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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 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Combustion Of Moving Droplets And Of Droplets Suspended Within A Convective Environment: Transient Numerical Results

The problem considered is that of a single-component liquid fuel (n-heptane) droplet undergoing evaporation and combustion in a hot, convective, low pressure, zero-gravity environment of infinite expanse. For a moving droplet, the relative velocity (U(sub infinity)) between the droplet and freestream is subject to change due to the influence of the drag force on the droplet. For a suspended droplet, the relative velocity is kept constant. The governing equations for the gas-phase and the liquid-phase consist of the unsteady, axisymmetric equations of mass, momentum, species (gas-phase only) and energy conservation. Interfacial conservation equations are employed to couple the two phases. Variable properties are used in the gas- and liquid-phase. Multicomponent diffusion in the gas-phase is accounted for by solving the Stefan-Maxwell equations for the species diffusion velocities. A one-step overall reaction is used to model the combustion. The governing equations are discretized using the finite volume and SIMPLEC methods. A colocated grid is adopted. Hyperbolic tangent stretching functions are used to concentrate grid points near the fore and aft lines of symmetry and at the droplet surface in both the gas- and liquid-phase. The discretization equations are solved using the ADI method with the TDMA used on each line of the two alternating directions. Iterations are performed within each time-step until convergence is achieved. The grid spacing, size of the computational domain and time-step were tested to ensure that all solutions are independent of these parameters. A detailed discussion of the numerical model is given.

Gogos, George↗
DOE OSTI2021

Loss and Isotopic Fractionation of Alkali Elements during Diffusion-Limited Evaporation from Molten Silicate: Theory and Experiments

Moderately volatile elements (MVEs) are variably depleted in planetary bodies, reflecting the imprints of nebular and planetary processes. Among MVEs, Na, K, and Rb are excellent tracers for unraveling the history of MVE depletion in planetary bodies because they have similar geochemical behaviors but can be chemically fractionated by evaporation and condensation processes. Furthermore, K and Rb are amenable to high-precision isotopic analyses, which can help constrain the conditions of evaporation and condensation. To quantitatively understand why Na, K, and Rb are depleted in planetary bodies, we have carried out vacuum evaporation experiments from basaltic melt at 1200 and 1400 °C to study their evaporation kinetics and isotopic fractionations. We chose this composition because it is relevant to evaporation from small differentiated planetesimals. The Rb isotopic compositions of the evaporation residues were measured by multicollector inductively coupled plasma mass spectrometry (MC-ICPMS), and the K isotopic compositions were measured along profiles across the residues by secondary ion mass spectrometry (SIMS). In the 1400 °C run products, we found that the concentrations of both K and Rb in the run products decreased from core to rim, which was accompanied by a heavy K isotope enrichment near the surface. This indicates that, in this run, evaporation was limited by diffusion. To use those data quantitatively, we derive analytical equations that describe the evaporation rate and isotopic fractionation associated with diffusion-limited evaporation from a sphere, slab, and cylinder in transient and quasi-steady state regimes. This model is used to tease out the roles that diffusive transport in the melt and evaporation at the melt/gas interface play in setting the elemental depletion and isotopic composition of the residue. Under our experimental conditions, volatility decreases in the order of Na, Rb, and K. Using our experimental results in a thermodynamic model, we have estimated the product γΓ of activity coefficients × evaporation coefficients of Na, Rb, and K. The measured isotopic compositions of the residues are well explained using Rayleigh distillations, whereby the relative volatilities of K and Rb isotopes are given by the square root of their masses. We use our results and previously published data to predict how K and Rb could have been lost as a function of temperature, melt composition, oxygen fugacity, and saturation degree relevant to Vesta’s building blocks. We find that the K and Rb depletions, K/Rb elemental fractionation, and δ 41 K and δ 87 Rb isotopic fractionations of Vesta (as sampled by howardite-eucrite-diogenite (HED) meteorites) are best explained by evaporation of submillimeter size objects for 0.1-10 years at moderate temperatures (~1050 °C) in a medium ~98.8% saturated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1993

On the generation of 'strong' magnetic fields

We rediscuss the nature of magnetic field generation in astrophysical systems. We show that as a result of ineffective three-dimensional turbulent diffusion in the presence of strong azimuthal magnetic fields, the standard dynamo equations are not likely to provide a reasonable description of magnetic dynamos in systems such as late-type stars and galaxies. Instead, we propose a new set of dynamo equations, which take into account the modifications of turbulent diffusion by strong magnetic fields.

