SEARCH · Search NASA

Results for “Numerical diffusion”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,603 records · Page 89

All sources NASA NTRS DOE OSTI

DOE OSTI2022

A flexible linear diffusion acceleration to k-eigenvalue neutron transport with SN discontinuous finite element method

In this paper, we derive a flexible linear diffusion acceleration (LDA) for k-eigenvalue neutron transport discretized with discontinuous finite element method (DFEM) and discrete ordinates(SN). This LDA is based on our two pieces of previous works: the flexible non linear diffusion acceleration (NDA) for DFEM-SN and LDA for k-eigenvalue neutron transport using pre-conditioned Jacobian-free Newton-Krylov with self-adjoint angular flux (SAAF), continuous finite element method(CFEM), and SN. We point out the differences between LDA and NDA for DFEM-SN and the difference between DFEM-SN and SAAF-CFEM-SN for LDA. Numerical tests are presented to compare the convergence behaviour of NDA and LDA. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients

In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.

convection–diffusion–reaction equation↗

DOE OSTI2019

Effects of grain boundaries on conversion efficiencies of single-crystal-like GaAs thin-film solar cells on flexible metal tapes

We present a numerical simulation study of the effects of low-angle grain boundaries (GBs) in a single-crystal-like GaAs thin-film material on its photovoltaic performance. Here, 1D and 2D modeling are employed to simulate a solar-cell (SC) device based on the properties of single-crystal-like GaAs thin films grown on metal tape. Properties include minority carriers’ mobility, carrier lifetimes, and diffusion length. The 1D model, by incorporating a uniform biaxially textured GaAs compared to single crystal GaAs, predicts an efficiency ~21% for average carrier lifetimes of 1 ns. This result is not consistent with an experimental results showing an efficiency of 4.3%. 1D simulation generally works well for the prediction of conventional crystalline SC I-V characteristics, but it fails for newly-developed single-crystal-like GaAs SC devices with different material properties and non-vertical device geometry. Hence, we develop a 2D model to study the effect of localized recombination centers in the material by defining different regions of defective low-angle grain boundaries and single crystalline intra-grains. The 2D model is comparable to the experimental results mainly due to its capability to consider localized material inhomogeneity and lateral carriers dynamic. The effect of grain boundary density on SC performance is studied by 2D modeling. Increasing the grain size of GaAs from 2 μm to 50 μm can improve efficiency from 4.8% to 12.3%. The open-circuit voltage (Voc) shows more sensitivity to varying grain boundary densities than other SC characteristic factors. The 2D model is also employed to study bulk passivation of GBs and suggests that an efficiency of ~19.5% is achievable in the single-crystal-like GaAs SCs even with a small grain size of 2 μm, if effective grain boundary passivation is applied.

14 SOLAR ENERGY↗

DOE OSTI2016

Mechanochemical spinodal decomposition: a phenomenological theory of phase transformations in multi-component, crystalline solids

Here, we present a phenomenological treatment of diffusion-driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes diffusional phase transformations that are accompanied by symmetry-breaking structural changes of the crystal unit cell and reveals the importance of a mechanochemical spinodal, defined as the region in strain-composition space, where the free-energy density function is non-convex. The approach is relevant to phase transformations wherein the structural order parameters can be expressed as linear combinations of strains relative to a high-symmetry reference crystal. The governing equations describing mechanochemical spinodal decomposition are variationally derived from a free-energy density function that accounts for interfacial energy via gradients of the rapidly varying strain and composition fields. A robust computational framework for treating the coupled, higher-order diffusion and nonlinear strain gradient elasticity problems is presented. Because the local strains in an inhomogeneous, transforming microstructure can be finite, the elasticity problem must account for geometric nonlinearity. An evaluation of available experimental phase diagrams and first-principles free energies suggests that mechanochemical spinodal decomposition should occur in metal hydrides such as ZrH 2-2c . The rich physics that ensues is explored in several numerical examples in two and three dimensions, and the relevance of the mechanism is discussed in the context of important electrode materials for Li-ion batteries and high-temperature ceramics.

