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A meshless stochastic method for Poisson–Nernst–Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Chemistry

Insight into pseudo-film-boiling in supercritical water under simplified interfacial conditions

The focus of this paper is the physics of supercritical water film boiling through the simulation of natural convection of supercritical water in a rectangular cavity. It has been widely believed that above a fluid's critical point, only one phase exists. However, recent research has indicated the existence of distinct gas-like and liquid-like regions separated by the Widom line, which is the locus of the maxima of the specific heat. Along the Widom line, density decreases sixfold, viscosity drops by a factor of two, while specific heat spikes by an order of magnitude. These variations, specifically in density and viscosity, produce a thick pseudo-interface and flow dynamics behavior akin to film-boiling, denoted here as pseudo-two-phase flow dynamics. When the cavity is heated from the bottom, a pseudo-film of gas-like fluid is formed at the heated wall, and the flow complexity evolves, characterized by the formation of multiple vortices. Results demonstrate the ability of modern conjugate heat transfer computational fluid dynamics to capture the pseudo two-phase regime, with the formation of a pseudo-film at the heated wall. Further, the boiling curve is studied, showing an increase in heat flux with an increase in the temperature differential between the wall and the pseudo-critical temperature. Furthermore, results also show a previously uncharacterized instability, where the convection cells in the cavity oscillate and can flip directions under certain conditions.

Computational fluid dynamics

Site-Projected Thermal Conductivity: Application to Defects, Interfaces, and Homogeneously Disordered Materials

With the rapid advance of high-performance computing and electronic technologies, understanding thermal conductivity in materials has become increasingly important. This study presents a novel method: the site-projected thermal conductivity that quantitatively estimates the local (atomic) contribution to heat transport, leveraging the Green–Kubo thermal transport equations. The effectiveness of this approach on disordered and amorphous graphene, amorphous silicon, and grain boundaries in silicon–germanium alloys is demonstrated. Amorphous graphene reveals a percolation behavior for thermal transport. The results highlight the potential of the method to provide new insights into the thermal behavior of materials, offering a promising avenue for materials design and performance optimization.

36 MATERIALS SCIENCE

Uniting Theory and Experiment to Deliver Flexible MOFS for Superior Methane (NG) Storage

The objective of the project was to use previous insights developed through synthesis and quantitative modeling of rigid metal–organic frameworks (MOFs) in an established synergistic theoretical/experimental team to create, modify, and evaluate flexible MOFs (FlexMOFs) for natural gas (NG) storage and release at practically useful pressures and transform the NG storage economy. The goal was reduced pressure absorbed natural gas (ANG) FlexMOF storage at operating pressures less than 100 bar with physisorption exploiting the favorable thermodynamics and kinetics of flexible porous material opening in response to adsorption. Hydrogen behavior in this context was also considered. The specific aim of the project was to design and develop a standard computational modeling methodology for, first, detailed atomistic retrodiction of FlexMOF gating behavior and ultimately prediction of the effects of functionalization and/or substitution on structural transitioning. The project was also geared towards the establishment of the interaction of methane with the framework and binding sites using modeling and the FlexMOF will be both internally and external validated as a SMART metric. This has value to the scientific community both from the obvious standpoint of providing a better understanding of the promising test case systems (CdIF-13 and the MIL-53(Al) series of MOFs), but also in providing an avenue of obtaining insight into these FlexMOF systems in general, which is of particular interest given the tendency of structure-function correlation to lag behind synthesis methodology (making the latter a hit or miss proposition for applications). This gap remains significant for FlexMOF systems whose gate opening behaviors complicate computational examination. The computational methodologies are relatively inexpensive in terms of both money and computational resources enhancing the general viability of these methodologies. The ultimate gain to the public will be in the application of these techniques to design systems for natural gas storage and use to cut down on green-house emissions.

