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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,405 records · Page 78
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Post-Transient Examination Results of RIA Commissioning Teats at the Transient Reactor Test Facility

Six reactivity-initiated-accident (RIA) commissioning tests have been performed at Idaho National Laboratory’s (INL) Transient Reactor Test Facility. Five of these tests were performed using fresh fuel rodlets, and the sixth test was performed using a previously irradiated rodlet from the ATF-2 irradiation experiment. These experiments demonstrate the ability to perform RIA testing including the ability to perform experiments using previously irradiated materials. Post-transient examinations revealed pellet cladding interactions and cladding ballooning depending on the initial boundary conditions of the test. Increased thickness of both zirconium oxide and alpha-zirconium were found in the cladding with tests performed at higher levels of total energy deposition. No oxide or alpha-zirconium was found in the test with the greatest amount of ballooning, which was also the test with the highest initial rod internal pressure. The highest energy deposition test (1110 J/g) resulted in failure of the rodlet. Fragmentation of the fuel pellets occurred in this test with the size of the fragments decreasing inversely to the pellet radius.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Hexagonal Geometries in MPACT

The MPACT code is a high-fidelity light-water reactor analysis code using whole-core pin-resolved neutron transport calculations on modern parallel-computing hardware. MPACT uses the 2D/1D method to solve 3D neutron transport problems by decomposing the problem into a stack of 2D slices, each of which is solved independently using the method of characteristics (MOC). The slices are then coupled axially using the P3 nodal expansion method (NEM-P3) for the 1D axial calculations. MPACT also employs the coarse mesh finite difference (CMFD) method to accelerate calculations. This manuscript details work supporting advanced reactor designs using hexagonal pins and hexagonal assemblies such as the VVER-1000. If performed correctly, MOC is geometry agnostic. However, MPACT previously had optimizations in place for Cartesian geometries, specifically in the modularization and current calculations. Sections 2 and 3 detail the changes made to MPACT to support MOC and CMFD calculations on hexagonal geometries. Section 4 reports results demonstrating solution consistency for problems run with and without CMFD acceleration, results demonstrating solution consistency when run in serial and parallel, and pincell results using the Monte Carlo code, McCard’s benchmark results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Discovering tungsten-based composites as plasma facing materials for future high-duty cycle nuclear fusion reactors

Abstract Despite of excellent thermal properties and high sputtering resistance, pure tungsten cannot fully satisfy the requirements for plasma facing materials in future high-duty cycle nuclear fusion reactions due to the coupled extreme environments, including the high thermal loads, plasma exposure, and radiation damage. Here, we demonstrated that tungsten-based composite materials fabricated using spark-plasma sintering (SPS) present promising solutions to these challenges. Through the examination of two model systems, i.e., tungsten-zirconium composite for producing porous tungsten near the surface and dispersoid-strengthened tungsten, we discussed both the strengths and limitations of the SPS-fabricated materials. Our findings point towards the need for future studies aimed at optimizing the SPS process to achieve desired microstructures and effective control of oxygen impurities in the tungsten-based composite materials.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

STAT7 v1.2 Verification and Validation Report

This report documents the software testing which has been performed for the STAT7 Version 1.2 (hereafter STAT7 v1.2) software, a code for the statistical propagation of uncertainties in steady-state thermal hydraulics (TH) analysis of plate-fueled research and test reactors. The key capabilities addressed in this testing were selected based on the use of the software for analysis work supporting the conversion to low-enriched uranium fuel of U.S. High-Performance Research Reactors (USHPRR) such as the Massachusetts Institute of Technology Research Reactor (MITR-II). This testing scope includes comparison of the code’s statistical processing capabilities using statistical tests, comparison of coolant property evaluations to NIST data tables, and systematic comparison of key TH solver capabilities to the results of hand calculations and to predictions from PLTEMP/ANL Version 4.4. The good agreement achieved in this testing campaign, within the acceptance criteria of a 1% relative difference, also demonstrates that these capabilities have been implemented in STAT7 v1.2 correctly.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Development and benchmarking of transient nodal code SIMULATE5-K neutron kinetics solver

