid form (i.e., salt-cooled solid-fueled). MSRs can be operated in either thermal or fast neutron spectra, as simple fissile convertors, or breeder reactors (e.g., utilizing both fissile and fertile fuels), as well as accelerator-driven sub-critical reactors or transuranic element burners. Operation of MSRs will necessitate management and treatment of the off-gas streams released to the headspace of the reactor where, in some designs, a cover gas can be circulated to remove certain fission products and maintain an inert atmosphere. An inert MSR cover gas swept over or sparged into the salt will confine radionuclides emerging from the free surface, including radioactive noble and non-noble gases, aerosols, and volatile species. The elements and compounds of these species will have a wide range of thermochemical and physical properties, some of which will decay to different products in the off-gas stream. Therefore, system components used to manage and treat MSR off-gas streams will need to be robust under dynamic reactor and chemistry conditions to support adequate reactor performance by managing the composition and species in the salt coolant and cover gas space. Off-gas system components would perform as a radionuclide boundary to the reactor vessel and a primary means for preventing radionuclide release; therefore, they are of high safety significance for MSR operations. This report reviews various technologies and materials for potential implementation in the design of an MSR off-gas system per a general conceptual framework. The reviewed technologies operate based on scrubbing, capture, delay, or separation of species in the off-gas stream. These include molten hydroxide scrubbers, solid sorbents, delay off-gas systems, particle traps, and cryogenic distillation. Since aspects of an off-gas system will be design-specific, the approach is to provide general discussions on attributes of these technologies and materials, including target off-gas stream species, operational parameters and conditions of importance to decontamination factors, implementation maturity, system component monitoring, potential off-normal conditions and considerations for waste products. The information aims to support the U.S. Nuclear Regulatory Commission in their safety evaluations for MSR designs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Informing and Engaging the Future Workforce on Generation IV International Forum Reactor Systems

Generation IV reactors are six nuclear reactor designs, Sodium Fast reactor (SFR), Very High Temperature Reactor (VHTR), Gas cooled Fast Reactor (GFR), Molten Salt Reactor (MSR), Lead Fast Reactor (LFR), and Supercritical Water Reactor (SCWR), that are considered to be the most promising in light of various criteria based on the following objectives: • continuation of the progress made by Generation III water reactors in terms of competitiveness and safety; • more effective use of uranium resources; • less radioactive waste, especially high-level, long-lived waste; • greater protection against malicious acts and the diversion or theft of nuclear materials. The GIF Education and Training Working Group (ETWG) launched two major initiatives in 2016 and in 2021 to not only inform and educate but also to engage the future workforce in support of these reactor systems. This paper will present an overview of the GIF EWTG webinar series as well as the 2021 Pitch your Gen IV Research Competition which is followed by the 2023 Pitch your Gen IV Research. Competition

Paviet, Patricia D.↗

DOE OSTI2023

Coupled SAM/Griffin Model of a Reference Pebble Bed High-Temperature Gas Cooled Reactor for Multi-Physics Simulations

An effort has been dedicated to developing a reference model for multi-physics coupled simulation of the pebble bed high-temperature gas-cooled reactor (PB-HTGR) with SAM and Griffin computer codes for safety analysis and licensing purpose. The reference problem of a prototypical reactor design serves as the foundation for the U.S. NRC (Nuclear Regulatory Commission) to verify the adequacy of computer codes and evaluation models for specific reactor types. In this work, a SAM model of the HTR-PM reactor has been developed based on publicly available design information and the multi-dimensional Pronghorn model developed by Idaho National Laboratory. The SAM HTR-PM model includes a multi-dimensional core region and 0- D/1-D fluid components. Additionally, a simplified air RCCS loop is modeled for decay heat removal. The Griffin model is based on a recent work by Idaho National Laboratory. The coupling between the models is achieved through the MOOSE MultiApp system. Both steady-state and transient scenarios were simulated to demonstrate the coupled model’s capability for multi-physics simulations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Expanding Benchmarks for Nuclear Data Validation [Slides]

The presentation discusses benchmarking in comparison to experimental truth, the integral experiments that were performed, and that benchmarks are evaluated experiments. It also discusses validation testing, and that the ultimate goal of the validation end product is to improve evaluated nuclear data for applications It does state that validation highlights errors in the Nuclear Data Pipeline that affect applications, for example: Missing Cd Capture Gammas in ENDF/B-VII.1. It acknowledges that additional types of experiments are needed to test data used in applications, and that validation experiments do not have to be complicated and expensive. The presentation also discusses different types of measurements including activation foil and fission chamber measurements, reactor kinetics measurements, and subcritical measurements. The presentation concludes with an experiment summary and states that all applications need validation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Hyperbranched PDMAEMA-functionalized SiO 2 microparticles: ATRP polymerization and grafting in a continuous flow reactor

Flow chemistry offers high reaction yield, kinetic control, improved safety, reliability, scalability, and greater degree of process control. Herein, hyperbranched polymer-grafted silica microparticles (HP-SMPs) are synthesized in a commercially available flow reactor through atom transfer radical polymerization. Initiator-anchored silica microparticles are obtained by in situ silanization in the flow reactor. Hyperbranched poly[2-(dimethylamino)ethylmethacrylate] chains are grafted onto the initiator-anchored SMPs through inimer–monomer ratio control. To demonstrate the efficiency and universality of this approach in grafting polymers onto SMPs, multiple hyperbranched polymeric structures are obtained by varying the inimer concentration. Dye absorption test is conducted to demonstrate the potential applications of HP-SMPs.

36 MATERIALS SCIENCE↗

DOE OSTI2020

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

VARI3D & PERSENT: Perturbation and Sensitivity Analysis (Revision 5)

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry-based transport code.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of “homogenized” parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code. This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARIational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporating the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results. In this manuscript, the relevant aspects of generalized perturbation theory and exact perturbation theory that apply to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios. This manuscript describes several perturbation and sensitivity problems, and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity analysis work, but also can visually plot the result for a more thorough understanding of the space and energy distribution (Section 5). Overall, PERSENT is observed to produce accurate reactivity worths and sensitivities for the displayed set of test problems and clearly demonstrates the need to have a transport-based sensitivity capability as evident from the thousands of percent errors observed in the 21-group hexagonal fast reactor problem (covered in Section 7). The uncertainty calculation capability is described in Section 3 and demonstrated in Section 7.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