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At least 325 records · Page 18

Implementing Ordinary Differential Equation Solvers in Rust Programming Language for Modeling Vehicle Powertrain Systems: Preprint

Efficient and accurate ordinary differential equation (ODE) solvers are necessary for powertrain and vehicle dynamics modeling. However, current commercial ODE solvers can be financially prohibitive, leading to a need for accessible, effective, open-source ODE solvers designed for powertrain modeling. Rust is a compiled programming language that has the potential to be used for fast and easy-to-use powertrain models, given its exceptional computational performance, robust package ecosystem, and short time required for modelers to become proficient. However, of the three commonly used (>3,000 downloads) packages in Rust with ODE solver capabilities, only one has more than four numerical methods implemented, and none are designed specifically for modeling physical systems. Therefore, the goal of the Differential Equation System Solver (DESS) was to implement accurate ODE solvers in Rust designed for the component-based problems often seen in powertrain modeling. DESS is a text-based software package that provides a flexible framework for building and solving systems of ODEs. This allows DESS to be included as a dependency for automotive powertrain models that require a variety of solvers and solver configurations. Seven explicit ODE solver methods have been implemented in DESS: Euler’s, Heun’s, midpoint, Ralston’s, classic Runge-Kutta, Bogacki-Shampine, and Cash-Karp. These represent five fixed-step methods and two adaptive-step methods. This paper shows that the solver implementations increase accuracy and computational efficiency compared to Euler's method when modeling a system of three thermal masses in Rust. DESS also includes features designed for modeling component-based physical systems. Users can define relationships between nodes in their system, which the package then translates into a system of equations, leading to simpler and more intuitive code. In the case of a three-thermal-mass system, the user can specify node thermal properties (e.g., thermal capacitance), how nodes are interconnected, and thermal conductance between nodes rather than providing a system of equations. The core contribution from this work is an open-source, text-based Rust package with ODE solvers for automotive powertrain modeling to support cost-free, fast, and accurate simulation.

ADVANCED PROPULSION SYSTEMS↗

Implementation and Simulation Results using Autonomous Aerobraking Development Software

An Autonomous Aerobraking software system is currently under development with support from the NASA Engineering and Safety Center (NESC) that would move typically ground-based operations functions to onboard an aerobraking spacecraft, reducing mission risk and mission cost. The suite of software that will enable autonomous aerobraking is the Autonomous Aerobraking Development Software (AADS) and consists of an ephemeris model, onboard atmosphere estimator, temperature and loads prediction, and a maneuver calculation. The software calculates the maneuver time, magnitude and direction commands to maintain the spacecraft periapsis parameters within design structural load and/or thermal constraints. The AADS is currently tested in simulations at Mars, with plans to also evaluate feasibility and performance at Venus and Titan.

Maddock, Robert W.↗

NASA Tech Briefs, July 2012

Topics covered include: Instrument Suite for Vertical Characterization of the Ionosphere-Thermosphere System; Terahertz Radiation Heterodyne Detector Using Two-Dimensional Electron Gas in a GaN Heterostructure; Pattern Recognition Algorithm for High-Sensitivity Odorant Detection in Unknown Environments; Determining Performance Acceptability of Electrochemical Oxygen Sensors; Versatile Controller for Infrared Lamp and Heater Arrays; High-Speed Scanning Interferometer Using CMOS Image Sensor and FPGA Based on Multifrequency Phase-Tracking Detection; Ultra-Low-Power MEMS Selective Gas Sensors; Compact Receiver Front Ends for Submillimeter-Wave Applications; Dynamically Reconfigurable Systolic Array Accelerator; Blocking Losses With a Photon Counter; Motion-Capture-Enabled Software for Gestural Control of 3D Mod; Orbit Software Suite; CoNNeCT Baseband Processor Module Boot Code SoftWare (BCSW); Trajectory Software With Upper Atmosphere Model; ALSSAT Version 6.0; Employing a Grinding Technology to Assess the Microbial Density for Encapsulated Organisms; Demonstration of Minimally Machined Honeycomb Silicon Carbide Mirrors; Polyimide Aerogel Thin Films; Nanoengineered Thermal Materials Based on Carbon Nanotube Array Composites; Composite Laminate With Coefficient of Thermal Expansion Matching D263 Glass; Robust Tensioned Kevlar Suspension Design; Focal Plane Alignment Utilizing Optical CMM; Purifying, Separating, and Concentrating Cells From a Sample Low in Biomass; Virtual Ultrasound Guidance for Inexperienced Operators; Beat-to-Beat Blood Pressure Monitor; Non-Contact Conductivity Measurement for Automated Sample Processing Systems; An MSK Radar Waveform; Telescope Alignment From Sparsely Sampled Wavefront Measurements Over Pupil Subapertures; Method to Remove Particulate Matter from Dusty Gases at Low Pressures; Terahertz Quantum Cascade Laser With Efficient Coupling and Beam Profile; Measurement Via Optical Near-Nulling and Subaperture Stitching; 885-nm Pumped Ceramic Nd:YAG Master Oscillator Power Amplifier Laser System; Airborne Hyperspectral Imaging System; Heat Shield Employing Cured Thermal Protection Material Blocks Bonded in a Large-Cell Honeycomb Matrix; and Asymmetric Supercapacitor for Long-Duration Power Storage.

