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These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.
Oak Ridge National Lab’s (ORNL) Metal Big Area Additive Manufacturing (mBAAM) and Hybrid Manufacturing teams in the Manufacturing Demonstration Facility (MDF) was tasked with developing a part that exceeded 24 inches in length and 100lbs in weight on a laser hotwire welding system. The Mazak VC-500A/5X AM HWD hybrid 5-axis CNC laser hotwire system was leveraged to complete the task. The proposed geometry was manufactured with 410 stainless steel on AISI1018 steel substrate in just over 36 hours of build time. The proposed geometry was sliced and additively manufactured in three segments; the base, and two extrusions measuring 10 inches in length and 14 inches in length. Production of this component demonstrated hybrid capabilities requiring fixed 5-axis rotations to complete geometry that exceeded the defined build volume of the machine. Multiple repairs of the part were conducted in-situ leveraging the additive and subtractive capabilities of the Mazak hybrid system. Significant overbuilding challenges were encountered and manually addressed by leveraging subtractive capabilities of the hybrid system. Future processes are presented for development to reduce overheating of top layers. Final part measurements exceeded 107 lbs. in weight and 24.5 inches in length along the principal axis; the largest and heaviest part created by a hybrid system at the MDF.
The project (Award DE-FE0032146), led by Baker Hughes in collaboration with the University of Wyoming, aims to develop composite PEEK (Polyether-ether-ketone) materials enhanced using coal-derived graphene-based additives suitable for additive manufacturing (3D printing). Coal char (CC), graphene oxide (GO), and reduced graphene oxide (rGO), derived from Powder River Basin (PRB) coal, were successfully integrated into commercial PEEK feedstock. The composite PEEK materials demonstrated tensile and flexural strengths and modulus, Shore hardness, and thermal properties similar to unfilled PEEK. Dielectric strength of 0.5% GO/PEEK is twice that of unfilled PEEK. However, tensile elongation and Izod impact toughness of the composite materials are lower than unfilled PEEK. The 10% CC/PEEK material also shows good recyclability albeit with slightly increased glass transition and cold crystallization temperatures. Filaments of the composite PEEK materials were fabricated using a Filabot system. 3D printing of the composite PEEK initially encountered feeding stoppage caused by the non-uniform diameter of the filament, which was resolved by reducing the nominal diameter from 1.75 to 1.65 mm. The printability of the composite PEEK filaments is limited in geometry and build time, driven by differences in base PEEK feedstock from the commercial PEEK filament at printing conditions. Prototype part printed using the composite filaments shows inconsistent bead width and bead interruption resulting in porosity. Preliminary process and economic evaluation using PRB coal char estimates the cost of GO to be $0.5/lb. Considering the small fraction expected in the composite PEEK, the GO cost is several orders of magnitude lower than the commercial PEEK filament. It is recommended that the printability of composite PEEK filaments to be improved by optimizing the composite PEEK material at the printing conditions and reducing the variations in filament extrusion. Also important is to identify the mechanisms of how coal-derived additives affect the composite PEEK performance and printing characteristics to allow customized material design and processing for target performance.
To dramatically increase the adaptability, performance, and safety of processes in support of the Defense Waste Processing Facility (DWPF), Savannah River National Lab (SRNL) plans to perform chemical and radiological compatibility testing on a wide variety of 3D printed materials of interest. The 3D printing process provides numerous strategic operational benefits such as rapid prototyping of complex designs and geometry specific to the needs of the nuclear waste disposition process, as well as on-demand rapid prototyping and iteration with materials that aren’t as accessible through traditional manufacturing methods. Reaction chemistry in simulated waste batches can be matched closely to its radioactive counterpart, but glass reactor vessels have limitations. Vessel geometry can play a big factor in mixing transport limitations, process chemistry, and degradation reaction kinetics. In addition, additive manufacturing allows for much more detailed vessel design than traditional alternatives. Waste processing techniques in DWPF also encounter extreme chemical environments including high pH, strong acids, abrasive slurries, and significant irradiation. To meet these challenges, a matrix of various polymer, ceramic, and metal additive manufacturing materials have been exposed to a suite of chemical environments of interest as well as radioactive dose (such as gamma radiation from 60 Co) to properly test their durability under these conditions. Mass change has been monitored over a period of up to a week in these conditions, as well as added characterization for surface modification through Scanning Electron Microscopy/Electron Dispersive X-ray analysis (SEM/EDX). Further chemical characterization has been monitored through Fourier-Transform InfraRed Spectroscopy (FTIR), with planned investigation via thermal and tensile strength degradation. While the direct product of this research is identification of material(s) that can withstand specific hazardous environments encountered by the mercury water wash tank in DWPF process simulation experiments, the reference base of materials will be used for many other nuclear processes in the pursuit of rapidly developed, cost-efficient, and highly specific devices for environmental remediation and much more.
