Results for “Model parameters” — Page 16

NASA NTRS2002

Hierarchies of Models: Toward Understanding Planetary Nebulae

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three-dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter-American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two-dimensional object and use these estimates to later examine its three-dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model.

Knuth, Kevin H.↗

NASA NTRS2003

Hierarchies of Models: Toward Understanding Planetary Nebulae

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three-dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter-American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two-dimensional object and use these estimates to later examine its three-dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model.

Knuth, Kevin H.↗

NASA NTRS2010

Seagrass Health Modeling and Prediction with NASA Science Data

Previous research has demonstrated that MODIS data products can be used as inputs into the seagrass productivity model developed by Fong and Harwell (1994). To further explore this use to predict seagrass productivity, Moderate Resolution Imaging Spectroradiometer (MODIS) custom data products, including Sea Surface Temperature, Light Attenuation, and Chlorophyll-a have been created for use as model parameter inputs. Coastal researchers can use these MODIS data products and model results in conjunction with historical and daily assessment of seagrass conditions to assess variables that affect the productivity of the seagrass beds. Current monitoring practices involve manual data collection (typically on a quarterly basis) and the data is often insufficient for evaluating the dynamic events that influence seagrass beds. As part of a NASA-funded research grant, the University of Mississippi, is working with researchers at NASA and Radiance Technologies to develop methods to deliver MODIS derived model output for the northern Gulf of Mexico (GOM) to coastal and environmental managers. The result of the project will be a data portal that provides access to MODIS data products and model results from the past 5 years, that includes an automated process to incorporate new data as it becomes available. All model parameters and final output will be available through the use National Oceanic and Atmospheric Administration?s (NOAA) Environmental Research Divisions Data Access Program (ERDDAP) tools as well as viewable using Thematic Realtime Environmental Distributed Data Services (THREDDS) and the Integrated Data Viewer (IDV). These tools provide the ability to create raster-based time sequences of model output and parameters as well as create graphs of model parameters versus time. This tool will provide researchers and coastal managers the ability to analyze the model inputs so that the factors influencing a change in seagrass productivity can be determined over time.

Robinson, Harold D.↗

DOE OSTI2026

Uncertainty Quantification and Sensitivity Analysis of Nuclear Construction Cost Reduction Pathways

High construction costs have plagued recent nuclear projects and they hamper the widespread deployment of nuclear technology. The Nuclear Cost Reduction Tool is a plant economic framework that quantifies the impact that various plant design and construction attributes have on construction costs and cost overruns and shows the positive effects of learning over a series of deployments. However, a downside of the current model is that all model outputs and capabilities are deterministic. To provide a more comprehensive view, this study evaluated the impact of model parameter uncertainty through a sensitivity analysis applied to 18 model parameters. This approach quantified the impact of model uncertainty on the output variables of Net Overnight Capital Cost (Net OCC), Construction Duration (CD), and Levelized Cost of Electricity (LCOE). Monte Carlo analysis revealed uncertainty distributions for these variables, showing that absolute uncertainty decreases over a series of deployments. A local sensitivity analysis showed that even small parameter perturbations (5%) can have a significant impact on project execution, highlighting areas that could reduce costs by billions across an order book of plants. The results of this study have improved the understanding of the model and identified the most impactful model parameters and construction attributes.

Levelized Cost of Electricity↗

NASA NTRS1994

Influence of mid-ocean ridges on Rossby waves

Influence of mid-ocean ridges on Rossby wave activity is discussed in simple models. Ridges can influence Rossby waves in two ways, topographic scattering to model parameters such as frequency, ridge height, and ridge width in both barotropic and baroclinic models. In the barotropic model, for certain model parameters there is perfect transmission of Rossby waves, while for some other model parameters the transmission is rather weak. In a two-layer model, if the frequency is not low enough, trapping of baroclinic signals around topography will occur. The mid-ocean ridge is generally not as efficient as the eastern boundary in generating barotropic waves except at high frequencies in a barotropic model. It is much more efficient than the eastern boundary generating baroclinic waves when wind forcing has a very large zonal scale, while less efficient when wind forcing has a short zonal scale.