Source record↗

NASA Tech Briefs, February 2011

Topics covered include: Multi-Segment Radius Measurement Using an Absolute Distance Meter Through a Null Assembly; Fiber-Optic Magnetic-Field-Strength Measurement System for Lightning Detection; Photocatalytic Active Radiation Measurements and Use; Computer Generated Hologram System for Wavefront Measurement System Calibration; Non-Contact Thermal Properties Measurement with Low-Power Laser and IR Camera System; SpaceCube 2.0: An Advanced Hybrid Onboard Data Processor; CMOS Imager Has Better Cross-Talk and Full-Well Performance; High-Performance Wireless Telemetry; Telemetry-Based Ranging; JWST Wavefront Control Toolbox; Java Image I/O for VICAR, PDS, and ISIS; X-Band Acquisition Aid Software; Antimicrobial-Coated Granules for Disinfecting Water; Range 7 Scanner Integration with PaR Robot Scanning System; Methods of Antimicrobial Coating of Diverse Materials; High-Operating-Temperature Barrier Infrared Detector with Tailorable Cutoff Wavelength; A Model of Reduced Kinetics for Alkane Oxidation Using Constituents and Species for N-Heptane; Thermally Conductive Tape Based on Carbon Nanotube Arrays; Two Catalysts for Selective Oxidation of Contaminant Gases; Nanoscale Metal Oxide Semiconductors for Gas Sensing; Lightweight, Ultra-High-Temperature, CMC-Lined Carbon/Carbon Structures; Sample Acquisition and Handling System from a Remote Platform; Improved Rare-Earth Emitter Hollow Cathode; High-Temperature Smart Structures for Engine Noise Reduction and Performance Enhancement; Cryogenic Scan Mechanism for Fourier Transform Spectrometer; Piezoelectric Rotary Tube Motor; Thermoelectric Energy Conversion Technology for High-Altitude Airships; Combustor Computations for CO2-Neutral Aviation; Use of Dynamic Distortion to Predict and Alleviate Loss of Control; Cycle Time Reduction in Trapped Mercury Ion Atomic Frequency Standards; and A (201)Hg+ Comagnetometer for (199)Hg+ Trapped Ion Space Atomic Clocks.

Source record↗

The SAS4A/SASSYS-1 Version 5.8 Safety Analysis Code System

SAS4A/SASSYS-1 is a software simulation tool used to perform deterministic analysis of anticipated events as well as design basis and beyond design basis accidents for advanced nuclear reactors. Detailed, mechanistic models of steady-state and transient thermal, hydraulic, kinetic, and mechanical phenomena are employed to describe the response of the reactor core, the reactor primary and secondary coolant loops, the reactor control and protection systems, and the balance-of-plant to accidents caused by changes in coolant flow, loss of heat rejection, or reactivity insertion. The consequences of single and double-fault accidents can be modeled, including fuel and coolant heating, fuel and cladding mechanical behavior, core reactivity feedbacks, coolant loop performance including natural circulation, and decay heat removal. Analyses are typically terminated upon demonstration of reactor and plant shutdown to permanently coolable conditions, or upon violation of design basis margins. The objective of the analysis is to quantify accident consequences as measured by the transient behavior of system performance parameters, such as fuel and cladding temperatures, reactivity, and cladding strain. Originally developed for analysis of sodium cooled reactors with oxide fuel clad by stainless steel, the models were subsequently extended and specialized to metallic fuel clad with advanced alloys and to several other coolant options, including lead, LBE, and water.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Thermal Structure Analysis of SIRCA Tile for X-34 Wing Leading Edge TPS