Vainshtein, S. I.↗
DOE OSTI2022

Simulations of neutron noise in the research reactor AKR-2: comparison between a discrete ordinates and a diffusion-based method

A diffusion-based and a discrete ordinates method are used to simulate a neutron noise experiment in the research reactor AKR-2 at the Technical University in Dresden, Germany. The AKR-2 reactor provides an interesting case for the comparison between the two methods because it is characterized by large heterogeneities and regions with low macroscopic neutron cross-sections. For the calculations, the same spatial discretization and the same set of two-energy macroscopic neutron cross-sections with isotropic scattering are used. Significant discrepancies between the diffusion-based and discrete ordinates methods are found in regions of the systems where the diffusion approximation is expected to be inaccurate in reproducing characteristics of the static neutron flux and neutron noise. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Mass Changes the Diffusion Coefficient of Particles with Ligand-Receptor Contacts in the Overdamped Limit

Inertia does not generally affect the long-time diffusion of passive overdamped particles in fluids. Yet a model starting from the Langevin equation predicts a surprising property of particles coated with ligands that bind reversibly to surface receptors: heavy particles diffuse more slowly than light ones of the same size. We show this by simulation and by deriving an analytic formula for the mass-dependent diffusion coefficient in the overdamped limit. We estimate the magnitude of this effect for a range of biophysical ligand-receptor systems, and find it is potentially observable for tailored micronscale DNA-coated colloids.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Direct Measurement of Diffusion Coefficients: Evidence for Diffusive Stochastic Heating in Collisionless Plasmas

Open questions in collisionless plasma dissipation can be addressed using space-based observations in different astrophysical environments, with implications for both astrophysical and laboratory plasma systems. We study a low-𝛽, highly imbalanced, sub-Alfvénic stream observed by Parker Solar Probe (PSP) to identify and distinguish between signatures of stochastic heating (SH) and resonant heating (RH) by parallel ion cyclotron waves (∥-ICWs). Prior work studying this stream [Trevor A. Bowen et al., Stochastic heating in the sub-Alfvénic solar wind, Phys. Rev. Lett. 135, 255201 (2025)] showed that the SH rate, accounting for intermittency, matched the amplitude of the local energy transfer (LET) rate, while the RH rate did not. This comparison relied on a number of assumptions regarding the nature of the diffusive process and the calculation of the LET rate. We introduce a novel technique of inverting the proton guiding center equation to empirically measure velocity-space diffusion coefficients using three-dimensional proton velocity distribution functions, from the ion electrostatic analyzer (the Solar Probe Analyzer for Ions) on PSP. Measured diffusion coefficients are used to determine phase-space heating rates, leading to a calculation of a fully kinetic heating rate independent of assumptions made in prior work. We show that scale-dependent analytic expressions for SH via noncoherent fluctuations match the empirical measurements from PSP data, provided that we account for intermittency in the heating calculation. In contrast, the derived heating rates for SH that accounts for the effects of the helicity barrier and heating rates for RH via ∥-ICWs do not peak in the same region of velocity space as the empirical measurements, nor do they reach the required magnitude. Our approach provides novel methodology to uniquely identify and constrain heating processes in collisionless plasmas and shows evidence of a Fokker-Planck-like diffusive process in the near-Sun solar wind.

Plasma kinetic theory↗
NASA NTRS1982

Numerical analysis and FORTRAN program for the computation of the turbulent wakes of turbomachinery rotor blades, isolated airfoils and cascade of airfoils

Turbulent wakes of turbomachinery rotor blades, isolated airfoils, and a cascade of airfoils were investigated both numerically and experimentally. Low subsonic and incompressible wake flows were examined. A finite difference procedure was employed in the numerical analysis utilizing the continuity, momentum, and turbulence closure equations in the rotating, curvilinear, and nonorthogonal coordinate system. A nonorthogonal curvilinear coordinate system was developed to improve the accuracy and efficiency of the numerical calculation. Three turbulence models were employed to obtain closure of the governing equations. The first model was comprised to transport equations for the turbulent kinetic energy and the rate of energy dissipation, and the second and third models were comprised of equations for the rate of turbulent kinetic energy dissipation and Reynolds stresses, respectively. The second model handles the convection and diffusion terms in the Reynolds stress transport equation collectively, while the third model handles them individually. The numerical results demonstrate that the second and third models provide accurate predictions, but the computer time and memory storage can be considerably saved with the second model.

