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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 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Numerical simulations of chaotic and complex spatiotemporal patterns in fractional reaction–diffusion systems

The generalized fractional reaction–diffusion equations which exist in the form of noninteger order partial differential equations have now found wide application for illustrating important and useful physical phenomena, such as subdiffusive and superdiffusive scenarios. The space fractional derivatives are defined in the Riesz sense on the intervals 0 < α < 1 and 1 < α ≤ 2. We propose robust numerical techniques, such as a spectral representation of the fractional Laplacian operator in conjunction with the exponential time differencing method, and present the equivalent relationship between the Riesz fractional derivative and fractional Laplacian operator. We apply these techniques to numerically solve a range of chaotic processes, such as the Chua’s equations, Rössler system, Lorenz and Lorenz-type systems. Simulation results revealed various complex and spatiotemporal chaos, spiral chaos, intermittent chaos and spots patterns in two-dimensional space fractional reaction–diffusion problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Modeling the diffusion of heat energy within composites of homogeneous materials using the uncertainty principle

The goal of this paper is to develop a highly accurate and efficient numerical method for the solution of a time-dependent partial differential equation with a piecewise constant coefficient, on a finite interval with periodic boundary conditions. The resulting algorithm can be used, for example, to model the diffusion of heat energy in one space dimension, in the case where the spatial domain represents a medium consisting of two homogeneous materials. The resulting model has, to our knowledge, not yet been solved in closed form through analytical methods, and is difficult to solve using existing numerical methods, thus suggesting an alternative approach. The approach presented in this paper is to represent the solution as a linear combination of wave functions that change frequencies at the interfaces between different materials. It is demonstrated through numerical experiments that using the Uncertainty Principle to construct a basis of such functions, in conjunction with a spectral method, a mathematical model for heat diffusion through different materials can be solved much more efficiently than with conventional time-stepping methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Global stability of a diffusive and delayed virus infection model with general incidence function and adaptive immune response

In this paper, the dynamical behaviors for a five-dimensional virus infection model with diffusion and two delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses and a general incidence function are investigated. The reproduction numbers for virus infection, antibody immune response, CTL immune response, CTL immune competition and antibody immune competition, respectively, are calculated. By using the Lyapunov functionals and linearization methods, the threshold conditions on the global stability of the equilibria for infection-free, immune-free, antibody response, CTL response and antibody and CTL responses, respectively, are established if the space is assumed as homogeneous. When the space is inhomogeneous, the effects of diffusion, intracellular delay and production delay are obtained by the numerical simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Characterising Ion-Irradiated FeCr: Hardness, Thermal Diffusivity and Lattice Strain

Ion-irradiated FeCr alloys are useful for understanding and predicting neutron damage in the structural steels of future nuclear reactors. Previous studies have largely focused on the structure of irradiation induced defects, probed by transmission electron microscopy (TEM), as well as changes in mechanical properties. Across these studies, a wide range of irradiation conditions has been employed on samples with different processing histories, which complicates the analysis of the relationship between defect structures and material properties. Furthermore, key properties, such as irradiation-induced changes in thermal transport and lattice strain, are little explored. Here we present a systematic study of Fe3Cr, Fe5Cr and Fe10Cr binary alloys implanted with 20 MeV Fe3+ ions to nominal doses of 0.01 dpa and 0.1 dpa at room temperature. Nanoindentation, transient grating spectroscopy (TGS) and X-ray micro-beam Laue diffraction were used to study the changes in hardness, thermal diffusivity and strain in the material as a function of damage and Cr content. Our results suggest that Cr leads to an increased retention of irradiation-induced defects, causing substantial changes in hardness and lattice strain. However, thermal diffusivity varies little with increasing damage and instead degrades significantly with increasing Cr content in the material. We find significant lattice strains even in samples exposed to a nominal displacement damage of 0.01 dpa. The defect density predicted from the lattice strain measurements is significantly higher than that observed in previous TEM studies, suggesting that TEM may not fully capture the irradiation-induced defect population. (C) 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

FeCr alloys↗
DOE OSTI2022

Predicting path-dependent diffusion barrier spectra in vast compositional space of multi-principal element alloys via convolutional neural networks