Hybrid manufacturing is a combination of additive and subtractive manufacturing in a single machine. Typically, planar substrate substrates are used for deposition and do not correspond to scenarios encountered in repair applications where the substrate can often be non-planar. Hybrid manufacturing opens the possibility for repairs by leveraging the five-axis mill to prepare the substrate for deposition. However, as the substrate geometry changes, so does the associated heat transfer during deposition and subsequent microstructures. This paper focuses on understanding the changes in microstructure and material properties with changing substrate geometries.
Many applications in magnetic confinement fusion require the efficient calculation of surface integrals with singular integrands. The singularity subtraction approaches typically used to handle such singularities are complicated to implement and low-order accurate. In contrast, we demonstrate that the Kapur–Rokhlin quadrature scheme is well-suited for the logarithmically singular integrals encountered for a toroidally axisymmetric confinement system, is easy to implement and is high-order accurate. As an illustration, we show how to apply this quadrature scheme for the efficient and accurate calculation of the normal component of the magnetic field due to the plasma current on the plasma boundary, via the virtual-casing principle.
Multi-site fatigue damage, hidden cracks in hard-to-reach locations, disbonded joints, erosion, impact, and corrosion are among the major flaws encountered in today's extensive fleet of aging aircraft and space vehicles. The use of in-situ sensors for real-time health monitoring of aircraft structures are a viable option to overcome inspection impediments stemming from accessibility limitations, complex geometries, and the location and depth of hidden damage. Reliable, structural health monitoring systems can automatically process data, assess structural condition, and signal the need for human intervention. Prevention of unexpected flaw growth and structural failure can be improved if on-board health monitoring systems are used to continuously assess structural integrity. Such systems are able to detect incipient damage before catastrophic failures occurs. Condition-based maintenance practices could be substituted for the current time-based maintenance approach. Other advantages of on-board distributed sensor systems are that they can eliminate costly, and potentially damaging, disassembly, improve sensitivity by producing optimum placement of sensors and decrease maintenance costs by eliminating more time- consuming manual inspections. This report presents a Sandia Labs-aviation industry effort to move SHM into routine use for aircraft maintenance. This program addressed formal SHM technology validation and certification issues so that the full spectrum of concerns, including design, deployment, performance and certification were appropriately considered. The Airworthiness Assurance NDI Validation Center (AANC) at Sandia Labs, in conjunction with Boeing, Delta Air Lines, Structural Monitoring Systems Ltd., Anodyne Electronics Manufacturing Corp. and the Federal Aviation Administration (FAA) carried out a certification program to formally introduce Comparative Vacuum Monitoring (CVM) as a structural health monitoring solution to a specific aircraft wing box application. Validation tasks were designed to address the SHM equipment, the health monitoring task, the resolution required, the sensor interrogation procedures, the conditions under which the monitoring will occur, the potential inspector population, adoption of CVM into an airline maintenance program and the document revisions necessary to allow for routine use of CVM as an alternate means of performing periodic structural inspects. To carry out the validation process, knowledge of aircraft maintenance practices was coupled with an unbiased, independent evaluation. Sandia Labs designed, implemented, and analyzed the results from a focused and statistically-relevant experimental effort to quantify the reliability of the CVM system applied to the Boeing 737 Wing Box fitting application. All factors that affect SHM sensitivity were included in this program: flaw size, shape, orientation and location relative to the sensors, as well as operational and environmental variables. Statistical methods were applied to performance data to derive Probability of Detection (POD) values for CVM sensors in a manner that agrees with current nondestructive inspection (NDI) validation requirements and also is acceptable to both the aviation industry and regulatory bodies. This report presents the use of several different statistical methods, some of them adapted from NDI performance assessments and some proposed to address the unique nature of damage detection via SHM systems, and discusses how they can converge to produce a confident quantification of SHM performance An important element in developing SHM validation processes is a clear understanding of the regulatory measures needed to adopt SHM solutions along with the knowledge of the structural and maintenance characteristics that may impact the operational performance of an SHM system. This report describes the major elements of an SHM validation approach and differentiates the SHM elements from those found in NDI validation. The activities conducted in this program demonstrated the feasibility of routine SHM usage in general and CVM in particular for the application selected. They also helped establish an optimum OEM-airline-regulator process and determined how to safely adopt SHM solutions. This formal SHM validation will allow aircraft manufacturers and airlines to confidently make informed decisions about the proper utilization of CVM technology. It will also streamline the regulatory actions and formal certification measures needed to assure the safe application of SHM solutions.