36 MATERIALS SCIENCE↗

DOE OSTI2015

ESTIMATION OF THE RELEASE TIME OF SOLAR ENERGETIC PARTICLES NEAR THE SUN

This paper investigates the onset time of solar energetic particle (SEP) events with numerical simulations and analyzes the accuracy of the velocity dispersion analysis (VDA) method. Using a three-dimensional focused transport model, we calculate the fluxes of protons observed in the ecliptic at 1 AU in the energy range between 10 MeV and 80 MeV. In particular, three models are used to describe different SEP sources produced by flare or coronal shock, and the effects of particle perpendicular diffusion in the interplanetary space are also studied. We have the following findings. When the observer is disconnected from the source, the effects of perpendicular diffusion in the interplanetary space and particles propagating in the solar atmosphere have a significant influence on the VDA results. As a result, although the VDA method is valid with impulsive source duration, low background, and weak scattering in the interplanetary space or fast diffusion in the solar atmosphere, the method is not valid with gradual source duration, high background, or strong scattering.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Investigation of low GWP Flammable Refrigerant Leak from Rooftop Units

One of the recent global trends in the air conditioning industry is to replace the high global warming potential (GWP) refrigerants such as R410A and R134A with alternative refrigerants that have lower GWP. However, most of these alternative refrigerants are classified as slightly flammable (classified by ASHRAE as A2L) which impose a potential fire risk. Therefore, research efforts have focused on the study of flammable refrigerants and their potential risk. In this paper, we present a numerical investigation to study one R32 (ASHRAE A2L) leak scenario from a 5 ton rooftop unit into a conference room with the dimensions of 40 Ã 30 Ã 8 ft (12.2 Ã 9.1 Ã 2.4 m). A catastrophic rupture of a Â-inch refrigerant line was simulated. A total charge of 15lb (6.8 kg) was leaked in 31.5 seconds. A mixture of air and refrigerant is diffused from four air diffusers mounted in the ceiling. The ducting system was simulated first to predict the air/refrigerant mixure entering the room from the four air diffusers.The total simulation time was 10 minutes to study the refrigerant diffusion and dispersion of the flammable refrigerant in the room after the inception of the leakage. The volume fraction is presented as a function of time at different monitoring points inside the room. The total room volume where the R32 concentration exceeds its LFL is quantified and presented as an indication of the risk of ignition.

Elatar, Ahmed↗

DOE OSTI2015

GRIZZLY Model of Multi-Reactive Species Diffusion, Moisture/Heat Transfer and Alkali-Silica Reaction for Simulating Concrete Aging and Degradation

Concrete is widely used in the construction of nuclear facilities because of its structural strength and its ability to shield radiation. The use of concrete in nuclear power plants for containment and shielding of radiation and radioactive materials has made its performance crucial for the safe operation of the facility. As such, when life extension is considered for nuclear power plants, it is critical to have accurate and reliable predictive tools to address concerns related to various aging processes of concrete structures and the capacity of structures subjected to age-related degradation. The goal of this report is to document the progress of the development and implementation of a fully coupled thermo-hydro-mechanical-chemical model in GRIZZLY code with the ultimate goal to reliably simulate and predict long-term performance and response of aged NPP concrete structures subjected to a number of aging mechanisms including external chemical attacks and volume-changing chemical reactions within concrete structures induced by alkali-silica reactions and long-term exposure to irradiation. Based on a number of survey reports of concrete aging mechanisms relevant to nuclear power plants and recommendations from researchers in concrete community, we’ve implemented three modules during FY15 in GRIZZLY code, (1) multi-species reactive diffusion model within cement materials; (2) coupled moisture and heat transfer model in concrete; and (3) anisotropic, stress-dependent, alkali-silica reaction induced swelling model. The multi-species reactive diffusion model was implemented with the objective to model aging of concrete structures subjected to aggressive external chemical attacks (e.g., chloride attack, sulfate attack, etc.). It considers multiple processes relevant to external chemical attacks such as diffusion of ions in aqueous phase within pore spaces, equilibrium chemical speciation reactions and kinetic mineral dissolution/precipitation. The moisture/heat transfer module was implemented to simulate long-term spatial and temporal evolutions of the moisture and temperature fields within concrete structures at both room and elevated temperatures. The ASR swelling model implemented in GRIZZLY code can simulate anisotropic expansions of ASR gel under either uniaxial, biaxial and triaxial stress states, and can be run simultaneously with the moisture/heat transfer model and coupled with various elastic/inelastic solid mechanics models that were implemented in GRIZZLY code previously. This report provides detailed descriptions of the governing equations, constitutive equations and numerical algorithms of the three modules implemented in GRIZZLY during FY15, simulation results of example problems and model validation results by comparing simulations with available experimental data reported in the literature. The close match between the experiments and simulations clearly demonstrate the potential of GRIZZLY code for reliable evaluation and prediction of long-term performance and response of aged concrete structures in nuclear power plants.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