03 NATURAL GAS

HFIR Activity Workbook Generator (HAWK) User Guide

The HFIR Activity WorkbooK generator (HAWK) is a Python code that automates and streamlines the activity calculation of samples after irradiation in the High Flux Isotope Reactor (HFIR). HAWK’s results provide estimates of the activity and nuclide inventory of irradiated specimens before they are moved to hot cell facilities, where they undergo post-irradiation examination. The samples’ activity results guide the packing of shipping containers and inform the accountable inventories for the hot cell facilities. The toolkit was originally developed by Charles Daily, a former R&D staff member at Oak Ridge National Laboratory (ORNL). As of May 2025, HAWK is developed by the Radiation Transport & HPC Methods Group (Nuclear Energy and Fuel Cycle Division) at ORNL. Figure 1 presents HAWK’s workflow. To use HAWK, users need to: 1. Develop an Excel input workbook (i.e., XLSX extension) containing data from the experiment’s materials, irradiation history (cycles), and irradiation positions. 2. Make minor edits to an existing template JSON file (i.e., auxiliary_data.JSON) and to the Python driver. The driver sets the necessary environment variables, defines the material compositions, and ultimately calls HAWK. Once configured, HAWK runs the Oak Ridge Isotope Generation code (ORIGEN) to calculate the masses, activities, and heat load at the end of irradiation for each isotope in the specimen. ORIGEN is part of SCALE, ORNL’s in-house computational tool for performing nuclear safety and design calculations. Following this step, HAWK postprocesses the results and generates three output workbooks summarizing the activity calculations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

Denoising of imaginary time response functions with Hankel projections

Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost—in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies. Published by the American Physical Society 2024

Yu, Yang (ORCID:0000000186178878)

SCALE 6.3 Validation: Nuclear Criticality Safety

The KENO codes have been used extensively around the world since their initial development in the 1960s. Therefore, a large number and wide range of validation reports have been generated for KENO by a variety of organizations. This section provides a synopsis of recent validation reports generated at ORNL, along with a brief list of some older validation reports generated in Oak Ridge, Tennessee. Some of the oldest reports are not attributed directly to ORNL, as the Y-12 Plant (currently the Y-12 National Security Complex), the K-25 Gaseous Diffusion Plant (now the East Tennessee Technology Park), and the X-10 Site (ORNL) were operated as a single entity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Sum-of-Fractions Method

Sum-of-fractions is a method intended to make sure a subcritical margin for aqueous solutions and slurries of fissionable isotopes exists. The method indicates that a system is subcritical if the sum of the ratios of the mass of each isotope (in a mixture) to its individual minimum subcritical mass limit is less than or equal to one. Historically, the basis of the sum-of-fractions has been derived from allowances given in the American National Standards Institute (ANSI)/ American Nuclear Society (ANS)-8.15-1981. However, the allowance was removed in ANSI/ANS-8.15-2014 due to a lack of technical basis. A methodology was developed to assess the validity of using the sum-of-fractions for water- or polyethylene-moderated systems for the following nuclides: 232U, 233U, 234U, 235U, 237Np, 236Pu, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, 241Am, 242mAm, 243Am, 242Cm, 243Cm, 244Cm, 245Cm, 246Cm, 247Cm, 249Cf, and 251Cf. The methodology uses available benchmark data for mixtures of 233U, 235U, and 239Pu to establish the calculational margin, and a mass limit reduction to establish the margin of subcriticality. Water- or polyethylene-moderated and -reflected mixtures containing the nuclides are evaluated with the code system, SCALE 6.2.4. Including the calculational margin, subcritical mass limits for each nuclide were computed for optimally water- or polyethylene-moderated and fully reflected systems. These masses were used to create nuclide mixtures in which the sum of the mass to subcritical mass limit ratios is one. The various nuclide mixtures were modeled over a range of moderation and demonstrate the keff does not exceed the calculational margin. For additional assurance of subcriticality, a significant mass reduction is applied to each computed minimum critical mass of the nuclides without adequate benchmark data consistent with the method in ANSI/ANS-8.15-2014.

criticality safety, Actinide

Relative sensitivity of plastic scintillator: A comparative analysis with 60 Co gamma rays, deuterium–deuterium, and deuterium–tritium neutrons

A plastic scintillator has found extensive application in the realm of high-energy physics and national security science. Many applications in those fields often involve the simultaneous production of photons, neutrons, and charged particles, which makes the relative sensitivity information for these different radiation types important. In this study, we have adopted a multi-head detector comprised of a plastic scintillator and high gain phototubes, which provides a large dynamic range and linearity. A comparative study on the relative sensitivities of plastic scintillators was facilitated by adopting three distinct radiation calibration sources (i.e., 60 Co γ rays, DD neutrons, and DT neutrons). Neutrons from a DD source generate a comparable level of scintillation to gamma rays emitted by 60 Co (i.e., 60 Co-γ/DD-n = 0.92 ± 16%). DT neutrons induce ~3.5 times the scintillation observed with DD neutrons (i.e., DT-n/DD-n = 3.5 ± 28%). In addition, the Geant4 simulation granted us valuable insights into the relative sensitivity of the scintillator. This comparative study will provide a useful database for users in diverse applications.