Packed beds are commonly found in many engineering systems and have been widely studied for decades. A relatively new packed bed system is the Pebble Bed Reactor, a type of generation-IV nuclear reactor. Unlike many of the packed beds encountered in chemical and process engineering applications, Pebble Bed Reactors are larger and operate at significantly higher Reynolds numbers. As a result of these differences, there is a very limited amount of information on the detailed flow physics that exist in these complex geometries. This work seeks to contribute to a growing database of flow data for Pebble Bed Reactor systems by performing Direct Numerical Simulations of the flow in an experimental bed of 67 pebbles for a range of conditions. Simulations are performed at a Prandtl number of 0.66 and Reynolds numbers from 300–600. These Reynolds numbers are chosen to gain additional knowledge on the spatial development of turbulence in these systems. Analysis of the Turbulent Kinetic Energy, turbulence anisotropy, and Turbulent Heat Flux is performed. Results demonstrate significant development of the TKE across the tested range of Reynolds numbers. Examination of both the TKE and THF reveal that development first occurs near the center of the bed and propagates radially as the flow moves further into the bed. Notable regions of negative production of turbulent kinetic energy are observed in regions where flow accelerates around pebble contact points. Furthermore, these regions are found to coincide with regions of 1-component turbulence.Kindly check and confirm, all authors email id is correctly identified.These are correct
Additive manufacturing is increasingly being employed to produce components of complex geometries in structural alloys because of the expected energy savings associated with the near-net-shape capability and the ability to build in novel internal features that are not possible with many conventional manufacturing approaches. However, because of the extreme thermal conditions encountered, the non-equilibrium microstructures produced during powder bed-based additive manufacturing processes must be subjected to custom post-heat treatment processes to recover the target mechanical properties. Phase-field models and simulation techniques have matured to a state where the microstructure evolution paths, and the morphologies of the resulting precipitate phases can be predicted reasonably accurately, considering alloy-specific thermodynamic and kinetic aspects of the nucleation and growth processes. However, phase-field simulations are computationally intensive, which precludes the ability to apply the simulations directly to the length scale of the entire component. Therefore, it is highly desirable to develop low-computational-cost surrogate models that effectively capture the physics at the microstructural length scale, while facilitating the design of optimized processing conditions resulting in location-specific targeted microstructures at the component scale. The work presented here demonstrates the application of the materials knowledge system framework to develop a surrogate model that effectively captures the microstructural path during annealing of a Ni–Mo–Nb alloy containing different Mo and Nb compositions known to segregate during solidification under additive manufacturing conditions. Specifically, the surrogate model built in this work is based on a Gaussian process autoregressive model informed by statistical representation of simulated microstructures using two-point correlations and dimensionality reduction through principal component analysis. In conclusion, this surrogate model is shown to capture the bifurcation of the microstructural path during precipitation, which yields a microstructure dominated by the $\gamma^{\prime\prime}$ phase at high Nb concentrations and the $\delta$ phase at low Nb concentrations.
