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NASA NTRS2019

Calculating Factors of Safety and Margins of Safety from Interaction Equations

This report presents the derivation of the relationship between the factor of safety, the margin of safety, and a given interaction equation in two- or three-dimensional space. Factors of safety and margins of safety can be calculated from these interaction equations using either the closed-form solutions provided or the numerical methods mentioned in this report. The dual definition of the factor of safety is presented.

Factor of Safety↗

DOE OSTI2024

Credible Criticality Safety Margin in the 30B Package with LEU+ UF 6 and Hypothetical Water Ingress

The commercial nuclear industry is pursuing advancements in fuel and reactor design that increase the uranium enrichment above 5 wt. % 235 U. These advancements will necessitate the ability to transport bulk quantities of UF 6 at increased enrichments. Currently, the 30B cylinder is the primary container used by the industry for UF 6 storage and transportation and has a long history of successful shipments. This container can support up to 2,277 kg of UF 6 at a maximum enrichment of 5 wt. % 235 U. Previous evaluations have assessed the potential impact of criticality safety for 30B transport at higher enrichments but assumed moderator intrusion would not require evaluation. Although current regulations allow for the exception of moderator intrusion for UF 6 packages through the design and quality control of the package content, this exception is limited to enrichments up to 5 wt. % 235 U. Thus, an investigation of moderator intrusion into a 30B cylinder should be performed. Moderator intrusion into a 30B cylinder is a unique condition for criticality safety evaluation in transportation because of the violent chemical reactions that occur between UF 6 and H 2 O. The resulting intrusion is strongly dependent on the breach size, breach location, breach interface solid/ullage of the UF 6 content, the UF 6 distribution (which is temperature dependent), and temperature/pressure conditions which are dynamic in accident conditions. Additionally, the complexity of the HF-UO 2 F 2 -H 2 O interface that occurs during the event can influence the potential solubility of uranium in the system, as well as influence the amount of UF 6 reaction with H 2 O. With the operating experience from Orano Federal Services LLC, the UF 6 chemical expertise from Oak Ridge National Laboratory (ORNL), and the criticality safety expertise from ORNL, this paper evaluates the neutronic conditions (i.e., k eff ) that apply the understood chemistry and experimental conditions that occur during moderator intrusion of a breached 30B cylinder under postulated accidents. This report examines the historical evaluations of UF 6 transport and expands these evaluations for the enrichments expected for nuclear industry advancement. These simulations primarily feature a homogeneous mixture of UF 6 and H 2 O as an infinite media system and as a sphere with water reflection given an impurity limit of 0.5 wt. % UF 6 . This report demonstrates that this H/U limit is valid up to 8 wt. % enrichment for both H 2 O and HF as the moderating mixture. The water-reflected homogeneous mixed spheres evaluated demonstrate the amount of safety margin applied by restricting the 30B cylinder impurity limit to 0.5 wt. %. Additionally, this report evaluates moderator ingress scenarios of a 30B cylinder. The 30B cylinder simulations vary the cylinder orientation, the mass of UF 6 in the system, the mass of H 2 O in the system, and how much H 2 O has reacted with UF 6 . The moderator ingress of a 30B cylinder was evaluated for the water-reflected homogeneous mixed spheres to demonstrate the amount of safety margin applied by restricting the 30B cylinder impurity limit to 0.5 wt. %. These simulations are standard practice and are independent of the UF 6 -H 2 O reaction. This work also explored more complex simulations that layer the H 2 O over the UF 6 , which incorporates the amount of reacted UF 6 as a separate layer and considers solubility limits of UO 2 F 2 in H 2 O as it is produced. This approach is intended to simulate the postulated event of a large hairline crack occurring on a submerged cylinder. Finally, this work considers the potential of H 2 O mixing into the UF 6 solid heterogeneously using a sponge-like model. The water ingress into the UF 6 is treated as random size spheres, and the reaction products form into a layer over the spheres.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