47 OTHER INSTRUMENTATION

Computational methods based on density functional theory for reactions and processes involving electronic spin (Final Technical Report)

This award supports one post-doctoral researcher for 1.5 years. Publications that acknowledge this grant: Refs. 1–14. Refs. 3,10,12 assess current methodology for the evaluation of magnetic exchange couplings in transition metal complexes. In particular, Ref. 10 validates the use of an approximate (non-iterative) Green’s function approach for the calculation of magnetic exchange couplings and will be the foundation for Thrust 2 in this proposal. Refs. 3 and 12 focus on widely used density functional approaches based on the standard energy differences methodology for the particular case of oxo-bridged Fe(III) complexes. Refs. 2,4–7,11 apply current methodologies to problems of practical interest in molecular magnetism. Ref. 13 presents a methodology to explicitly simulate the dynamics of open quantum systems within density functional theory (DFT) calculations based on the Liouville-von Neumann equation of motion for quantum systems driven out-of-equilibrium. Ref. 8 uses non-collinear spin DFT to explain the mechanical behavior of magnetic mono-atomic Pt wires produced in break-junction experiments in the presence of a magnetic field.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Green’s Function Perspective on the Nonlinear Density Response of Quantum Many-Body Systems

We derive equations of motion for higher order density response functions using the theory of thermodynamic Green’s functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin–Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.

Density Functional Theory

In the Mix : A Workshop Merging Computational Chemistry and Electrochemistry Alongside Data Science

As chemistry expands to more complex and interdisciplinary areas, a new generation of diverse researchers must engage with science and learn effective cross-disciplinary collaboration and communication. To these ends, we designed and implemented In the Mix, a graduate student-led, two-day workshop for undergraduate students promoting collaborative science in the context of energy storage innovations. Here, the interactive workshop was designed for future and emerging researchers to gain hands-on experience with data science, computational chemistry, and electrochemistry techniques that are critical for developing materials for battery technologies. Participants also visited commercial renewable energy facilities to help them connect discovery-based research with industry and broader societal considerations. The workshop content and structure ensured that participants experienced the interrelatedness of the fields and understood the importance of collaborative research to yield scientific advances with real-world applications. An external team evaluated the workshop and participants’ perceptions of their experiences. While our research context was energy storage, the workshop goals and outcomes are applicable to other contexts. Interdisciplinary, experiential workshops are a key avenue to broadening participation in science and research, and the ideas presented here can be readily modified for other scientific contexts and/or incorporated as broader impact activities.

25 ENERGY STORAGE

The MOOSE fluid properties module

The Fluid Properties module within the Multiphysics Object-Oriented Simulation Environment (MOOSE) is used to compute fluid properties for numerous applications, ranging from nuclear reactor thermal hydraulics to geothermal energy. Those applications drove the development of the module to enable numerous different fluid equations of states, property lookups with primitive and conserved flow variable to cater to pressure and density-driven solvers, and an object-oriented design facilitating expansion and maintenance. Each fluid property is implemented in its own class but inherits capabilities such as automatic differentiation, automated out-of-bounds handling or variable conversion capabilities. Here, this paper presents the module, its design, its user and developer interface, its content in terms of fluids and properties, and several of its applications showing its major role in the MOOSE simulation ecosystem.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Multihead Attention U‐Net for Magnetic Particle Imaging–Computed Tomography Image Segmentation