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The previously established ExaCA software for performance portable alloy grain structure simulation has been updated to better represent the solidification behavior during complex alloy processing conditions, such as those encountered during metal additive manufacturing (AM), and for improved performance and scalability. Here, an extension to the time–temperature history input data format and the core ExaCA algorithm to include an arbitrary number of melting and solidification events yielded improved prediction of texture for various melt pool geometries, expanding the range of AM-relevant conditions that can be accurately simulated. Improved heat transport process simulation coupling, including the creation of large raster datasets from single track time–temperature history data and in-memory coupling with the new, performance portable finite difference code Finch, were also demonstrated in example studies on the effect of multilayer AM microstructure predictions on hatch spacing and cell size, respectively. Additional new features are detailed and demonstrated, including the ability to perform simulations using various interfacial response function forms, execute simulations on state-of-the-art hardware, improved usability through post-processing versatility, and improved strong and weak scaling performance. The performance, physics, and versatility improvements demonstrated here will further enable large-scale studies on AM process–microstructure relationships that were not previously possible. Furthermore, the usability improvements and ability to run coupled AM process–microstructure simulations using the Finch-ExaCA workflow will facilitate broader use of this open-source software by the computational materials community.
As part of a program to measure phase transition timescales in materials under dynamic compression, we have designed new x-ray imaging diagnostics to record multiple x-ray diffraction measurements during a single laser-driven experiment. Our design places several ns-gated hybrid CMOS (hCMOS) sensors within a few cm of a laser-driven target. The sensors must be protected from an extremely harsh environment, including debris, electromagnetic pulses, and unconverted laser light. Another key challenge is reducing the x-ray background relative to the faint diffraction signal. Building on the success of our predecessor (Target Diffraction In Situ), we implemented a staged approach to platform development. First, we built a demonstration diagnostic (Gated Diffraction Development Diagnostic) with two hCMOS sensors to confirm we could adequately protect them from the harsh environment and also acquire acceptable diffraction data. This allowed the team to quickly assess the risks and address the most significant challenges. Here, we also collected scientifically useful data during development. Leveraging what we learned, we recently developed a much more ambitious instrument (Flexible Imaging Diffraction Diagnostic for Laser Experiments) that can field up to eight hCMOS sensors in a flexible geometry and participate in back-to-back shots at the National Ignition Facility (NIF). The design also allows for future iterations, such as faster hCMOS sensors and an embedded x-ray streak camera. The enhanced capabilities of the new instrument required a much more complex design, and the unexpected issues encountered on the first few shots at NIF remind us that complexity has consequences. Our progress in addressing these challenges is described herein, as is our current focus on improving data quality by reducing x-ray background and quantifying the uncertainties of our diffraction measurements.
Studies of Ni–yttria-stabilized zirconia (YSZ) fuel electrode degradation mechanisms in solid oxide electrolysis cells (SOECs) are complicated by the different possible Ni–YSZ microstructures and compositions, and the variations in the H 2 /H 2 O ratio encountered in an electrolysis stack. Here, in this study, we describe a life testing scheme aimed at providing survey results on degradation as a function of the H 2 O–H 2 composition, with life tests carried out at five different steam contents from 90% to 10%. A Ni–YSZ-supported symmetric cell geometry is employed both with and without infiltrated nanoscale gadolinia-doped ceria (GDC). Impedance spectroscopy is utilized to observe changes in electrochemical characteristics during the life test, and a transmission-line-based equivalent circuit is used to model the data. Post-test electrode microstructures were observed. The results suggest that the GDC infiltrant reduces the electrode polarization resistance and provides more stable electrode polarization over a range of conditions.
A combination of ab initio and classical molecular dynamic simulations was used to explore the adsorption/desorption and diffusion characteristics of ion-exchange resins for extraction of organic anions in electrically-driven separation processes. We considered two classes of carboxylate mixtures that are commonly encountered in bioprocessing separations: a short chain fatty acid mixture (acetate/butyrate) and an aromatic mixture (ferulate/coumarate). The suitability of several resin materials including PFC100E, IRC86, PFA444 and IRA67 was interrogated. The decomposition of the interaction energies by the symmetry-adapted perturbation theory and the classical molecular dynamic simulations of organic diffusion together reveal that the geometries of the organic anions and the functional groups of the resins, as well as their Columbic interactions, are the controlling factors in the diffusion process of the organic compounds in these resins. Additionally, classical simulations also show that modifying the functionality of resin beads, the magnitude of electric fields, and the ratio of organic mixtures may provide an effective way to control the diffusion rate and obtain selective separation of these organic mixtures. Finally, a general suggestion for favorable separation conditions is summarized.