Wang, Liping↗

NASA NTRS2005

Advanced Method to Estimate Fuel Slosh Simulation Parameters

The nutation (wobble) of a spinning spacecraft in the presence of energy dissipation is a well-known problem in dynamics and is of particular concern for space missions. The nutation of a spacecraft spinning about its minor axis typically grows exponentially and the rate of growth is characterized by the Nutation Time Constant (NTC). For launch vehicles using spin-stabilized upper stages, fuel slosh in the spacecraft propellant tanks is usually the primary source of energy dissipation. For analytical prediction of the NTC this fuel slosh is commonly modeled using simple mechanical analogies such as pendulums or rigid rotors coupled to the spacecraft. Identifying model parameter values which adequately represent the sloshing dynamics is the most important step in obtaining an accurate NTC estimate. Analytic determination of the slosh model parameters has met with mixed success and is made even more difficult by the introduction of propellant management devices and elastomeric diaphragms. By subjecting full-sized fuel tanks with actual flight fuel loads to motion similar to that experienced in flight and measuring the forces experienced by the tanks these parameters can be determined experimentally. Currently, the identification of the model parameters is a laborious trial-and-error process in which the equations of motion for the mechanical analog are hand-derived, evaluated, and their results are compared with the experimental results. The proposed research is an effort to automate the process of identifying the parameters of the slosh model using a MATLAB/SimMechanics-based computer simulation of the experimental setup. Different parameter estimation and optimization approaches are evaluated and compared in order to arrive at a reliable and effective parameter identification process. To evaluate each parameter identification approach, a simple one-degree-of-freedom pendulum experiment is constructed and motion is induced using an electric motor. By applying the estimation approach to a simple, accurately modeled system, its effectiveness and accuracy can be evaluated. The same experimental setup can then be used with fluid-filled tanks to further evaluate the effectiveness of the process. Ultimately, the proven process can be applied to the full-sized spinning experimental setup to quickly and accurately determine the slosh model parameters for a particular spacecraft mission. Automating the parameter identification process will save time, allow more changes to be made to proposed designs, and lower the cost in the initial design stages.

Schlee, Keith↗

DOE OSTI2024

Comparison of steady-state analytical wake models implemented in wind farm analysis software

A common set of mathematical wind turbine wake models are implemented in a few, well-adopted computational tools for wind farm wake modelling. Although the referenced mathematical formulations are common, implementation details may lead to differences in results. This study presents a systematic comparison of the implementation of mathematical wake models in open source, Python-based wind turbine wake modelling software, and a set of the models are directly compared. Despite aligning only the mathematical model parameters and retaining the default computational model parameters, good agreement is found across most of the model implementations, and additional agreement is expected upon further parameters alignment.

17 WIND ENERGY↗

NASA NTRS2016

Dynamic Modeling from Flight Data with Unknown Time Skews

A method for estimating dynamic model parameters from flight data with unknown time skews is described and demonstrated. The method combines data reconstruction, nonlinear optimization, and equation-error parameter estimation in the frequency domain to accurately estimate both dynamic model parameters and the relative time skews in the data. Data from a nonlinear F-16 aircraft simulation with realistic noise, instrumentation errors, and arbitrary time skews were used to demonstrate the approach. The approach was further evaluated using flight data from a subscale jet transport aircraft, where the measured data were known to have relative time skews. Comparison of modeling results obtained from time-skewed and time-synchronized data showed that the method accurately estimates both dynamic model parameters and relative time skew parameters from flight data with unknown time skews.

Morelli, Eugene A.↗

DOE OSTI2023

Open-Loop Control Co-Design of Semisubmersible Floating Offshore Wind Turbines Using Linear Parameter-Varying Models

Here, this paper discusses a framework to design elements of the plant and control systems for floating offshore wind turbines in an integrated manner using linear parameter-varying models. Multiple linearized models derived from aero-elastic simulation software in different operating regions characterized by the incoming wind speed are combined to construct an approximate low-fidelity model of the system. The combined model is then used to generate open-loop, optimal control trajectories as part of a nested control co-design strategy that explores the system’s power production and stability using the platform pitch tilt as a proxy in the context of crucial plant and control design decisions. The radial distance between the central and outer columns and the diameter of the outer columns of the semisubmersible platform are the plant design variables. The platform stability and power production are studied for different plant design decisions. The effect of plant decisions on subsequent power production and stability response of the floating wind turbine is quantified in terms of the levelized cost of energy. The results show that the inner-loop constraints and the plant design decisions affect the turbine’s power and, subsequently, the cost of the system.