The emergent multi-principal element alloys (MPEAs) provide a vast compositional space to search for novel materials for technological advances. How to screen promising compositions from such an ample design space for targeted properties is a grand challenge. In this report, we demonstrate the state-of-the-art deep learning technology—convolutional neural network (CNN)—in predicting path-dependent vacancy migration energy barrier spectra, which are critical to diffusion behavior and many high-temperature properties, in the hyperdimensional composition space of MPEAs. The developed CNN model, fully capturing local chemical features surrounding each vacancy, accurately and efficiently predicts migration energy barrier of MPEAs with different degrees of chemical short-range order and at any unseen compositions. By varying the size of the local region encapsulating vacancy in the CNN model, we reveal that the length scale influencing vacancy migration is surprisingly extensive, up to its six nearest neighboring shells. The efforts of the CNN model make it promising for developing a database of diffusion barriers for various MPEA systems, which would have profound implications for accelerating alloy screening and discovering new compositions with desirable properties.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Transport Upscaling under Flow Heterogeneity and Matrix-Diffusion in Three-Dimensional Discrete Fracture Networks

For this work, we investigate the combined effects of network scale flow variability and retention due to matrix-diffusion on the scaling behavior of transport through fractured media. Two of the principal mechanisms controlling the transport of solutes through fractured low-permeability media are broad distributions of flow velocities and retention times in the solid matrix. We study the relative impact of these two processes under different initial conditions using a set of three-dimensional discrete fracture network simulations. We use these simulations to develop and calibrate an upscaled continuous time random walk (CTRW) approach for advective transport based on an Ornstein-Uhlenbeck model for the particle velocities that accounts for the fracture-matrix coupling using a compound Poisson process. This CTRW model can be conditioned on the initial solute distribution and allows to observe late-time scaling behavior at distances beyond what is feasible to observe using high-fidelity direct numerical simulations. We determine that the initial distribution of particles leads to marked differences in the persistent long-term scale behavior in the solute travel time distributions, even those undergoing retention due to matrix diffusion through implementation and analysis of the model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Synthesis of wafer-scale SWCNT forests with remarkably invariant structural properties in a bulk-diffusion-controlled kinetic regime

Robust synthesis of vertically aligned carbon nanotubes (VACNT) at large scale is required to accelerate deployment of numerous cutting-edge devices to emerging commercial applications. To address this need, this work demonstrates that the structural characteristics of single-walled CNTs (SWCNTs) produced in a growth regime dominated by bulk diffusion of the gaseous carbon precursor are remarkably invariant over a broad range of process conditions (precursor concentration increased up to 30-fold, catalyst substrate area from 1 cm 2 to 180 cm 2 , growth pressure from 20 to 790 mbar, and gas flowrates up to 8-fold). A simple growth kinetics model is derived that accounts for both reactant bulk diffusion and competing byproduct formation in the presence of excess hydrogen, which quantitatively reproduces the experimental data in the entire isothermal parameter space. The model enables critical predictions for process scale-up optimization including a potential 6-fold increase in CNT production rate, a ~90% carbon conversion efficiency in select conditions, and elimination of reaction rate decay observed at high pressures by using a hydrogen-free growth environment. This model-guided opportunity to substantially improve synthesis throughput and efficiency, in conjunction with the remarkably invariant CNT properties, is appealing for reliable VACNT device fabrication at both small and industrial scales.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Beyond the effectiveness factor: Multi-step reactions with intraparticle diffusion limitations

Though common in many industrial chemical processes, multi-step reactions occurring within porous catalyst particles provide significant challenges to previously established modeling frameworks. In this work, a system of reaction-diffusion equations is solved analytically via eigenanalysis. The intraparticle concentration profiles are integrated over the particle volume to obtain effectiveness factors for each reacting species, referred to herein as a multi-step effectiveness vector (MEV). The MEV solution is tested for the case of uniform flow past a stationary catalyst particle with a state-of-the-art, multi-step reaction scheme for fluid catalytic cracking (FCC). Outputs from particle-resolved direct numerical simulation (DNS) are compared to outputs from ordinary differentials with effective reaction closures coming from the MEV solution, the classic single-step effectiveness factor (SEF) (R. Aris, 'The mathematical theory of diffusion and reaction in permeable catalysts: The theory of the steady state,' Oxford University Press, 1975), and utilizing the intrinsic rates as-is. When compared to DNS, the MEV solution shows excellent agreement for the formation of all species and quantitatively captures the intraparticle concentration profiles. By contrast, the intrinsic treatment shows an over-prediction for product formation and the SEF treatment shows mixed levels of accuracy that depend upon the reaction coupling. Specifically, the SEF treatment accurately characterizes product formation if the kinetic scheme is weakly coupled but shows significant departure if stronger coupling is present. The computational cost associated with the MEV solution is associated with eigendecomposition of the Thiele matrix, an N x N matrix where N is the number of reacting components. Overall, the method is shown to be relatively easy to implement and may significantly enhance the fidelity of chemical reactor simulations that employ multi-step reaction schemes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Tracer particle transport dynamics in the diffusive sandpile cellular automaton