This paper will describe in detail thermal/structural analyses of SIRCA tiles which were performed at NASA Ames under the The Tile Analysis Task of the X-34 Program. The analyses used the COSMOS/M finite element software to simulate the material response in arc-jet tests, mechanical deflection tests, and the performance of candidate designs for the TPS system. Purposes of the analysis were to verify thermal and structural models for the SIRCA tiles, to establish failure criteria for stressed tiles, to simulate the TPS response under flight aerothermal and mechanical load, and to confirm that adequate safety margins exist for the actual TPS design.

Milos, Frank S.↗

Implementation and verification of a user-defined element (UEL) for coupled thermal-hydraulic-mechanical-chemical (THMC) processes in saturated geological media

Efficient and accurate modeling of the coupled thermal-hydraulic-mechanical-chemical (THMC) processes in various rock formations is indispensable for designing energy geo-structures such as underground repositories for high-level nuclear wastes. Here, this work focuses on developing and verifying an implicit finite element solver for generic coupled THMC problems in geological settings. Starting from the mass, momentum, and energy balance laws, a specialized set of governing equations and a thermoporoelastic constitutive model is derived. This system is then solved by an implicit finite element (FE) scheme. Specifically, the residuals and the Jacobians are scripted in a user-defined element (UEL) subroutine which is then combined with the general-purpose FE software Abaqus Standard to solve initial-boundary value problems. Considering the complexity of the system, the UEL development follows a stepwise manner by first solving the coupled hydraulic-mechanical (HM) and thermal-hydraulic-mechanical (THM) equations before moving on to the full THMC problem. Each implementation step consists of at least one verification test by comparing computed results with closed-form analytical solutions to ensure that the various coupling effects are correctly realized. To demonstrate the robustness of the algorithm and to validate the UEL, a three-dimensional case study is performed with reference to the in-situ heating test of ATLAS at Belgium in 1980s. A hypothetical radionuclide leakage event is then simulated by activating the chemical-concentration degree of freedom and prescribing a constant high concentration at the heater's surface. The model predicts a limited contaminated regime after six years considering both diffusion and advection effects on species transport.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

GDSA - Modeling and Integration – ORNL: PFLOTRAN modeling

This report summarizes work done at Oak Ridge National Laboratory (ORNL) related to post-closure criticality consequence analysis of dual-purpose canister (DPC) direct disposal in unsaturated alluvium. PFLOTRAN software was used to model the behavior of a breached DPC with low water infiltration rates and unsaturated conditions in alluvial deposits such that a low-power criticality event occurs with a focus on thermal hydrological constraints on criticality timing and power output. This summary describes initial exploration of those thermal hydrological processes and of the long-term average power output from a criticality event that could be sustained without driving water out of the DPC package and thereby terminating the criticality event. The objectives are (1) to identify, for different groundwater infiltration rates, the time at which the DPC fills with water sufficiently to potentially initiate criticality; (2) to bound the power output that could be produced by a criticality event that would thermally drive water out of the package at various percolation rates; and (3) provide an estimate of how the size of a package breach affects the water infiltration and therefore the possibility timing of criticality.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Elevating SolTrace's Capabilities for the Next Generation of Concentrating Solar Analysis