17 WIND ENERGY↗

DOE OSTI2022

Calibration of cloud and aerosol related parameters for solar irradiance forecasts in WRF-solar

Model parameters are a major source of uncertainty in numerical weather prediction. Recently, the Weather Research and Forecasting model with Solar extensions (WRF-Solar) has been upgraded by enhancing the treatment of sub-grid scale cloud and aerosols with augmentations of a sub-grid scale cloud scheme (CLD3) and an upgraded aerosol-aware Thompson-Eidhammer scheme (TE14). However, the value of model parameters associated with these parameterizations are assigned based on limited measurements or theoretical calculations. Calibrating the most sensitive parameters has the potential to improve solar irradiance predictions. Here, we adopted a multiobjective surrogate-based optimization (SBO) framework to calibrate nine parameters used in CLD3 and TE14 that lead to the largest sensitivity in simulated irradiance. The normalized mean-absolute-error (NMAE) of global horizontal irradiance (GHI) and direct normal irradiance (DNI) are minimized by calibrating WRF-Solar over two regions including the Southern Great Plains (SGP) and Central California, in order to focus on parameter calibration under cloudy conditions with different aerosol loading. The results show that generalized linear model (GLM)-based surrogate models approximate physical models well, particularly when the third order and three-way interaction terms are considered. The SBO framework efficiently searches the parameter space for optimal solutions with less computational costs than directly calibrating the physical model. We first calibrate CLD3 parameters over the less-polluted SGP region. Optimized CLD3 parameters alone result in NMAE reduction by 14% for the site-mean and up to 33% for individual cases over the SGP region. With further calibration of TE14 parameters over the Central California during active fire periods, the optimized parameters lead to over 20% reductions of NMAE. Our investigation reveals, however, that optimizing TE14 has a limited impact on irradiance simulations under less-polluted conditions in the SGP.

14 SOLAR ENERGY↗

DOE OSTI2024

Steam Generator Model Design Parameter Sensitivity Study Using Advanced Optimization Tools

This study focuses on design parameter sensitivity studies pertaining to a steam generator (SG) model, using both Python and machine-learning tools. The SG model is a mathematical representation (including fluid flow and heat transfer equations/models/correlations) of a steam-generating unit in a pressurized water reactor (PWR)-type small modular reactor (SMR) system. Design studies involve changing the model’s input design parameters (e.g., temperature, pressure, mass flow rate) to observe the resulting effects on the output of the system (e.g., heat transfer coefficient [HTC], Nusselt number, heat transfer performance). Sensitivity studies analyze the degree to which system output and/or desired parameters (e.g., HTC or heat transfer performance) are sensitive to changes in input parameters. By using machine-learning tools such as the Risk Analysis Virtual Environment (RAVEN) developed at Idaho National Laboratory (INL), detailed design parametric sensitivity studies and model optimization were performed. Six input parameters—namely, the pressure, temperature, and mass flow rate for the inlet of the primary-side (hot fluid) and secondary-side (cold fluid) of the SG—were randomly perturbed via RAVEN’s Monte Carlo Sampler module, using uniform distributions (±1% relative changes). The analysis results give valuable insights into SG system performance and optimization, and provide justification for researching optimized sensor placement to effectively monitor and obtain experimental data.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Steam Generator Model Design Parameter Sensitivity Study Using Advanced Optimization Tools