Magnetic particle imaging (MPI) is an emerging noninvasive molecular imaging modality with high sensitivity and specificity, exceptional linear quantitative ability, and potential for successful applications in clinical settings. Computed tomography (CT) is typically combined with the MPI image to obtain more anatomical information. Herein, a deep learning‐based approach for MPI‐CT image segmentation is presented. The dataset utilized in training the proposed deep learning model is obtained from a transgenic mouse model of breast cancer following administration of indocyanine green (ICG)‐conjugated superparamagnetic iron oxide nanoworms (NWs‐ICG) as the tracer. The NWs‐ICG particles progressively accumulate in tumors due to the enhanced permeability and retention (EPR) effect. The proposed deep learning model exploits the advantages of the multihead attention mechanism and the U‐Net model to perform segmentation on the MPI‐CT images, showing superb results. In addition, the model is characterized with a different number of attention heads to explore the optimal number for our custom MPI‐CT dataset.

Juhong, Aniwat

Degenerate coupled-cluster theory

A size-extensive, converging, black-box, ab initio coupled-cluster (ΔCC) ansatz is introduced that computes the energies and wave functions of states from any degenerate or nondegenerate Slater-determinant references with any numbers of α- and β-spin electrons, any patterns of orbital occupancy, any spin multiplicities, and any spatial symmetries. For a nondegenerate reference, it reduces to the single-reference coupled-cluster ansatz. For a degenerate multireference, it is a natural coupled-cluster extension of degenerate Møller–Plesset perturbation (ΔMP) theory. For ionized and electron-attached references, it is a coupled-cluster Green’s function, although the present theory is convergent toward the full-configuration-interaction limits, while the Feynman–Dyson many-body Green’s function (MBGF) theory generally is not. Its single-excitation instance is a projection Hartree–Fock theory as per the Thouless theorem, which may be useful for core ionizations, high-spin states, and possibly electron affinities. Additionally, a new multireference coupled-cluster theory for a general model space is developed. This quasidegenerate coupled-cluster (QCC) theory is exactly converging, but not black-box, and intended for strong correlation. Determinant-based, general-order algorithms of ΔCC and QCC theories are implemented and compared with configuration-interaction (CI) and equation-of-motion coupled-cluster (EOM-CC) theories through octuple excitations and with ΔMP and MBGF theories up to the nineteenth order. An algebraic, optimal-scaling algorithm of the ΔCC theory is computer-synthesized at the levels of single excitations (ΔCCS) and of single and double excitations (ΔCCSD). As a result, the order of performance is QCC ≈ ΔCC > EOM-CC > CI at the same order or QCC ≈ ΔCC > ΔMP > MBGF at the same cost scaling.

Hirata, So [University of Illinois at Urbana-Champ

A simple three-component mixing problem for the evaluation of a new reaction rate model

A simple computational mixing problem is presented which can be utilized to assess the behavior of Reynolds-averaged reaction rate models in a problem with temporally varying mixedness. In this problem, three mixing components are homogeneously distributed but initially separated in a triply periodic domain. Further, these components are initialized within a Taylor–Green-like velocity field, which creates a mixing history evolving from the so-called “no-mix limit” to a well-mixed state. Large-eddy simulation results from this problem in configurations involving both premixed and nonpremixed reactants are then compared with zero-dimensional Reynolds-averaged Navier–Stokes results utilizing a new model for multicomponent reacting mixtures. The new model is shown to appropriately respect the no-mix limit and outperforms an earlier model (Morgan, 2022), particularly at early times when components are near the no-mix limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Para-particle oscillator simulations on a trapped-ion quantum computer

Deformed oscillators allow for a generalization of the standard fermions and bosons, namely, for the description of para-particles. Such particles remain hypothetical and unobserved in nature; yet, they can model physical phenomena, such as topological phases of matter. Here, we report the digital quantum simulation of para-particle oscillators by mapping para-particle states to the state of a qubit register, which allows us to identify the para-particle oscillator Hamiltonian as an XY model and further digitize the system onto a universal set of gates. In both instances, the gate depth grows polynomially with the number of qubits used. To establish the validity of our results, we experimentally simulate the dynamics of para-fermions and para-bosons, demonstrating full control of para-particle oscillators on a quantum computer. Furthermore, we compare the overall performance of the digital simulation of dynamics of the driven para-Fermi oscillator to a recent analog quantum simulation result.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Fundamental Studies of the Vibrational, Electronic, and Photophysical Properties of Tetrapyrrolic Architectures