SolTrace is an open-source Monte Carlo ray tracing software developed at NREL. SolTrace can characterize concentrating solar thermal (CST) collector optical performance and is CST technology agnostic. Shown in Fig. 1, SolTrace is a foundational tool in NREL's CST system and component modeling suite. SolTrace's generic surface elements can flexibly model novel collector and receiver designs to predict spatial and temporal flux distributions - critical to understand for CST component design, performance prediction, and system integration. Since its initial development, SolTrace has over 1,650 references on Google Scholar, over 9,800 downloads since 2017, and has served the CST research and development community as a benchmark of 3rd party verification. SolTrace provides users with many options for defining surface shape and boundaries. However, SolTrace provides limited documentation which can result in a steep learning curve for new users. Additionally, SolTrace lacks the computational performance required to evaluate optical performance of a CST system over the course of a year and/or iteratively over design parameters in a timely manner. To address this, we are working towards a new release of SolTrace that enables increased computational throughput by implementing ray tracing acceleration structures and enabling GPU parallelization. Additionally, we are working to improve SolTrace's usability, accessibility, and maintainability by (1) automating solar position time-dependent simulation processes, (2) creating general CST collector templates of grouped elements, (3) updating the user interface to better visualize model inputs and outputs, and (4) creating a user support network through forums, "how to" videos, and documentation.

14 SOLAR ENERGY↗

Simulation requirements for the Large Deployable Reflector (LDR)

Simulation tools for the large deployable reflector (LDR) are discussed. These tools are often the transfer function variety equations. However, transfer functions are inadequate to represent time-varying systems for multiple control systems with overlapping bandwidths characterized by multi-input, multi-output features. Frequency domain approaches are the useful design tools, but a full-up simulation is needed. Because of the need for a dedicated computer for high frequency multi degree of freedom components encountered, non-real time smulation is preferred. Large numerical analysis software programs are useful only to receive inputs and provide output to the next block, and should be kept out of the direct loop of simulation. The following blocks make up the simulation. The thermal model block is a classical heat transfer program. It is a non-steady state program. The quasistatic block deals with problems associated with rigid body control of reflector segments. The steady state block assembles data into equations of motion and dynamics. A differential raytrace is obtained to establish a change in wave aberrations. The observation scene is described. The focal plane module converts the photon intensity impinging on it into electron streams or into permanent film records.

Soosaar, K.↗

ISS Material Science Research Rack HWIL Interface Simulation

In this paper, the first Material Science Research Rack (MSRR-1) hardware-in-the-loop (HWIL) interface simulation is described. Dynamic Concepts developed this HWIL simulation system with funding and management provided by the Flight Software group (ED14) of NASA-MSFC's Avionics Department. The HWIL system has been used both as a flight software development environment and as a software qualification tool. To fulfill these roles, the HWIL simulator accurately models the system dynamics of many MSRR-1 subsystems and emulates most of the internal interface signals. The modeled subsystems include the Experiment Modules, the Thermal Environment Control System, the Vacuum Access System, the Solid State Power Controller Module, and the Active Rack Isolation Systems. The emulated signals reside on three separate MIL-STD-1553B digital communication buses, the ISS Medium Rate Data Link, and several analog controller and sensor signals. To enhance the range of testing, it was necessary to simulate several off-nominal conditions that may occur in the interfacing subsystems.

Williams, Philip J.↗

Synthetic Scene Generation of the Stennis V and V Target Range for the Calibration of Remote Sensing Systems

The verification and validation (V&V) target range developed at Stennis Space Center is a useful test site for the calibration of remote sensing systems. In this paper, we present a simple algorithm for generating synthetic radiance scenes or digital models of this target range. The radiation propagation for the target in the solar reflective and thermal infrared spectral regions is modeled using the atmospheric radiative transfer code MODTRAN 4. The at-sensor, in-band radiance and spectral radiance for a given sensor at a given altitude is predicted. Software is developed to generate scenes with different spatial and spectral resolutions using the simulated at-sensor radiance values. The radiometric accuracy of the simulation is evaluated by comparing simulated with AVIRIS acquired radiance values. The results show that in general there is a good match between AVIRIS sensor measured and MODTRAN predicted radiance values for the target despite the fact that some anomalies exist. Synthetic scenes provide a cost-effective way for in-flight validation of the spatial and radiometric accuracy of the data. Other applications include mission planning, sensor simulation, and trade-off analysis in sensor design.