Modeling the measured effect of a nitroplasticizer (BDNPA/F) on cookoff of a plastic bonded explosive (PBX 9501)

Here, we have used a modified version of the Sandia Instrumented Thermal Ignition (SITI) experiment to develop a pressure-dependent, five-step ignition model for a plastic bonded explosive (PBX 9501) consisting of 95 wt% octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazoncine (HMX), 2.5 wt% Estane® 5703 (a polyurethane thermoplastic), and 2.5 wt% of a nitroplasticizer (NP): BDNPA/F, a 50/50 wt% eutectic mixture bis(2,2-dinitropropyl)-acetal (BDNPA) and bis(2,2-dinitropropyl)-formal (BDNPF). The five steps include desorption of water, decomposition of the NP to form NO2, reaction of the NO2 with Estane® and HMX, and decomposition of HMX. The model was fit using our experiments and successfully validated with experiments from five other laboratories with scales ranging from about 2 g to more than 2.5 kg of PBX. Our experimental variables included density, confinement, free gas volume, and temperature. We measured internal temperatures, confinement pressure, and ignition time. In some of our experiments, we used a borescope to visually observe the decomposing PBX. Our observations included the endothermic β–δ phase change of the HMX, a small exothermic temperature excursion in low-density unconfined experiments, and runaway ignition. We hypothesize that the temperature excursion in these low density experiments was associated with the NP decomposing exothermically within the PBX sample. This reactant-limited temperature excursion was not observed with our thermocouples in the high-density experiments. For these experiments, we believe the binder diffused to the edges of our high density samples and decomposed next to the highly conductive wall as confirmed by our borescope images.

42 ENGINEERING↗

DOE OSTI2013

Response of a partial wall to an external perturbation of rotating plasma

In this paper, we present the response of a 3D thin multiply connected wall to an external kink mode perturbation in axisymmetric tokamak configurations. To calculate the contribution of the plasma perturbed magnetic field in the vacuum region, we have made use of the concept of surface currents [following C. V. Atanasiu, A. H. Boozer, L. E. Zakharov, and A. A. Subbotin, Phys. Plasmas 6, 2781 (1999)]. The wall response is expressed in terms of a stream function of the wall surface currents, which are obtained by solving a diffusion type equation, taking into account the contribution of the wall currents themselves iteratively. The use of stream function makes the approach applicable for both well-studied earlier Resistive Wall Modes and for Wall Touching Kink Modes, which were discovered recently as a key phenomenon in disruptions [L. E. Zakharov, S. A. Galkin, and S. N. Gerasimov, Phys. Plasmas 19, 055703 (2012)]. New analytical expressions, suitable for numerical calculations of toroidal harmonics of the vacuum magnetic fields from the surface currents on axisymmetric shells, are derived.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Dynamic heterogeneity in crossover spin facilitated model of supercooled liquid and fractional Stokes-Einstein relation