This study focuses on design parameter sensitivity studies pertaining to a steam generator (SG) model, using both Python and machine-learning tools. The SG model is a mathematical representation (including fluid flow and heat transfer equations/models/correlations) of a steam-generating unit in a pressurized water reactor (PWR)-type small modular reactor (SMR) system. Design studies involve changing the model’s input design parameters (e.g., temperature, pressure, mass flow rate) to observe the resulting effects on the output of the system (e.g., heat transfer coefficient [HTC], Nusselt number, heat transfer performance). Sensitivity studies analyze the degree to which system output and/or desired parameters (e.g., HTC or heat transfer performance) are sensitive to changes in input parameters. By using machine-learning tools such as the Risk Analysis Virtual Environment (RAVEN) developed at Idaho National Laboratory (INL), detailed design parametric sensitivity studies and model optimization were performed. Six input parameters—namely, the pressure, temperature, and mass flow rate for the inlet of the primary-side (hot fluid) and secondary-side (cold fluid) of the SG—were randomly perturbed via RAVEN’s Monte Carlo Sampler module, using uniform distributions (±1% relative changes). The analysis results give valuable insights into SG system performance and optimization, and provide justification for researching optimized sensor placement to effectively monitor and obtain experimental data.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2020

Simulation and Emulation of X-Ray Diffraction from Dynamic Compression Experiments

Many important aspects of the dynamic thermo-mechanical response of materials occur at the mesoscale, i.e. a physical scale of interactions smaller than what can be adequately described by homogenous behaviors, yet larger than the scale of the atomic lattice. Concurrent advancements in computational power, continuum theory, and experimental diagnostics are enabling unprecedented understanding of such interactions. However, we cannot develop a sufficient level of confidence in such mesoscale capability until the constitutive description of the underlying constituents is reliably representative of their actual physical behavior. Therefore, there is a strong need to combine experimental, modeling, and data-science techniques to validate models of the thermomechanical response of individual single crystals. One experimental diagnostic with high potential impact to shock physics and materials science is in-situ x-ray diffraction. This paper is primarily focused on simulation of x-ray diffraction in shock physics, but with an aim toward quantifying parametric uncertainty of simulation models. Here, we develop and demonstrate a data-science and model-driven approach to constrain the parameterization of continuum models of crystal lattice deformation associated with the shock response of crystalline materials. The framework is built around the connection between continuum hydrodynamic simulations of lattice deformation and a new Bragg diffraction simulation code, BarberShop. The dynamic deformation of a crystal lattice is modeled using the DiscoFlux model within an arbitrary Lagrangian-Eulerian hydrodynamic code, FLAG. These detailed continuum simulations of lattice deformation can be computationally slow, thus a statistical model is used to emulate the evolution of lattice deformation fields in time and across the considered model parameter space. Emulated lattice deformation fields can then be generated rapidly for any combination of physics model parameters. In turn, these fields can be fed into BarberShop to realize a rapid prediction of Bragg diffraction patterns associated with particular values of physics model parameters. The framework enables parameterization of the single crystal model to obtain Bragg diffraction patterns that most closely resemble a corresponding measurement. Furthermore, the framework naturally provides sensitivities of the lattice deformation to the physics parameters. We highlight the utility of this framework through the application to a synthetic closed-loop inverse problem leading to the parameterization of a single crystal material model. As a model problem, we consider the dynamic response of the energetic molecular crystal, cyclotrimethylenetrinitramine (or RDX), under dynamic compression induced by simulated flyer plate impact experiments.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Flood hazard model calibration using multiresolution model output

Riverine floods pose a considerable risk to many communities. Improving flood hazard projections has the potential to inform the design and implementation of flood risk management strategies. Current flood hazard projections are uncertain, especially due to uncertain model parameters. Calibration methods use observations to quantify model parameter uncertainty. With limited computational resources, researchers typically calibrate models using either relatively few expensive model runs at high spatial resolutions or many cheaper runs at lower spatial resolutions. This leads to an open question: is it possible to effectively combine information from the high and low resolution model runs? We propose a Bayesian emulation–calibration approach that assimilates model outputs and observations at multiple resolutions. As a case study for a riverine community in Pennsylvania, we demonstrate our approach using the LISFLOOD-FP flood hazard model. Here, the multiresolution approach results in improved parameter inference over the single resolution approach in multiple scenarios. Results vary based on the parameter values and the number of available models runs. Our method is general and can be used to calibrate other high dimensional computer models to improve projections.