Risk-Informed Safety Margin Characterization Methods Development Work

This report summarizes the research activity developed during the Fiscal year 2014 within the Risk Informed Safety Margin and Characterization (RISMC) pathway within the Light Water Reactor Sustainability (LWRS) campaign. This research activity is complementary to the one presented in the INL/EXT-??? report which shows advances Probabilistic Risk Assessment Analysis using RAVEN and RELAP-7 in conjunction to novel flooding simulation tools. Here we present several analyses that prove the values of the RISMC approach in order to assess risk associated to nuclear power plants (NPPs). We focus on simulation based PRA which, in contrast to classical PRA, heavily employs system simulator codes. Firstly we compare, these two types of analyses, classical and RISMC, for a Boiling water reactor (BWR) station black out (SBO) initiating event. Secondly we present an extended BWR SBO analysis using RAVEN and RELAP-5 which address the comments and suggestions received about he original analysis presented in INL/EXT-???. This time we focus more on the stochastic analysis such probability of core damage and on the determination of the most risk-relevant factors. We also show some preliminary results regarding the comparison between RELAP5-3D and the new code RELAP-7 for a simplified Pressurized Water Reactors system. Lastly we present some conceptual ideas regarding the possibility to extended the RISMC capabilities from an off-line tool (i.e., as PRA analysis tool) to an online-tool. In this new configuration, RISMC capabilities can be used to assist and inform reactor operator during real accident scenarios.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2017

Real-Time Prediction of Safety Margins in the National Airspace

Underlying all operations in the National Airspace System (NAS) is the concept of safety. Safety, as defined by acceptable levels of risk, is to be maintained at all times. The real-time safety monitoring (RTSM) framework is under development to provide an automated system to quantify safety in the NAS, estimate the current level of safety, and predict the future evolution of safety and the occurrence of events that pose an increased risk to flights so that these occurrences can be managed strategically rather than mitigated reactively. This paper presents the mathematical framework, the models, and the monitoring and prediction algorithms used to achieve this. RTSM computes safety as expressed through a set of safety margins based on user-defined safety metrics, thresolds, and events. Sources of uncertainty are modeled and propagated through the predictions in order to compute the probabilistic evolution of safety and the probability of events that introduce increased risk to operations. A prototype implementation is discussed and results demonstrating feasibility are presented. The results highlight the kinds of predictions that can be computed and the fidelity that is currently achieved.

national airspace system↗

DOE OSTI2021

Safety Margins for the Delineation of the Left Anterior Descending Artery in Patients Treated for Breast Cancer

Cardiac toxicity after breast cancer (BC) radiation therapy is partly due to the large radiation doses to coronary arteries. The left anterior descending artery (LAD) is particularly exposed. A first step in achieving robust dose constraints to the LAD during treatment planning is homogeneous delineation based on guidelines. LAD delineation can be problematic due to heart movements. The aim of the study was to establish a safety margin for delineation of the LAD in patients with BC.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2015

Reduced Order Model Implementation in the Risk-Informed Safety Margin Characterization Toolkit

The RISMC project aims to develop new advanced simulation-based tools to perform Probabilistic Risk Analysis (PRA) for the existing fleet of U.S. nuclear power plants (NPPs). These tools numerically model not only the thermo-hydraulic behavior of the reactor primary and secondary systems but also external events temporal evolution and components/system ageing. Thus, this is not only a multi-physics problem but also a multi-scale problem (both spatial, µm-mm-m, and temporal, ms-s-minutes-years). As part of the RISMC PRA approach, a large amount of computationally expensive simulation runs are required. An important aspect is that even though computational power is regularly growing, the overall computational cost of a RISMC analysis may be not viable for certain cases. A solution that is being evaluated is the use of reduce order modeling techniques. During the FY2015, we investigated and applied reduced order modeling techniques to decrease the RICM analysis computational cost by decreasing the number of simulations runs to perform and employ surrogate models instead of the actual simulation codes. This report focuses on the use of reduced order modeling techniques that can be applied to any RISMC analysis to generate, analyze and visualize data. In particular, we focus on surrogate models that approximate the simulation results but in a much faster time (µs instead of hours/days). We apply reduced order and surrogate modeling techniques to several RISMC types of analyses using RAVEN and RELAP-7 and show the advantages that can be gained.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1972

Safety margins in the implementation of planetary quarantine requirements

The formulation of planetary quarantine requirements, and their implementation as determined by a risk allocation model, is discussed. The model defines control safety margins with particular emphasis on utility in achieving the desired minimization of excessive margins, and their effect on implementation procedures.