Overall, substantial progress was made on developing BCDI techniques in the direction of imaging defects in multi-crystal samples. Section 2.1 describes a new method to reconstruct the 3D atomic displacement field within a grain from multiple coherently resolved diffraction peaks. The key development is the ability to recover a best fit to the grain shape at the same time as the internal displacement (strain) variation with no prior knowledge of the microstructure. This is complemented by the development of a method, Sec. 2.2, to separate out sets of Laue reflections that belong to a single grain (and thus be able to index its orientation) in the commonly encountered situation in which the beam illuminates several grains in a given location. This is essential for enabling collection of coherent diffraction data (at APS 34-ID-C) from neighboring grains. All experiments depend on the quality of samples used. Although good progress has been made with thin film samples, we are working with a broader range of geometries. A new sample design uses a high-Z metal (e.g., Pt) deposited in a sub-micron trench in a low-Z metal (e.g., Al) so that the grain size is prevented from exceeding the current limit for BCDI. We also report in section 3.1 on successfully applying NF-HEDM to a fine-grain Mg sample that would normally be considered out of scope for the method. This represents progress towards being able to map out polycrystalline samples in 3D before performing BCDI on individual grains. We further report in section 3.2 on preliminary NF-HEDM characterization of a sample of UO2 that has sub-micron grains; the data imply the capability of mapping fine-grain polycrystals at 1-ID-E, again for the purposes of BCDI in the bulk. Lastly, our plan is to load grains in polycrystalline samples by inducing thermal stress. We also report the experimental measurements of the Ti- 6Al-4V alloy obtained at the European Synchrotron Radiation Facility (ESRF), which had been indexed and mapped via HEDM at APS in section 9. As discussed below, however, technique development pre-occupied the team throughout the project which meant that we did not make any significant progress towards answering the original hypotheses as stated in the proposal. In summary, we assert that we have made good progress in methods and samples and future work taking advantage of this progress is likely to obtain and analyze BCDI data from multiple adjacent grains in 3D polycrystals. Obtaining such data depends on re-gaining access to the Advanced Photon Source, which is anticipated in late summer or the Fall. In all cases, work has involved close collaboration with faculty, staff, postdocs and students from Brigham Young University (BYU), the Los Alamos National Laboratory and APS beamlines 1-ID and 34-ID.
Nuclear fuels using alloys of uranium, or metallic fuels, have many beneficial properties. The classical metallic fuel design uses a loose fitting cylindrical “slug” of fuel placed inside stainless-steel cladding tubes where the gap is filled with sodium. This sodium bond is liquid at operating temperature and conducts heat from the slug to the cladding, especially in early life before fuel swells into contact with the cladding. Despite the benefits of sodium bonding, there is a desire to develop metallic fuel technologies without it chiefly to reduce chemical reaction hazards in spent fuel storage from sodium fast reactors operating on once-through fuel cycles. Elimination of the sodium bond may also help unlock potential benefits for fuel fabrication, reactor neutronics, and compatibility with other types of reactors. Creating a sodium-free metallic fuel revolves around the problem of manufacturing fuel slug geometries which are in close contact with the cladding at beginning of life to facilitate heat transport while alleviating fuel-cladding chemical interactions (FCCI) at this interface and providing enough free volume to accommodate fuel swelling. Accelerating development and qualification of this fuel system will require careful selection of design and manufacturing options. To this end, a design trade-off study was performed to evaluate candidate options. Several design and manufacturing options were assessed, weighted, scored, and ranked with respect to fabrication, normal reactor operation, off-normal scenarios, and back-end considerations. This effort was performed both for “baseline” needs, which represented a once-through fuel cycle at temperatures and burnups known to be viable for sodium-bonded metallic fuel, and for “enhanced” needs to represent opportunities for closed fuel cycles and/or more aggressive temperatures/burnups. The outcomes of this study prioritized a baseline technology using U-Zr alloy with additives to mitigate FCCI, produced in annular slug geometry by continuous casting, clad in austenitic stainless-steel alloy, and followed by a final step to swage the cladding down to close the gap. This study prioritized an enhanced fuel technology using U-Mo alloy, also produced by continuous casting into an annular geometry, followed by coating/plating with an FCCI barrier on the slug, again with a final step to swage the cladding diameter down using oxide dispersion strengthened steel. It was noted that development of the enhanced fuel technology would entail more risk, thus U-Zr alloy was put forth as a backup to U-Mo if challenges are encountered with FCCI barriers, and advanced ferritic/martensitic steels are put forth as a backup to oxide dispersion strengthened steels if swaging and welding are found unworkable.