The ability to capture and utilize light in the near-ultraviolet (NUV), visible and near-infrared (NIR-I and NIR-II) spectral regions (i.e., 320–400, 400–700, 700–1000, 1000–1700 nm) is essential for any solar-energy conversion scheme. Nature employs chlorophylls and bacteriochlorophylls in light-harvesting architectures to absorb light in the blue and red/NIR regions. Accessory pigments (carotenoids, bilins) augment absorption of the (bacterio)chlorophylls in the green region. The harvested energy is funneled to a reaction center protein, where charge separation occurs. Subsequent migration of the electron and the hole stabilizes and stores the energy from light via redox chemistry. The long-term objective of the Bocian/Holten&Kirmaier/Lindsey research program under this DOE grant has been to develop tetrapyrrole-based molecular architectures that absorb sunlight, funnel energy and separate charge with high efficiency. Integral to the program has been iterative cycles of design, synthesis and characterization that provided deep insights into the relationships between chemical composition, electronic structure, and key static and dynamic properties (vibrational, redox, photophysical, energy/charge transfer) of tetrapyrrolic systems. Such architectures included monomers, dyads, larger arrays, and complexes with accessory components. The objective was to develop molecular designs and guiding principles to enhance current and future energy-conversion schemes. Molecular arrays targeted to address one or more fundamental questions concerning light harvesting and energy/charge transfer were constructed from analogues of the naturally occurring hemes, chlorophylls and bacteriochlorophylls. Diverse, tunable synthetic building blocks were prepared that spanned the three respective tetrapyrrole families, which are the porphyrins, chlorins and bacteriochlorins. Thus, the research focused on porphyrins as well as synthetic surrogates for chlorophylls (chlorins, 13 1 -oxophorbines and chlorin-imides) and bacteriochlorophylls (bacteriochlorins, bacterio-13 1 -oxophorbines and bacteriochlorin-imides), generically termed hydroporphyrins. Although the three tetrapyrrole classes (porphyrins, chlorins and bacteriochlorins) absorb light strongly in the violet-blue spectral region, the long-wavelength absorption band typically lies in the green-orange, red, and NIR regions, respectively, with increasing intensity. Understanding the spectra, electronic structure, and energy/charge-transfer properties of such tetrapyrrolic macrocycles is of central importance for the rational design of molecular architectures for solar-energy conversion. Our integrated program of molecular design and synthesis coupled with a variety of spectroscopic, electrochemical, and computational studies have probed from first principles how structural and electronic properties of tetrapyrrolic macrocycles dictate spectral properties as well as the rates of ground-state hole/electron transfer and excited-state energy flow in multicomponent architectures. Individual molecules and multicomponent architectures were designed to test ideas of fundamental importance, often requiring the development of new synthetic methodology. The members of the collaborative team had almost daily discussions by phone and/or e-mail concerning design of molecules, flow of compounds between the labs, planning of physical characterization studies, discussing results and analysis and integrating into design of next generation architectures, and the preparation of manuscripts. Furthermore, students and postdocs in the different labs routinely communicated with one another to facilitate the advancement of the research activities. In short, a highly integrated and collaborative research program was well established among the groups. The research effort involved molecular design and synthesis of synthetic molecular architectures by the Lindsey group integrated with physicochemical and photophysical characterization by the Bocian group and the Holten&Kirmaier group (Figure 2). The Bocian group carried out electrochemical, electron paramagnetic resonance (EPR), resonance Raman (RR), and Fourier-transform infrared (FT-IR) studies, as well as density functional theory (DFT) calculations and the time-dependent extension (TDDFT) to gain insight into excited-state properties. The Holten&Kirmaier group carried out static and time-resolved absorption and fluorescence spectroscopy studies and simulated absorption spectra using molecular orbital (MO) energies from DFT as input to the four-orbital model to complement the TDDFT calculations. The combined measurements provided understanding of the vibrational/electronic properties of the individual molecules and the changes that occur upon incorporation into multicomponent architectures. This information underpinned elucidating the mechanisms and timescales of ground-state hole/electron transfer and excited-state energy and charge transfer.

14 SOLAR ENERGY