The confinement properties of the diffusive running sandpile are characterized by tracking the motion of a population of marked grains of sand. It is found that, as the relative strength of the avalanching to the diffusive transport channel is varied, a point is reached at which the particle global confinement time and the probability density functions of the jump-sizes and waiting-times of the tracked grains experience a sudden change, thus revealing a dynamical transition, that is consistent with previous studies (Newman DE et al., Phys Rev Lett 2002;88(20):204304). Across this transition, the sandpile moves from a regime characterized by self-similarity and memory, where avalanches of all possible sizes dominate transport across the system, to another regime where transport is taken over by near system-size, quasi-periodic avalanches. Values for the fractional transport exponents that quantify effective transport across the sandpile prior to the transition are also obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Diffuse back-illumination temperature imaging (DBI-TI), a novel soot thermometry technique

To meet stringent emissions regulations on soot emissions, it is critical to further advance the fundamental understanding of in-cylinder soot formation and oxidation processes. Among several optical techniques for soot quantification, diffuse back-illumination extinction imaging (DBI-EI) has recently gained traction mainly due to its ability to compensate for beam steering, which if not addressed, can cause unacceptably high measurement uncertainty. Until now, DBI-EI has only been used to measure the amount of soot along the line of sight, and here, we extend the capabilities of a DBI-EI setup to also measure in-cylinder soot temperature. This proof of concept of diffuse back-illumination temperature imaging (DBI-TI) as a soot thermometry technique is presented by implementing DBI-TI in a single cylinder, heavy-duty, optical diesel engine to provide 2-D line-of-sight integrated soot temperature maps. The potential of DBI-TI to be an accurate thermometry technique for use in optical engines is analyzed. The achievable accuracy is due in part to simultaneous measurement of the soot extinction, which circumvents the uncertainty in dispersion coefficients that depend on the optical properties of soot and the wavelength of light utilized. Analysis shows that DBI-TI provides temperature estimates that are closer to the mass-averaged soot temperature when compared to other thermometry techniques that are more sensitive to soot temperature closer to the detector. Furthermore, uncertainty analysis and Monte Carlo (MC) simulations provide estimates of the temperature measurement errors associated with this technique. The MC simulations reveal that for the light intensities and optical densities encountered in these experiments, the accuracy of the DBI-TI technique is comparable or even better than other established optical thermometry techniques. Thus, DBI-TI promises to be an easily implementable extension to the existing DBI-EI technique, thereby extending its ability to provide comprehensive line-of-sight integrated information on soot.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Slip delocalization and diffusion mediated carbide formation during fatigue of a nickel-base superalloy

Fatigue crack initiation at high temperatures occurs at microscopic fatigue shear bands that form near twin boundaries in polycrystalline nickel-base superalloys that contain minimal metallurgical defects. The associated dislocation sub-structure is complex and dependent on thermal and mechanical conditions. Here we show the formation of fine-scale carbide precipitates along these fatigue shear bands in a nickel-base superalloy during fatigue above 650 °C. The formation of carbide precipitates is studied using calculations of bulk and pipe diffusion. The contribution of pipe diffusion is observed to be critical in the formation of fine-scale carbides and occurs coincident with the delocalization of slip during fatigue.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Double Diffusion Maps and their Latent Harmonics for scientific computations in latent space

In this work, we introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion Maps on those latent coordinates allows the approximation of the reduced dynamical models. This second round enables mapping the latent space coordinates back to the full ambient space (what is called lifting); it also enables the approximation of full state functions of interest in terms of the reduced coordinates. In our work, we develop and test three different reduced numerical simulation methodologies, either through pre-tabulation in the latent space and integration on the fly or by going back and forth between the ambient space and the latent space. The data-driven latent space simulation results, based on the three different approaches, are validated through (a) the latent space observation of the full simulation through the Nyström Extension formula, or through (b) lifting the reduced trajectory back to the full ambient space, via Latent Harmonics. Latent space modeling often involves additional regularization to favor certain properties of the space over others, and the mapping back to the ambient space is then constructed mostly independently from these properties; here, we use the same data-driven approach to construct the latent space and then map back to the ambient space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Exponential Runge-Kutta Parareal for non-diffusive equations

Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial time-stepping methods. However, like many parallel-in-time methods it can fail to converge when applied to non-diffusive equations such as hyperbolic systems or dispersive nonlinear wave equations. Here, this paper explores the use of exponential integrators within the Parareal iteration. Exponential integrators are particularly interesting candidates for Parareal because of their ability to resolve fast-moving waves, even at the large stepsizes used by coarse propagators. This work begins with an introduction to exponential Parareal integrators followed by several motivating numerical experiments involving the nonlinear Schrödinger equation. These experiments are then analyzed using linear analysis that approximates the stability and convergence properties of the exponential Parareal iteration on nonlinear problems. The paper concludes with two additional numerical experiments involving the dispersive Kadomtsev-Petviashvili equation and the hyperbolic Vlasov-Poisson equation. These experiments demonstrate that exponential Parareal methods offer improved time-to-solution compared to serial exponential integrators when solving certain non-diffusive equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