Cao, Chang-Yong↗

Scaling Building Energy Audits through Machine Learning Methods on Novel Drone Image Data

Building energy audits are time-consuming and labor-intensive. This paper describes a new method using machine learning (ML) techniques on novel data sources (drone images) to improve the identification of building characteristics and retrofit opportunities, and thereby reduce the effort for audits. The new ML method includes: (1) Building footprint extraction using line extraction, polygonization, and polygon-merging, (2) Building envelope extraction using PIX4d modeling software to reconstruct a building 3D model, (3) Visualization tool for viewing images from the 3D model, (4) Window-to-wall ratio (WWR) using state-of-art deep neural network semantic segmentation, (5) Envelope thermal anomaly detection using an unsupervised machine learning clustering algorithm, and (6) Rooftop energy equipment detection based on an object detection algorithm. The testing of this method involved a comparison of additional ML-generated information overlaid on current ‘state-of-practice’ audit and remote assessment baselines using evaluation metrics: labor time and associated cost, marginal benefits of using ML-generated information in workflows for audits and remote assessments, integration potential with existing processes and tools, and replicability/scalability of the method. In two test buildings in California that had comprehensive drawings and meter data available, the ML method effectively generated a building footprint, envelope, rooftop equipment, WWR, and locations of envelope thermal anomalies. Projected target segments of the ML method are sites with minimal drawings and energy data, and underserved sectors such as multistoried housing, disadvantaged communities, and schools for which the ML method can enable identification of building asset characteristics and prioritization of envelope retrofits and decentralized energy equipment retrofits.

Singh, Reshma↗

Computational Study of Oxidative Etch Pitting in FiberForm and the Effect on Its Material Properties

Erosion of carbon due to oxidation does not occur uniformly but through the formation of localized etch pits because of active surface sites. These active sites are formed due to the presence of atomic defects on the carbon surface, and have much higher reactivity compared to average non-defective sites. Thus, these active sites are first to react during ablation, resulting in their removal. This causes all the neighboring atoms to be defective and increase their reactivity, thus leading to the localized carbon removal around these “active” sites. In this manner, these highly reactive defective sites serve as nucleation sites for the formation and growth of etch pits with potentially detrimental effects on the structural integrity. In order to understand the influence of these etch pits on the material properties of carbon fiber microstructures, we have developed a new capability within direct simulation Monte Carlo (DSMC) to capture the etch pit formation process. This capability is developed within the DSMC code SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) and can model the material removal in presence of active sites leading to the formation of etch pits. The focus of the current work will be to study the effect of etch pits on the material properties of FiberForm, a commonly used base material within many thermal protection system materials (TPS). The microstructure of virgin FiberForm obtained directly from X-ray microtomography experiments is used within SPARTA to obtain the ablated geometries with etch pits. These pitted microstructures are then imported within the Porous Microstructure Analysis (PuMA) software and various material properties such as elasticity, thermal conductivity, and permeability are computed. The variation of these properties as a result of the complex evolution of the surface topology due to etch pit formation is studied and analyzed. Furthermore, the effect of pitting is compared to the case of shrinking fibers, which has been the standard for modelling ablation of carbon structures; and significant differences are observed. Thus, such a physically realistic modeling of material removal through the formation of etch pits will be helpful in predicting the degradation of carbon-based TPS more accurately during oxidation; as well as other mechanisms such as spallation, which involves the removal of chunks of material into the flow due to etch pit growth. This will ultimately improve our understanding of the failure modes in these materials due to ablation.

Carbon Ablators↗

Computational Study of Oxidative Etch Pitting in FiberForm and the Effect on Its Material Properties

Erosion of carbon due to oxidation does not occur uniformly but through the formation of localized etch pits because of active surface sites. These active sites are formed due to the presence of atomic defects on the carbon surface, and have much higher reactivity compared to average non-defective sites. Thus, these active sites are first to react during ablation, resulting in their removal. This causes all the neighboring atoms to be defective and increase their reactivity, thus leading to the localized carbon removal around these “active” sites. In this manner, these highly reactive defective sites serve as nucleation sites for the formation and growth of etch pits with potentially detrimental effects on the structural integrity. In order to understand the influence of these etch pits on the material properties of carbon fiber microstructures, we have developed a new capability within direct simulation Monte Carlo (DSMC) to capture the etch pit formation process. This capability is developed within the DSMC code SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) and can model the material removal in presence of active sites leading to the formation of etch pits. The focus of the current work will be to study the effect of etch pits on the material properties of FiberForm, a commonly used base material within many thermal protection system materials (TPS). The microstructure of virgin FiberForm obtained directly from X-ray microtomography experiments is used within SPARTA to obtain the ablated geometries with etch pits. These pitted microstructures are then imported within the Porous Microstructure Analysis (PuMA) software and various material properties such as elasticity, thermal conductivity, and permeability are computed. The variation of these properties as a result of the complex evolution of the surface topology due to etch pit formation is studied and analyzed. Furthermore, the effect of pitting is compared to the case of shrinking fibers, which has been the standard for modelling ablation of carbon structures; and significant differences are observed. Thus, such a physically realistic modeling of material removal through the formation of etch pits will be helpful in predicting the degradation of carbon-based TPS more accurately during oxidation; as well as other mechanisms such as spallation, which involves the removal of chunks of material into the flow due to etch pit growth. This will ultimately improve our understanding of the failure modes in these materials due to ablation.