This report examines the sensitivity of salt cavern Mechanical Integrity Tests (MIT) to uncertainties in key test parameters. MIT's are used by cavern operators to detect and quantify leak rates in access wells in underground salt storage caverns and involve a suite of measured and assumed parameters that have a direct impact on the sensitivity of the testing to detect actual leaks from the cavern storage system. Determining the sensitivity of the testing to these different parameters provides a basis for understanding the results from, and informing the design criteria for, this type of testing. Without fully understanding the sensitivity of the test to the testing parameters, it is possible that the test results may not accurately reflect the integrity of the cavern system; an actual leak may be missed, or an intact system may be interpreted as leaking. This report reviews the main parameters included in MITs and examines how selected changes in their values can impact test results. The deviations used in the sensitivity analyses were designed to be within the ranges believed to be similar to those which may be encountered during testing. The results show that small, plausible fluctuations in some of the parameters measured values can have a significant impact on the testing results. Of the parameters studied here, the sensitivity analyses showed the order of importance to be (from highest to lowest): nitrogen-oil interface depth measurement, well bore temperature, well head pressure, and finally the internal geometry of the testing interval.
This report details the progress and activities of Idaho National Laboratory (INL) on the Nuclear Regulatory Commission (NRC) project “Development and Modeling Support for Advanced Non-Light Water Reactors.” The deliverables completed for this report are: Deliverable 1c: the capability to model gas mixtures was added to Pronghorn. A test problem mimicking the conditions achieved in a depressurized loss of forced cooling (DLOFC) event was solved with both RELAP-5 and Pronghorn. Pronghorn employed a finite vol ume method with the Kurganov-Tadmor discretization. The comparison between the mass fraction spatial profiles computed with RELAP-5 and Pronghorn clearly shows the presence of numerical artifacts (i.e., overly diffusive behavior at low Mach numbers). We confirmed that the problem disappears at higher Mach numbers. We recommend future work on the implementation of a low Mach finite volume formulation to better treat low Mach number problems. Deliverable 2a: we demonstrated two approaches to model the radiation/conduction/natural convection heat transfer across a stagnant gas for the PBMR-400 design using Pronghorn. The first approach is based on the net radiation method, which relies on the computation of view factors with the Multiphysics Object-Oriented Simulation Environment (MOOSE) ray tracing capability. The second method is a traditional thermal resistance approach. The test problems include both 2D and 3D geometries. In all cases, the results show very good agreement during a DLOFC transient. This confirms that the faster thermal resistance method produces solutions that are equivalent to the net radiation method for this geometry. Deliverable 3d: we demonstrated the use of the advection kernel for the delayed neutron precursor equation in Griffin with a 2D MSFR model. The results appear physical but further verification is recommended. We also recommend the addition of conjugate heat transfer to compute the temperatures and model the thermomechanic behavior of the reflectors and other structures. Significant memory and performance issues were encountered in the 3D axisymmetric model. Future work is recommended in this area. Task 8g: this task allows multidimensional MOOSE applications to be coupled to system codes (RELAP-7 and SAM). We implemented a faster multiphysics iteration coupling algorithm, which provides an overall 6× acceleration of the 3D-1D coupling of the core multidi- mensional fluid flow solver and the 1D primary and secondary loop model.