Kinetically constrained models have gained much interest as models that assign the origins of interesting dynamic properties of supercooled liquids to dynamical facilitation mechanisms that have been revealed in many experiments and numerical simulations. In this work, we investigate the dynamic heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the model that linearly interpolates between the strong liquid-like behavior and the fragile liquid-like behavior by an asymmetry parameter b. When the asymmetry parameter is sufficiently small, smooth fragile-to-strong transition is observed both in the relaxation time and the diffusion constant. Using these physical quantities, we investigate fractional Stokes-Einstein relations observed in this model. When b is fixed, the system shows constant power law exponent under the temperature change, and the exponent has the value between that of the Frederickson-Andersen model and the East model. Furthermore, we investigate the dynamic length scale of our systems and also find the crossover relation between the relaxation time. We ascribe the competition between energetically favored symmetric relaxation mechanism and entropically favored asymmetric relaxation mechanism to the fragile-to-strong crossover behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Transition from weak to strong turbulence in magnetized plasmas

Abstract The scaling of turbulent heat flux with respect to electrostatic potential is examined in the framework of a reduced (4D) kinetic system describing electrostatic turbulence in magnetized plasmas excited by the ion temperature gradient instability. Numerical simulations were instigated by, and tested the predictions of generic renormalized turbulence models like the 2D fluid model for electrostatic turbulence (Zhang and Mahajan 1993 Phys. Fluids B 5 2000). A fundamental, perhaps, universal result of this theory-simulation combination is the demonstration that there exist two distinct asymptotic states (that can be classified as weak turbulence (WT) and strong turbulence (ST) states) where the turbulent diffusivity Q scales quite differently with the strength of turbulence measured by the electrostatic energy ∥ ϕ ∥ 2 . In the case of WT Q ∝ ∥ ϕ ∥ 2 , while in ST Q has a weaker dependence on the electrostatic energy and scales as ∥ ϕ ∥ .

Bratanov, Vasil↗

DOE OSTI2018

Use of Physics Based Management Optimization for Groundwater Remedy Design - 18671

Numerical modeling coupled with formal mathematical optimization techniques was used to design a groundwater remedy strategy to address a carbon tetrachloride (CCl{sub 4}) plume covering several square miles. The optimization approach, methodology, and project costs are described. The site consists of a large grain elevator in Nebraska. CCl{sub 4} was used as a fumigant and subsequently impacted soils and groundwater. Remedy design focused on the more diffuse plume, which extended approximately 4.5 miles down gradient of the source area. An eleven-layer model was developed and calibrated to observed groundwater conditions. This model was linked with formal optimization techniques to identify the best design capable of meeting client specified requirements and well location limitations. The planned system included requirements on the location of extraction and injection wells, total system flow rate, number of management periods, and specific constraints limiting further plume expansion. A separate trinitrotoluene (TNT) contaminant plume from a third party was located vertically above the leading edge of the CCl{sub 4} plume within the same aquifer. A further constraint imposed was that the design could not affect or cause additional migration of the TNT plume. Optimal system design was determined using HydroGeoLogic's Physics Based Management Optimization (PBMO{sup TM}) system. Over 38,000 candidate solutions consisting of different combinations of pumping and injection wells locations and rates, were evaluated through flow modeling coupled with either particle tracking or fully convective-dispersive transport simulations to determine the optimal design. Planning for installation of the optimal design is underway. Simulations were completed on a distributed computing platform consisting of 3 Quad Core PCs. Flow and particle tracking simulations required less than 2 minutes per simulation. Coupled flow and transport simulation run times were generally between 30-40 minutes per simulation. The total costs for developing the groundwater flow model and completing the subsequent optimal design were approximately $400,000. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2016

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. The latter demystifies the Maxwell's demon by statistically describing non-isolated systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

The impact of immobile zones on the transport and retention of nanoparticles in porous media

Nanoparticle transport and retention within porous media is treated by conceptualizing the porous media as a series of independent collectors (e.g., Colloid Filtration Theory). This conceptualization assumes that flow phenomena near grain–grain contacts, such as immobile zones (areas of low flow), exert a negligible influence on nanoparticle transport and assumes that retention and release of particles depends only on surface chemistry. This study investigated the impact of immobile zones on nanoparticle transport and retention by employing synchrotron X–ray computed microtomography (SXCMT) to examine pore–scale silver nanoparticle distributions during transport through three sand columns: uniform iron oxide, uniform quartz, and well–graded quartz. Extended tailing was observed during the elution phase of all experiments suggesting that hydraulic retention in immobile zones, not detachment from grains, was the source of tailing. A numerical simulation of fluid flow through an SXCMT data set predicted the presence of immobile zones near grain–grain contacts. SXCMT–determined silver nanoparticle concentrations observed that significantly lower nanoparticle concentrations existed near grain–grain contacts throughout the duration of all experiments. In addition, the SXCMT–determined pore–scale concentration gradients were found to be independent of surface chemistry and grain size distribution, suggesting that immobile zones limit the diffusive transport of nanoparticles toward the collectors. Furthermore, these results suggest that the well–known overprediction of nanoparticle retention by traditional CFT may be due to ignoring the influences of grain–grain contacts and immobile zones. As such, accurate prediction of nanoparticle transport requires consideration of immobile zones and their influence on both hydraulic and surface retention.