Carbon Ablators↗

Big-data Efficient and Automated Science Transfer (BEAST): An Open-Source Software Architecture for Arc Jet Data Management, Modeling, and Automation

Big-data Efficient and Automated Science Transfer (BEAST) was conceived to address the existing ground testing data management of the NASA Ames arc jet facilities (e.g., manually entered Excel files and USB drive data transfers). These data management practices were seen as a choke point for future thermal protection system (TPS) development as they limit statistical tracking, resolution of diagnostics, coordination between video/time series, data throughput, and data processing speed/efficiency. Consequently, BEAST was developed to provide a new data infrastructure with streamlined data collection, processing, transfer, and analysis. This new framework also seeks to implement the FAIR principles of data stewardship: Findable, Accessible, Interoperable, and Reusable. The BEAST framework is based on a combination of the Python Django web framework and the Python data stack to provide a monolithic, open-source platform for data management, automation, and machine learning. This architecture was chosen for maintainability and scalability for a small, in-house development team. This paper will describe the application framework, deployment, and discuss the benefits and future plans for the system.

Data management↗

Big-data Efficient Automated Science Transfer (BEAST): an open-source software architecture for arc jet data management, modeling, and automation

Big-data Efficient and Automated Science Transfer (BEAST) was conceived to address the existing ground testing data management of the NASA Ames arc jet facilities (e.g., manually entered Excel files and USB drive data transfers). These data management practices were seen as a choke point for future thermal protection system (TPS) development as they limit statistical tracking, resolution of diagnostics, coordination between video/time series, data throughput, and data processing speed/efficiency. Consequently, BEAST was developed to provide a new data infrastructure with streamlined data collection, processing, transfer, and analysis. This new framework also seeks to implement the FAIR principles of data stewardship: Findable, Accessible, Interoperable, and Reusable. The BEAST framework is based on a combination of the Python Django web framework and the Python data stack to provide a monolithic, open-source platform for data management, automation, and machine learning. This architecture was chosen for maintainability and scalability for a small, in-house development team. This paper will describe the application framework, deployment, and discuss the benefits and future plans for the system.

Data management↗

The STAT7 Code for Statistical Propagation of Uncertainties in Steady State Thermal Hydraulics Analysis of Plate Fueled Reactors

The STAT7 software was developed to perform steady-state thermal hydraulic analyses. Application of the software is for non-power research and test reactors, including conversion to low-enriched uranium fuel of U.S. High-Performance Research Reactors such as MITR-II. Since it can be necessary to repeat analysis during fuel reloading, STAT7 accommodates flexibility in analyzing many realistic aspects of reactor fuel management. STAT7 uses a Monte Carlo approach to model common fabrication parameters and other key reactor analysis uncertainties required for research and test reactor thermal hydraulic analyses. These safety calculations are ultimately intended to protect against high fuel plate temperatures due to critical heat flux or departure from nucleate boiling or onset of flow instability; but additional margin is obtained by basing the limiting safety settings on avoiding onset of nucleate boiling. STAT7 can simultaneously analyze all of the axial nodes of all of the fuel plates and all of the coolant channels for one lateral stripe of a fuel element. The stripes run the length of the fuel, from the bottom to the top. Power splits are calculated for each axial node of each plate to determine how much of the power goes out each face of the plate. By running STAT7 multiple times, full core analysis can be performed by analyzing the margin to onset of nucleate boiling and onset of flow instability for each axial node of each stripe of each plate of each element in the core.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