Hah, C.↗
DOE OSTI2022

($\mathrm{INVITED}$)Counter-ion effect on the diffusion behavior of $\mathrm{Y}$b, $\mathrm{L}$u, and $\mathrm{N}$d ions in $\mathrm{YAG}$ transparent ceramics

The ability to fabricate additively manufactured laser waveguides with sharp dopant concentration interfaces is limited by diffusion of the dopants at the temperatures required to fully densify the material. Compositional analysis of bilayer samples, where each layer was either undoped YAG or YAG doped with Yb, Lu, or Nd, were fabricated such that all combinations were available for testing. Samples were fabricated at both 1750°C and 1850°C to determine the diffusion behavior of each dopant alone and also in the presence of a second dopant. It was found that the experimental concentration profiles exhibited both intragranular (bulk) and grain boundary contributions, and thus fitting to a complementary error function equation required the use of two diffusion coefficients. Nd always diffused further along grain boundaries than the other dopants, due in part to its small segregation coefficient in YAG. It is shown that the presence of Nd as a counter dopant inhibits intragranular diffusion of other dopants while enhancing their grain boundary diffusion. All the observed trends were attributed to a combination of intragranular lattice strain due to: dopant ions replacing yttrium substitutionally, the relative driving forces for the segregation of dopant ions to grain boundaries, and the ability of one dopant to affect the diffusion of a different dopant in the other direction to maintain charge neutrality.

36 MATERIALS SCIENCE↗
NASA NTRS1973

Comments on the reconnexion rate of magnetic fields.

The reconnection rate of magnetic fields is crucial in understanding the fields found in turbulent flows in the solar photosphere and in the galaxy, and in flare phenomena. The behavior of magnetic fields in the neighborhood of an X-type neutral point is examined. The treatment is kinematic specifying the velocity field v and constructing solutions to the hydromagnetic equation for B. The calculations demonstrate that the reconnection rate is controlled by the diffusion in the near neighborhood of the neutral point, and is not arbitrarily large, as has been suggested by similarity solutions of the complete field and fluid equations for vanishing diffusion.

Parker, E. N.↗
DOE OSTI2024

Implicit-explicit Runge-Kutta for radiation hydrodynamics I: Gray diffusion

Radiation hydrodynamics are a challenging multiscale and multiphysics set of equations. To capture the relevant physics of interest, one typically must time step on the hydrodynamics timescale, making explicit integration the obvious choice. On the other hand, the coupled radiation equations have a scaling such that implicit integration is effectively necessary in non-relativistic regimes. A first-order Lie-Trotter-like operator split is the most common time integration scheme used in practice, alternating between an explicit hydrodynamics step and an implicit radiation solve and energy deposition step. However, such a scheme is limited to first-order accuracy, and nonlinear coupling between the radiation and hydrodynamics equations makes a more general additive partitioning of the equations non-trivial. Here, we develop a new formulation and partitioning of radiation hydrodynamics with gray diffusion that allows us to apply (linearly) implicit-explicit Runge-Kutta time integration schemes. In conclusion, we prove conservation of total energy in the new framework, and demonstrate 2nd-order convergence in time on multiple radiative shock problems, achieving error 3–5 orders of magnitude smaller than the first-order Lie-Trotter operator split at the hydrodynamic CFL, even when Lie-Trotter applies a 3rd-order TVD Runge-Kutta scheme to the hydrodynamics equations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Emulators for Scarce and Noisy Data: Application to Auxiliary-Field Diffusion Monte Carlo for Neutron Matter

Understanding the equation of state (EOS) of pure neutron matter is necessary for interpreting multimessenger observations of neutron stars. Reliable data analyses of these observations require well-quantified uncertainties for the EOS input, ideally propagating uncertainties from nuclear interactions directly to the EOS. This, however, requires calculations of the EOS for a prohibitively larger number of nuclear Hamiltonians, solving the nuclear many-body problem for each one. Quantum Monte Carlo methods, such as auxiliary-field diffusion Monte Carlo (AFDMC), provide precise and accurate results for the neutron matter EOS, but they are very computationally expensive, making them unsuitable for the fast evaluations necessary for uncertainty propagation. Here, we employ parametric matrix models to develop fast emulators for AFDMC calculations of neutron matter and use them to directly propagate uncertainties of coupling constants in the Hamiltonian to the EOS. As these uncertainties include estimates of the effective field theory truncation uncertainty, this approach provides robust uncertainty estimates for use in astrophysical data analyses. In conclusion, this Letter will enable novel applications such as using astrophysical observations to put constraints on coupling constants for nuclear interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2006

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Gnoffo, Peter A.↗
DOE OSTI2023

Automated Symbolic Upscaling: 1. Model Generation for Extended Applicability Regimes

Abstract In porous media theory, upscaling techniques are fundamental to deriving rigorous Darcy‐scale models for flow and reactive transport in subsurface systems. Due to limitations in classical techniques, a number of ad hoc approaches have been proposed to address physical regimes in which reactive time scales are similar to, or faster than, diffusive time scales. In Part 1 of this two part series, we present a strategy for expanding the applicability of classical homogenization theory by generalizing the assumed closure form. We detail the implementation of this strategy on two reactive mass transport problems with moderately reactive physics. The strategy produces nontrivial homogenized models with emergent terms and effective parameters that couple reactive, diffusive, and advective transport. The differences in equation forms between the macroscopic and pore‐scale descriptions advise caution to further studies where the forms of macroscopic equations are assumed, as opposed to rigorously derived. Numerical validation is provided for each problem to show that the error estimates of homogenization theory are satisfied, and to justify the implemented strategy. In Part 2, the presented strategy is automated using symbolic computing to expedite its implementation.