SIMULATE5-K is Studsvik's next generation best estimate transient code. The time dependent diffusion equation is solved with a nodal method consistent with that implemented in the licensed core design code SIMULATE5. Arbitrary number of neutron and delayed neutron precursor groups can be used. For the solution of the spatial problem, the coupling coefficients used to relate the node leakages are found by first converting the time dependent diffusion equation to a static diffusion equation with the use of flux and delayed neutron precursor dynamic frequencies. Once the static-like equations are obtained, the multi-group analytical nodal model is used to obtain the coupling coefficients, expressing the node leakage in terms of adjacent node average fluxes. The coupling coefficients are then inserted into the time dependent nodal balance equation. For the time integration, the time dependent neutron balance equation is solved with the frequency transformation method. The treatment of the temporal dependence yields a fixed source problem which can be solved utilizing the existing fixed-source methodology. The primary purpose of this paper is to describe the neutron kinetics methodology implemented in SIMULATE5-K. The accuracy of the method is demonstrated for a series of well-known, neutronic-only benchmark problems. (author)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Neutronic Consideration of TREAT Facility Fuel SiC Recladding

The Transient Reactor Test (TREAT) Facility is an air-cooled reactor composed of graphite-urania fuel encapsulated in zirconium alloy canisters and surrounded by ~2 ft (~61 cm) of nuclear grade graphite. The primary role of TREAT is to provide in-pile nuclear-heated safety research via transient testing [1]. Benchmark efforts have demonstrated sensitivity of TREAT neutronics models to graphite cross section data and key neutron poisons found in the fuel assemblies [2]. During fabrication of TREAT fuel assemblies, a small concentration of boron was inadvertently introduced with variable concentration into the aggregate of fuel blocks prepared for TREAT use. The concentration of boron, and its respective uncertainty, represent the most sensitive component in a neutronics study; unfortunately, nothing can be done to reduce or otherwise mitigate its impact. Hydrogen in the fuel blocks reduces the mean free path of the core and its true quantity and uncertainty is approximated. The hydrogen remains from pitch binder used in the fuel fabrication process and was not completely released due to incomplete fuel graphitization. Destructive fuel testing is necessary to quantify the actual hydrogen content and to improve benchmark model quality. A third neutron poison of some significance is the hafnium impurity in the Zircaloy-3 (Zry-3) assembly cladding. The quantity of hafnium is expected to be within nominal manufacturing limits for nuclear grade zircaloy. Recladding the fuel assemblies with material that is less neutron absorbing is expected to benefit reactor neutron economy. Moreover, TREAT’s total transient energy is restricted based on the rate of Zry-3 oxidation in TREAT’s air coolant environment. Hence, cladding with more benign air reaction kinetics could dramatically uprate the facility’s experimental capability. Silicon carbide (SiC) has been proposed as a candidate material for recladding TREAT assemblies, as SiC/SiC demonstrate favorable properties within nuclear environments [3]. The current operational limits of TREAT are restricted by the oxidation of Zry-3. Change of the cladding to SiC could feasibly double the current temperature limitation. Recladding opportunities allow for previously damaged fuel assemblies to be returned to service, as Zry-3 is not commercially available. The initial effort required to consider proceeding with any recladding effort is to neutronically characterize key reactor parameters while replacing Zry-3 with SiC. A characterization summary, with respective results, is provided herein.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

GaN HEMT Fabrication for Radiation-Hardened Sensing and Communications Electronics

Gallium nitride (GaN), a wide bandgap semiconductor, has vast potential to address two environment conditions associated with the application of electronics to nuclear power: elevated temperatures, and high levels of radiation. A process was developed at The Ohio State University (OSU) to enable fabrication of complex digital and analog electronics circuits for application to nuclear power environments such as locations near or in the reactor core or in spent nuclear fuel casks. Radio frequency (RF)-grade GaN high electron mobility transistor (HEMT) devices were fabricated as part of this process. These were fabricated as depletion mode and enhancement mode devices. They have been electrically characterized and have demonstrated the expected performance. Behavioral models (Verilog-A) were developed from these device measurements to enable electrical simulation of GaN HEMT devices and circuits using common electronics simulation tools based on Simulation Program with Integrated Circuit Emphasis (SPICE). A similar set of GaN HEMT devices is being developed to provide lower speed devices for logic and analog functions. These accomplishments position this technology for effective application to sensor interfacing, signal processing, and data communications in nuclear power plants, including operation in or near the reactor core.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