multiresolution↗

DOE OSTI2024

Implicit neural representations for experimental steering of advanced experiments

Scattering measurements using electrons, neutrons, or photons are essential for obtaining microscopic insights into materials. However, limited facility availability and high-dimensional scattering data necessitate more efficient experimental steering techniques. Here, we report a machine learning method that guides scattering data collection and facilitates real-time estimation of model parameters, given a reliable forward model to simulate experimental signals. We employ implicit neural representations as efficient surrogates that link model parameters with simulated spectroscopies. This enables a Bayesian optimal experimental design framework to estimate the probability distributions of parameters from high-dimensional scattering data. We demonstrate the proposed method using inelastic neutron scattering with simulated and real experimental data, highlighting the method’s ability to provide real-time parameter estimation with quantified uncertainties and to deliver informed experimental guidance that reduces experimental time while maximizing scientific output. This approach paves the way for accelerated discoveries in condensed matter through scattering measurements.

36 MATERIALS SCIENCE↗

NASA NTRS1994

Computational control of flexible aerospace systems

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed based on several incomplete versions. The verification of the code had been conducted by comparing the results with those examples for which the exact theoretical solutions can be obtained. The theoretical background of the package and the verification examples has been reported in a technical paper submitted to the Joint Applied Mechanics & Material Conference, ASME. A brief USER'S MANUAL had been compiled, which includes three parts: (1) Input data preparation; (2) Explanation of the Subroutines; and (3) Specification of control variables. Meanwhile, a theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modeling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide an embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

Sharpe, Lonnie, Jr.↗

NASA NTRS1994

Computational Control of Flexible Aerospace Systems

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years of the project. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed. A theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modelling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide a embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

Sharpe, Lonnie, Jr.↗

DOE OSTI2022

Uncertainty Quantification of Calculated Temperatures for the AGR 5/6/7 Experiment

This report documents the quantification of uncertainty of the calculated temperature data for the Advanced Gas Reactor (AGR) 5/6/7 fuel irradiation experiment conducted in the Advanced Test Reactor at Idaho National Laboratory in support of the Advanced Reactor Technologies? research and development program. Recognizing uncertainties inherent in physics and thermal simulations of the AGR 5/6/7 capsules, the results of the numerical simulations are used in combination with statistical analysis methods to improve qualification of measured data. The calculated fuel temperatures for AGR tests are also used for validation of the fission product transport and fuel performance simulation models. These crucial roles of the calculated fuel temperatures in ensuring achievement of the AGR experimental program objectives require accurate determination of the model temperature uncertainties. This report covers temperature uncertainty results for each of the five AGR 5/6/7 capsules. To quantify the uncertainty of calculated temperatures determined using the ABAQUS finite element heat transfer code, this study identifies and analyzes model parameters of potential importance to the calculated temperatures of fuel compacts and thermocouples. The selection of input parameters for uncertainty quantification is based on the ranking of their influences upon temperature predictions. Thus, selected input parameters include those with high sensitivity and those with the largest uncertainty. Propagation of model parameter uncertainty and sensitivity is then used to quantify the overall uncertainty of calculated temperatures. Measurement uncertainty, analysis of modeling assumptions, and expert judgment are used as the basis to quantify the uncertainty range for selected input parameters. The input uncertainties are dynamic, accounting for the effect of unplanned events and changes in thermal properties of capsule components over extended exposure to high temperatures and fast neutron irradiation. The sensitivity analysis performed in this work went beyond the traditional local sensitivity. Using experimental design, analysis of pairwise interactions of model parameters was performed to establish sufficiency of the time dependent first order (linear) expansion terms in constructing the temperature response surface. To achieve completeness, uncertainty propagation made use of pairwise noise correlations of model parameters. Furthermore, using an interpolation scheme over the input parameter domain, the analysis obtains time dependent sensitivity over the test campaign duration. This allows computation of uncertainty for the calculated fuel temperatures and the calculated graphite temperatures at thermocouple locations during the entire irradiation period.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