Schalkowsky, S.↗

DOE OSTI2014

ANALYSIS OF SAFETY IMPACTS FROM EXTERNAL FLOODING USING THE RISK-INFORMED SAFETY MARGIN CHARACTERIZATION (RISMC) TOOLKIT

The existing fleet of U.S. nuclear power plants is in the process of extending its lifetime and increasing the power generated from these plants via power uprates. In order to evaluate the impact of these factors on the safety of the plant, the Risk-Informed Safety Margin Characterization (RISMC) project aims to provide insight to decision makers through a series of simulations of the plant dynamics for different initial conditions (e.g., probabilistic analysis and uncertainty quantification). This paper demonstrates how Idaho National Laboratory (INL) researchers use the RISMC Toolkit to investigate complex nuclear plant phenomena using RAVEN and RELAP-7. The analysis focused on a highly relevant topic currently facing some nuclear power plants – specifically flooding issues. This research and development looked at challenges to a hypothetical pressurized water reactor, including: (1) a potential loss of off-site power followed by the possible loss of all diesel generators (i.e., a station black-out event), (2) earthquake induced station-blackout, and (3) a potential earthquake induced tsunami flood. The analysis is performed by using a set of codes: a thermal-hydraulic code (RELAP-7), a flooding simulation tool (NEUTRINO) and a stochastic analysis tool (RAVEN) – these are currently under development at INL. Using RAVEN, we were able to perform multiple RELAP-7 simulation runs by changing specific parts of the model in order to reflect specific aspects of different scenarios, including both the failure and recovery of critical components. The simulation employed traditional statistical tools (such as Monte-Carlo sampling) and more advanced machine-learning based algorithms to perform uncertainty quantification in order to understand changes in system performance and limitations as a consequence of power uprate. Qualitative and quantitative results obtained gave a detailed picture of the issues associated with potential accident scenarios. These types of insights can provide useful material for decision makers to perform risk-informed margins management.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Basin-wide variation in tree hydraulic safety margins predicts the carbon balance of Amazon forests

Abstract Tropical forests face increasing climate risk 1,2 , yet our ability to predict their response to climate change is limited by poor understanding of their resistance to water stress. Although xylem embolism resistance thresholds (for example, $$\varPsi $$ Ψ 50 ) and hydraulic safety margins (for example, HSM 50 ) are important predictors of drought-induced mortality risk 3–5 , little is known about how these vary across Earth’s largest tropical forest. Here, we present a pan-Amazon, fully standardized hydraulic traits dataset and use it to assess regional variation in drought sensitivity and hydraulic trait ability to predict species distributions and long-term forest biomass accumulation. Parameters $$\varPsi $$ Ψ 50 and HSM 50 vary markedly across the Amazon and are related to average long-term rainfall characteristics. Both $$\varPsi $$ Ψ 50 and HSM 50 influence the biogeographical distribution of Amazon tree species. However, HSM 50 was the only significant predictor of observed decadal-scale changes in forest biomass. Old-growth forests with wide HSM 50 are gaining more biomass than are low HSM 50 forests. We propose that this may be associated with a growth–mortality trade-off whereby trees in forests consisting of fast-growing species take greater hydraulic risks and face greater mortality risk. Moreover, in regions of more pronounced climatic change, we find evidence that forests are losing biomass, suggesting that species in these regions may be operating beyond their hydraulic limits. Continued climate change is likely to further reduce HSM 50 in the Amazon 6,7 , with strong implications for the Amazon carbon sink.

Science & Technology - Other Topics↗

NASA NTRS2022

Calculating Factors of Safety and Margins of Safety from Interaction Equations for Preloaded Bolts

This report presents the derivation of the factored interaction equations for preloaded bolts in two- or three-dimensional space. This is an extension of the previous work of the first author which covered factored interaction equations consisting of load or stress-ratios which were either solely constant or solely varying quantities. The factored interaction equations for preloaded bolts consist of an axial load-ratio that is a combination of a constant quantity, preload and thermal load at preload, and a varying quantity, tensile and bending loads, and was not covered under the previous work. Two forms of the factored interaction equations for preloaded bolts, arising from two perspectives, are presented and compared. Closed form solutions for the tensile, shear, and bending loads as functions of the other concurrent loads that produces zero margin of safety are presented.