42 ENGINEERING↗
DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Diffusion coefficient and nucleation density studies on electrochemical deposition of aluminum from chloroaluminate ionic liquid electrolytes

In this study, aluminum was electrodeposited from ionic liquids comprising a melt of alkyl imidazolium chlorides and aluminum chloride (AlCl 3 ). The ionic liquids utilized in this study were 1-ethyl-3-methyl-imidazolium chloride (EMIC)-AlCl 3 , 1-butyl-3-methylimidazolium chloride (BMIC)-AlCl 3 , and 1-hexyl-3-methyl-imidazolium chloride (HMIC)-AlCl 3 at the AlCl 3 mole fraction of 0.667 (molar ratio of 1:2). The electrochemical behavior of chloroaluminate species in the three ionic liquids was investigated by cyclic voltammetry (CV) and chronoamperometry (CA) techniques at different temperatures. The cyclic voltammograms indicated that the reduction of Al 2 Cl 7 – species to metallic aluminum followed a diffusion-controlled phenomenon. Moreover, even at a less negative applied potential, the higher current density was obtained for EMIC-AlCl 3 ionic liquid. That indicates that EMIC-AlCl 3 favors less energy consumption during the electrodeposition. The chronoamperometric analysis revealed that the onset of aluminum deposition from such ionic liquids proceeds via a three-dimensional instantaneous nucleation process. The concentrations of Al 2 Cl 7 – ions in the ionic liquids were calculated based on the thermodynamic data, which were 2520, 2271, and 2035 mol m –3 for EMIC-AlCl 3 , BMIC-AlCl 3 , and HMIC-AlCl 3 , respectively. The diffusion coefficient (D) values of Al 2 Cl 7 – species in such ionic liquids were also calculated at various temperatures. The D values determined from the CA technique at 363 K are 2.16 × 10 –11 , 1.03 × 10 –11 , and 0.87 × 10 –11 m 2 s –1 for EMIC-AlCl 3 , BMICAlCl 3 , and HMIC-AlCl 3 , respectively. In addition, the D value increased as temperature increased and decreased as the hydrocarbon group in the ionic liquid increased. As a result, the calculated grain sizes of nucleation range from 2 to 4 μm for these ionic liquids and are in good agreement with experimental data obtained from SEM micrographs.

42 ENGINEERING↗
DOE OSTI2023

Evolving radon diffusion through earthen barriers at uranium waste disposal sites

Field measurements of Rn-222 fluxes from the tops and bottoms of compacted clay radon barriers were used to calculate effective Rn diffusion coefficients (D Rn ) at four uranium waste disposal sites in the western United States to assess cover performance after more than 20 years of service. Values of D Rn ranged from 7.4 × 10 -7 to 6.0 × 10 -9 m 2 /s, averaging 1.42 × 10 -7 . Water saturation (S W ) from soil cores indicated that there was relatively little control of D Rn by S W , especially at higher moisture levels, in contrast to estimates from most steady-state diffusion models. Further, this is attributed to preferential pathways intrinsic to construction of the barriers or to natural process that have developed over time including desiccation cracks, root channels, and insect burrows in the engineered earthen barriers. A modification to some models in which fast and slow pathway D Rn values are partitioned appears to give a good representation of the data; 4% of the fast pathway was needed to fit the data regression. For locations with high S w and highest D Rn (and fluxes) at each site, the proportion of fast pathway ranged from 1.7% to 34%, but for many locations with lower fluxes, little if any fast pathway was needed.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Non-equilibrium molecular dynamics studies of thermal diffusion of hydrogen isotopes in low concentration zirconium hydrides

Tritium permeability in zirconium-based tritium getter critically impacts tritium storage and environmental safety during operation of tritium-producing burnable absorber rods (TPBARs). Previous experiments indicated that during irradiation operation, the hydrogen equilibrium pressured is increased. Further experimental and modeling studies suggested that the enhanced tritium release observed for reactor scale assemblies might be related to a thermal diffusion known as the Soret effect. A direct measurement of the Soret factor, however, has not been performed. To improve TPBAR and other nuclear applications, here we have applied two non-equilibrium molecular dynamics methods to study thermal diffusion of hydrogen isotopes in low-concentration zirconium hydrides. One of the methods produces sufficiently converged results to distinguish crystal orientation, isotope type, and concentration effects. In conclusion, with this method, crystal orientation, isotope type, and concentration effects are discussed.

36 MATERIALS SCIENCE↗