42 ENGINEERING↗

DOE OSTI2016

An alternative realization of the exact non-Markovian stochastic Schrödinger equation

Based on the path integral approach, we derive a new realization of the exact non-Markovian stochastic Schrödinger equation (SSE). The main difference from the previous non-Markovian quantum state diffusion (NMQSD) method is that the complex Gaussian stochastic process used for the forward propagation of the wave function is correlated, which may be used to reduce the amplitude of the non-Markovian memory term at high temperatures. The new SSE is then written into the recently developed hierarchy of pure states scheme, in a form that is more closely related to the hierarchical equation of motion approach. Numerical simulations are then performed to demonstrate the efficiency of the new method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Decoupling Grain-Boundary, Grain-Interior, and Surface Recombination with Cathodoluminescence

In this work, we combine quantitative cathodoluminescence (CL) with time-resolved photoluminescence (TRPL) and numerical simulations to determine grain-boundary, grain-interior, and surface recombination parameters in standard CdTe thin films. CL intensities from thousands of grains are analyzed to accumulate statistics and chart variations with grain size. Grain-boundary contrast results for small grains indicate that the grain-boundary recombination velocity, S GB , decreases significantly with CdCl 2 treatment, but S GB is increased by subsequent Cu-diffusion. Furthermore, within a given sample, data suggests that S GB is nearly independent of grain size. The back-surface recombination velocity, S, is extracted from TRPL measurements incident on the back surface, and CL profiles are simulated to determine the grain-interior lifetime, t GI . Finally, CL intensity vs. grain size relationships are simulated to check for self-consistency of the S GB , S, and t GI values.

14 SOLAR ENERGY↗

DOE OSTI2016

The evolution of the mass-transfer functions in liquid Yukawa systems

The results of analytic and numerical investigation of mass-transfer processes in nonideal liquid systems are reported. Calculations are performed for extended 2D and 3D systems of particles that interact with a screened Yukawa-type Coulomb potential. The main attention is paid to 2D structures. A new analytic model is proposed for describing the evolution of mass-transfer functions in systems of interacting particles, including the transition between the ballistic and diffusion regimes of their motion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

Enabling Predictive Simulation and UQ of Complex Multiphysics PDE Systems by the Development of Goal-Oriented Variational Sensitivity Analysis and A Posteriori Error Estimation Methods

It was demonstrated that a posteriori analyses in general and in particular one that uses adjoint methods can accurately and efficiently compute numerical error estimates and sensitivity for critical Quantities of Interest (QoIs) that depend on a large number of parameters. Activities include: analysis and implementation of several time integration techniques for solving system of ODEs as typically obtained from spatial discretization of PDE systems; multirate integration methods for ordinary differential equations; formulation and analysis of an iterative multi-discretization Galerkin finite element method for multi-scale reaction-diffusion equations; investigation of an inexpensive postprocessing technique to estimate the error of finite element solution of the second-order quasi-linear elliptic problems measured in some global metrics; investigation of an application of the residual-based a posteriori error estimates to symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems; a posteriori analysis of explicit time integrations for system of linear ordinary differential equations; derivation of accurate a posteriori goal oriented error estimates for a user-defined quantity of interest for two classes of first and second order IMEX schemes for advection-diffusion-reaction problems; Postprocessing finite element solution; and A Bayesian Framework for Uncertain Quantification of Porous Media Flows.

97 MATHEMATICS AND COMPUTING↗