Pietrzyk, Kyle↗
DOE OSTI2020

Theoretical formulation of phase space microbunching instability in the presence of intrabeam scattering for single-pass or recirculation accelerators

Microbunching instability (MBI) has been one of the most challenging issues in designs of high-brightness beam transport lines for single-pass or recirculating accelerators. Although the intrabeam scattering (IBS) has long been studied in lepton or hadron storage rings as a slow diffusion process or in high-intensity proton linear accelerators as one mechanism for the beam halo, the effects of IBS on single-pass or recirculating electron accelerators have drawn attention only in the recent two decades due to emergence of linac-based or energy-recovery-linac-based fourth-generation light sources, which require high-quality electron beams during the beam transport. In this paper we develop a theoretical formulation of microbunching instability in the presence of IBS for single-pass or recirculation accelerators. To quantify MBI with inclusion of IBS, we start from the Vlasov-Fokker-Planck (VFP) equation, combining both collective interactions and incoherent IBS effects. The linearized VFP equation and the corresponding friction and diffusion coefficients are derived. The evolutions of the resultant density and energy modulations are formulated as a set of coupled integral equations. The theoretical formulation is then applied to a recirculating beamline design. The results from the semianalytical calculation are compared and show good agreement with massive particle tracking simulations.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion

Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here, we introduce a computational framework, regularization by denoising using diffusion models for partial differential equations (RED-DiffEq), by integrating physics-driven inversion and data-driven learning. RED-DiffEq leverages pretrained diffusion models as a regularization mechanism for PDE-governed inverse problems. We apply RED-DiffEq to solve the full waveform inversion problem in geophysics, a challenging seismic imaging technique that seeks to reconstruct high-resolution subsurface velocity models from seismic measurement data. Our method shows enhanced accuracy and robustness compared to benchmark methods. Additionally, it exhibits strong generalization and domain decomposition capacity, enabling the inversion of more complex velocity models with larger domains than those used in training the diffusion model. Our framework can also be directly applied to diverse PDE-governed inverse problems.

Shan, Siming [Yale University, New Haven, CT (Unit↗
DOE OSTI2021

Challenging Practices of Algebraic Battery Life Models through Statistical Validation and Model Identification via Machine-Learning

Various modeling techniques are used to predict the capacity fade of Li-ion batteries. Algebraic reduced-order models, which are inherently interpretable and computationally fast, are ideal for use in battery controllers, technoeconomic models, and multi-objective optimizations. For Li-ion batteries with graphite anodes, solid-electrolyte-interphase (SEI) growth on the graphite surface dominates fade. This fade is often modeled using physically informed equations, such as square-root of time for predicting solvent-diffusion limited SEI growth, and Arrhenius and Tafel-like equations predicting the temperature and state-of-charge rate dependencies. In some cases, completely empirical relationships are proposed. However, statistical validation is rarely conducted to evaluate model optimality, and only a handful of possible models are usually investigated. This article demonstrates a novel procedure for automatically identifying reduced-order degradation models from millions of algorithmically generated equations via bi-level optimization and symbolic regression. Identified models are statistically validated using cross-validation, sensitivity analysis, and uncertainty quantification via bootstrapping. On a LiFePO 4 /Graphite cell calendar aging data set, automatically identified models utilizing square-root, power law, stretched exponential, and sigmoidal functions result in greater accuracy and lower uncertainty than models identified by human experts, and demonstrate that previously known physical relationships can be empirically "rediscovered" using machine learning.

25 ENERGY STORAGE↗
NASA NTRS1985

Experimental study of a three-dimensional, shear-driven, turbulent boundary layer using a three-dimensional laser Doppler velocimeter

Experimental data have been obtained in a three-dimensional, shear-driven, turbulent boundary layer subjected to sudden transverse strain. Measurements made with a newly developed, three-dimensional laser Doppler velocimeter include all components of mean flow, turbulent Reynolds stresses, and triple-product correlations. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) are extracted from the data. It was shown experimentally that eddy viscosity is strongly direction-dependent (not a scalar), indicating a need for full Reynolds stress modeling. Turbulence models for eddy viscosity, stress diffusion, pressure rate-of-strain, and anisotropy of Reynolds stresses are tested using the data. Calculations using a Reynolds stress equation model are compared with the data.

Driver, D. M.↗