CFD Simulations to Support Pronghorn Modeling of a Molten Salt Fast Reactor

To assist with the deployment of next generation molten salt reactors (MSRs), the DOE NEAMS program is developing advanced simulation capabilities. As part of this work, the high-fidelity CFD tool, Nek5000 was used to inform model development for the engineering scale tool, Pronghorn. The particular case chosen was the EVOL molten salt fast reactor concept. This concept uses an open core design, which is well known to be sensitive to the particular geometry and can have complex flow behavior that varies across a range of conditions. This makes it an idea candidate for demonstration of the Hi2Lo concept of using higher fidelity models to benchmark lower fidelity models. Simulations of the EVOL design were performed using both LES (high-fidelity) and RANS (moderate-fidelity) in Nek5000. The LES results indicated discrepancies in 2-D axisymmetric RANS, indicating that the core is better modeled in RANS with a 3-D wedge representation of a portion of the core, which can accurately account for the effect of the inlet channels. Finally, results from the 3-D RANS were used to modify an existing turbulence model in Pronghorn. Improvement in the calibrated Pronghorn model was demonstrated. Future work is suggested to focus on expanding the LES calculation to provide a more direct point of comparison for both the RANS and Pronghorn models as well as incorporating more of the relevant MSR physics (such as delayed neutron precursor tracking) into the model.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Improving an Acoustic Vehicle Detector Using an Iterative Self-Supervision Procedure

In many non-canonical data science scenarios, obtaining, detecting, attributing, and annotating enough high-quality training data is the primary barrier to developing highly effective models. Moreover, in many problems that are not sufficiently defined or constrained, manually developing a training dataset can often overlook interesting phenomena that should be included. To this end, we have developed and demonstrated an iterative self-supervised learning procedure, whereby models are successfully trained and applied to new data to extract new training examples that are added to the corpus of training data. Successive generations of classifiers are then trained on this augmented corpus. Using low-frequency acoustic data collected by a network of infrasound sensors deployed around the High Flux Isotope Reactor and Radiochemical Engineering Development Center at Oak Ridge National Laboratory, we test the viability of our proposed approach to develop a powerful classifier with the goal of identifying vehicles from continuously streamed data and differentiating these from other sources of noise such as tools, people, airplanes, and wind. Using a small collection of exhaustively manually labeled data, we test several implementation details of the procedure and demonstrate its success regardless of the fidelity of the initial model used to seed the iterative procedure. Finally, we demonstrate the method’s ability to update a model to accommodate changes in the data-generating distribution encountered during long-term persistent data collection.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Phase I Summary of Management Activities - Advanced Construction Technology Initiative Project

As the end of the year is approached, it is essential to review the National Reactor Innovation Center (NRIC) management activities undertaken during the Advanced Construction Technology Initiative (ACTI) project. The ACTI project was launched to support a transformation in nuclear energy construction, management, and deployment costs, enabling nuclear energy to make important contributions to the energy systems of the future. This transformation will increase the confidence of investors, energy system planners, policymakers, and ultimately consumers in the capability of nuclear energy to meet future needs; thus, it represents a critical element of advanced nuclear energy system demonstration. Development and/or demonstration project(s) will consider regulatory requirements for commercial nuclear implementation and will incorporate strategies to develop regulator experience and review of the technology. GE Hitachi (GEH), a leading player in the nuclear industry that offers a range of products and services including nuclear reactor design, fuel supply, and decommissioning solutions, submitted a proposal for the ACTI project. GEH was awarded the contract for the first phase of the project.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Reactor Pressure Vessel Fracture Mechanics Development and Concrete Application Testing for Grizzly

The Grizzly code is being developed to address degradation issues in nuclear reactor structures and components. For light-water reactors, Grizzly currently has capabilities to simulate degradation processes and their effects on structural integrity in two key areas: reactor pressure vessels (RPVs) and reinforced concrete structures. This report documents improvements made to Grizzly’s ability to address both of these structural systems. For RPVs, the reduced-order models (ROMs) used in fracture mechanics calculations have been expanded to allow their application over a broader range of the parameter space than was permitted by the previous models. The ROMs currently used in Grizzly for the evaluation of flaws that are fully embedded within the RPV (as opposed to surface-breaking flaws) are based on a model that is known to be conservative, indicating higher stress intensity factors than would be obtained from direct simulations. A more accurate model that eliminates these excess conservatisms has been recently included in the American Society of Mechanical Engineers Boiler and Pressure Vessel Code but was not applicable for flaws near the RPV surface, which is where the most critical flaws are usually located. That model has recently been extended for increased applicability in this near-surface region. The ROMs for embedded flaws in the Grizzly code have been expanded to include these recent extensions, which permit their use in a much broader set of cases than previously possible. Direct 3D simulations have been used to check these ROMs and have shown good agreement in most cases, although there are still some cases that need further investigation. There are considerable benefits to using these these more accurate and less conservative ROMs for embedded flaws. On a benchmark probabilistic fracture mechanics problem tested here, the conditional probability of fracture initiation computed for a population of flaws in a single plate in an RPV decreased by over a factor of 3. To address aging in reinforced concrete structures, a capability to simulate multiple degradation mechanisms, including alkali-silica reaction and radiation-induced volumetric expansion has been developed in Grizzly over the past several years. This had previously been demonstrated on laboratory-scale specimens but not on full-scale nuclear concrete structures with reinforcement. To demonstrate the applicability of Grizzly to the analysis of large-scale structures of interest, a full 3D model of a representative reinforced concrete structure, including a complex arrangement of reinforcing bars, was developed and demonstrated in Grizzly.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Assessment of Flow-Enhanced Electrochemical Sensor Testing and Deployments