interaction equations↗

DOE OSTI2020

THERMAL SAFETY MARGIN CALCULATION OF THE MP-2 EXPERIMENT IN THE ADVANCED TEST REACTOR

The Mini-Plate 2 (MP-2) irradiation test is a fueled experiment designed for irradiation in multiple test locations in the Advanced Test Reactor (ATR) at the Idaho National Laboratory (INL). The experiment is a drop-in test where small aluminum-clad fuel plate samples (mini plates) are cooled directly by the ATR Primary Coolant System (PCS) water. The MP-2 fuel plate experiment will be irradiated in several different irradiation locations of the ATR. This fueled experiment contains aluminum-clad fuel mini plates consisting of monolithic U-Mo. Four different types of fuel plates with fuel meat thickness and cladding are part of the MP-2 test. A thermal analysis has been performed on the MP-2 experiment. A method for calculating Departure from Nucleate Boiling Ratio (DNBR) and Flow Instability Ratio (FIR) during a reactivity transient using the commercial finite element and heat transfer code ABAQUS is discussed. At the start of an ATR cycle the heat generation rate of the fueled experiment is high and the heat rate multiplier from the outer shim control cylinders is low, while the reverse is true at the end of the ATR cycle. Thermal analyses at 10 day increments during the cycle calculate the DNBR and FIR during a reactivity transient. This technique calculates DNBR for the fuel plate surfaces and FIR for all water components for each finite element surface and node at various times during the ATR cycle. Heat rates vary with time during the transient calculation that are provided by a detailed physics analysis. Oxide growth on the fuel plates is also incorporated Results from the transient calculations are displayed with the ABAQUS post processor. By calculating these parameters at each location in the finite element model, conservatism is replaced with accuracy. This allows for a greater margin for the thermal hydraulic safety parameters.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2016

Data Analysis Approaches for the Risk-Informed Safety Margins Characterization Toolkit

In the past decades, several numerical simulation codes have been employed to simulate accident dynamics (e.g., RELAP5-3D, RELAP-7, MELCOR, MAAP). In order to evaluate the impact of uncertainties into accident dynamics, several stochastic methodologies have been coupled with these codes. These stochastic methods range from classical Monte-Carlo and Latin Hypercube sampling to stochastic polynomial methods. Similar approaches have been introduced into the risk and safety community where stochastic methods (such as RAVEN, ADAPT, MCDET, ADS) have been coupled with safety analysis codes in order to evaluate the safety impact of timing and sequencing of events. These approaches are usually called Dynamic PRA or simulation-based PRA methods. These uncertainties and safety methods usually generate a large number of simulation runs (database storage may be on the order of gigabytes or higher). The scope of this paper is to present a broad overview of methods and algorithms that can be used to analyze and extract information from large data sets containing time dependent data. In this context, “extracting information” means constructing input-output correlations, finding commonalities, and identifying outliers. Some of the algorithms presented here have been developed or are under development within the RAVEN statistical framework.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Development of an Advanced Computational Fluid Dynamics Technology for the Next-Generation Nuclear Reactor System Analysis and Safety Margin Characterization Code

This report describes the research activities we have conducted at NCSU for our NEUP project. The work toward achieving the objectives of the project is reported. The significant achievements and accomplishments are presented. A number of numerical experiments are conducted to demonstrate that the goal of the proposed work has been successfully achieved. Issues, recommendations, and future work are discussed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

Integration of Human Reliability Analysis Models into the Simulation-Based Framework for the Risk-Informed Safety Margin Characterization Toolkit

This report presents an application of a computation-based human reliability analysis (HRA) framework called the Human Unimodel for Nuclear Technology to Enhance Reliability (HUNTER). HUNTER has been developed not as a standalone HRA method but rather as framework that ties together different HRA methods to model dynamic risk of human activities as part of an overall probabilistic risk assessment (PRA). While we have adopted particular methods to build an initial model, the HUNTER framework is meant to be intrinsically flexible to new pieces that achieve particular modeling goals. In the present report, the HUNTER implementation has the following goals: • Integration with a high fidelity thermal-hydraulic model capable of modeling nuclear power plant behaviors and transients • Consideration of a PRA context • Incorporation of a solid psychological basis for operator performance • Demonstration of a functional dynamic model of a plant upset condition and appropriate operator response This report outlines these efforts and presents the case study of a station blackout scenario to demonstrate the various modules developed to date under the HUNTER research umbrella.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2017

LOCA and LOFA Safety Margin Analysis for U-10Mo Monolithic LEU Fuel Conversion of the MURR{sup R} Reactor