The goal of our activities in FY24 was to enable advanced materials accountancy for molten salt reactors (MSRs) through the development and optimization of robust flow-enhanced electrochemical sensors (FEES) using a safeguards-focused sensor testing platform called the modular flow instrumentation testbed (MFIT). Flow-enhanced electrochemical sensors are a type of electroanalytical sensor that have been developed at Argonne National Laboratory to be installed directly into MSR flow conduits to make measurements of the salt composition. These sensors represent a significant improvement in capabilities compared to earlier electroanalytical sensors that instead can only be operated in quiescent conditions. Previous work has focused on testing of the FEES in flowing conditions provided by the MFIT to assess the accuracy and precision of the sensor measurements. This year, the FEES technical readiness was increased by (1) demonstrating the use of optimized sensor techniques to achieve measurements in very high-concentration MSR-relevant salts, (2) leveraging new multimodal sensors and automation approaches to reduce measurement uncertainties, and (3) fabricating and deploying sensors to industrial partners to improve their ability to make measurements in challenging environments. Additionally, we also ran the sensors during complex system operations involving combined flow and purification activities to demonstrate safeguards-relevant measurements during online processing for MSRs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Demonstrate the Out-of-Pile Performance of a Real-Time Measurement System to Measure Thermal Conductivity Based on Photo Thermal Radiometry

SUMMARY The goal of this project is to develop a fiber-based instrument to perform in-reactor thermal conductivity measurements of fuels and materials. This instrument is based on photothermal radiometry (PTR) and involves heating a sample locally and measuring the induced temperature gradient by collecting blackbody radiation [2]. Thermal conductivity of the sample is extracted by comparing experimental results with a continuum-based model [3,4]. As a laser-based technique, PTR is a non-contact measurement technique that can be performed remotely and non-destructively. In addition, it has several advantages over other photothermal techniques, making it an ideal approach for in-situ measurement of thermal conductivity of nuclear fuels. Because blackbody radiation increases with emissivity and temperature, the PTR technique works well with unprepared surfaces, and measurement accuracy increases with temperature. Moreover, this approach is capable of measuring samples with irregular or poorly defined boundary conditions, which is a common situation for friable spent fuels.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Development of an Improved RELAP5-3D Model for the High Temperature Test Facility

High-temperature gas-cooled reactors (HTGRs) are rapidly approaching deployment. Confidence in transient analysis of these systems for design, optimization, and licensing calculations requires modeling and simulation tools that have been validated against data relevant to HTGR conditions. The High Temperature Test Facility (HTTF) is an integral effects thermal hydraulics test facility for prismatic HTGRs. In spring and summer of 2019, HTTF was used for a series of experiments that now serve as the basis for the OECD/NEA Thermal Hydraulic Code Validation Benchmark for High Temperature Gas-Cooled Reactors using HTTF Data (HTGR T/H Benchmark). This benchmark contains problems for systems code, computational fluid dynamics (CFD), and coupled systems code/CFD modeling representing lower plenum mixing and both the depressurized and pressurized conduction cooldown (DCC and PCC respectively) transients. Benchmark problems include exercises for code-to-code and code-to-data comparisons as well as an exercise for error scaling between HTTF and the Modular High Temperature Gas-Cooled Reactor, which serves as the basis for the HTTF design. Previous analysis as part of the HTGR T/H benchmark used a RELAP5-3D model developed at Idaho National Laboratory (INL) and demonstrated an ability to reproduce trends in the measured data but difficulties reproducing experimental values within their uncertainty. These difficulties were largely attributed to assumptions made during the development of the initial RELAP5-3D model, which predated the HTTF experiments. A significant cause of difficulty reproducing the measured temperatures may be the radial nodalization of the previous RELAP5-3D model. The new model provides a finer nodalization to assess the impact of radial nodalization and allows for asymmetric heating within the core, which was a feature of multiple HTTF experiments. In this paper, we present the new RELAP5-3D model of HTTF. In addition to describing the new model, this paper compares the new and old models and provides results for a full-power steady state, a DCC, and a PCC in HTTF. These analyses are based on the code-to-code comparison exercises for the DCC and PCC problems of the HTGR T/H benchmark. We present the results of these exercises from the new model and compare them to the results of the old model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Identification and Quantification of Technetium Species in Hanford Waste Tank AN-102