The University of Missouri Research Reactor (MURR{sup R}) is a multi-disciplinary research and education facility providing a broad range of analytical and irradiation services to the research community and the commercial sector. The source of neutrons for the experimental facilities of MURR{sup R} is a compact 10 MW core fueled with highly-enriched uranium (HEU) fuel. The continued presence of HEU fuel in civilian installations such as research and test reactors poses a threat to national and international security. Therefore, most research and test reactors, both domestic and international, have started a program of conversion to the use of low-enriched uranium (LEU) fuel. MURR{sup R} is one of five U.S. high-performance research and test reactors (USHPRRs) that are actively collaborating with the U.S. National Nuclear Security Agency (NNSA) Office of Material Management and Minimization (M3) to develop a suitable LEU fuel replacement for the currently required HEU fuel. A new type of high-density LEU fuel based on an alloy of uranium and molybdenum is currently undergoing qualification testing, and is expected to allow the conversion of all USHPRRs. As a part of the LEU conversion of MURR{sup R}, an analysis of core behavior under a set of accident conditions for a core fueled with an LEU monolithic alloy of uranium and 10 wt% molybdenum (U-10Mo) has been conducted. This paper presents the newest results for the loss-of-coolant accidents (LOCAs) and loss-of-flow accidents (LOFAs). Other classes of accidents have also been investigated but were not included here. Namely, reactivity insertion accidents (RIAs), fuel failure during operations accidents (FFAs), and fuel handling accidents (FHAs)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2015

Improved Sampling Algorithms in the Risk-Informed Safety Margin Characterization Toolkit

The RISMC approach is developing advanced set of methodologies and algorithms in order to perform Probabilistic Risk Analyses (PRAs). In contrast to classical PRA methods, which are based on Event-Tree and Fault-Tree methods, the RISMC approach largely employs system simulator codes applied to stochastic analysis tools. The basic idea is to randomly perturb (by employing sampling algorithms) timing and sequencing of events and internal parameters of the system codes (i.e., uncertain parameters) in order to estimate stochastic parameters such as core damage probability. This approach applied to complex systems such as nuclear power plants requires to perform a series of computationally expensive simulation runs given a large set of uncertain parameters. These types of analysis are affected by two issues. Firstly, the space of the possible solutions (a.k.a., the issue space or the response surface) can be sampled only very sparsely, and this precludes the ability to fully analyze the impact of uncertainties on the system dynamics. Secondly, large amounts of data are generated and tools to generate knowledge from such data sets are not yet available. This report focuses on the first issue and in particular employs novel methods that optimize the information generated by the sampling process by sampling unexplored and risk-significant regions of the issue space: adaptive (smart) sampling algorithms. They infer system response from surrogate models constructed from existing samples and predict the most relevant location of the next sample. It is therefore possible to understand features of the issue space with a small number of carefully selected samples. In this report, we will present how it is possible to perform adaptive sampling using the RISMC toolkit and highlight the advantages compared to more classical sampling approaches such Monte-Carlo. We will employ RAVEN to perform such statistical analyses using both analytical cases but also another RISMC code: RELAP-7.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

Credible Criticality Safety Margin in the 30B Package with LEU+ UF 6 and Hypothetical Water Ingress

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Gains in operational flexibility, safety margins, and cost efficiencies via integrated Plant Reload Optimization platform

The U.S. Department of Energy Light Water Reactor Sustainability Program Risk-Informed Systems Analysis Pathway Plant Reload Optimization Project aims to develop an integrated, comprehensive framework offering an all-in-one solution for reload evaluations with a special focus on optimizing core design. Optimizing the fuel loading pattern is one of the most important considerations in reducing the amount of new fuel used in the core. Due to thousands of possible core configuration options, finding optimal solutions is an unachievable task for a human. The Plant ReLoad Optimization platform, which supports artificial-intelligence-based reactor core designing, is now fully capable of handling realistic problems. The Plant ReLoad Optimization platform development project aims to build a reactor core design tool that includes reactor safety and fuel performance analyses and uses artificial intelligence to support the optimization of core design solutions. The NSGA-II (Non-dominated Sorting Genetic Algorithm II) optimizer was developed and tested within RAVEN (Risk Analysis and Virtual ENvironment) to handle many constraints by using an augmented objectives methodology. The demonstration was performed with constrained multiobjective optimization of a 17 × 17 pressurized-water reactor core loading patterns to minimize fuel cost and maximize fuel cycle length.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