Technetium-99 (Tc) generated from the fission of 235U and 239Pu in high yields is one of the most difficult contaminants to be addressed at the U.S. Department of Energy Hanford Site. In strongly alkaline solutions typifying Hanford tank waste, Tc exists as pertechnetate (TcO4-) (oxidation state VII) as well as in reduced forms (oxidation state < VII) collectively known as non-pertechnetate species. Designing strategies for effective Tc management, including separation and immobilization, necessitates understanding the molecular structure of the non- pertechnetate species and their identification in the actual tank waste samples, which would facilitate development of new treatment technologies effective for dissimilar Tc species. Toward this objective, a spectroscopic library of the Tc(I) [fac-Tc(CO)3]+ and Tc(IV, VII) compounds was generated using a range of techniques and applied to the characterization of the actual tank waste supernatant collected from the tank 241-AN-102 at Hanford, WA. A sample of the 241-AN-102 tank waste supernatant was processed to adjust Na concentration to about 5.6 M and remove 137Cs by spherical resorcinol-formaldehyde (sRF) ion exchange resin. Cesium-loaded sRF column was eluted with 0.5 M HNO3. As received AN-102, Cs-depleted AN-102 effluent, and sRF eluate fractions were comprehensively characterized for chemical composition and speciation of Tc using 99Tc nuclear magnetic resonance spectroscopy and X-ray absorption spectroscopy. It was demonstrated for the first time that non-pertechnetate Tc present in the 241-AN-102 tank waste is composed of several low-valent Tc species, including the Tc(I) [fac-Tc(CO)3]+ and Tc(IV) compounds. This is the second experimental observation of the [fac-Tc(CO)3]+ species in the Hanford tank waste and the first demonstration of multiple forms of non-pertechnetate species existing simultaneously in the waste, cumulatively highlighting their importance for the waste processing.

Low Activity Waste (LAW), High Level Waste, nuclea↗
DOE OSTI2021

Incorporation and Assembly of a Light-Emitting Enzymatic Reaction into Model Protein Condensates

Eukaryotic cells partition enzymes and other cellular components into distinct subcellular compartments to generate specialized biochemical niches. A subclass of these compartments form in the absence of lipid membranes, via liquid-liquid phase separation of proteins to form biomolecular condensates or “membraneless organelles” such as nucleoli, stress granules, and P-bodies. Because of their ability to form compartments from simple starting materials, membraneless organelles are an attractive target for engineering new functionalities in both living cells and protocells. In this work, we demonstrate incorporation of novel enzymatic activity in protein coacervates with a light-generating enzyme, NanoLuc, to produce bioluminescence. Using condensates comprised of the disordered RGG domain of C. elegans LAF-1, we show functionalization of condensates with enzymatic activity in vitro and that localization to protein coacervates enhances the assembly and activity of split enzymes. To build condensates that function as light emitting reactors, we designed a NanoLuc enzyme flanked by RGG domains. Furthermore, the resulting condensates concentrated NanoLuc by 10-fold over bulk solution and display significantly increased net reaction rates. We further show that condensate viscosity impacts light emission due to diffusion-limited behavior. By splitting NanoLuc enzyme into its constituent components, we demonstrate that NanoLuc activity can be reconstituted via co-condensation. Further, we demonstrate control of the spatial localization of enzyme within condensates by targettng NanoLuc to the surface of in vitro condensates. Collectively, this work demonstrates that membraneless organelles can be endowed with localized enzymatic activity, and that this activity can be spatially and temporally controlled via enzyme reconstitution and design of protein surfactants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Vidyut3d: A GPU accelerated fluid solver for non-equilibrium plasmas on adaptive grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure three-electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate ~ 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. Here, the method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

42 ENGINEERING↗