SEARCH · Engineering Papers

Results for “diffusion equation”

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 1,693 records · Page 94

All sources NASA NTRS DOE OSTI

DOE OSTI2019

Fluctuating hydrodynamics of electrolytes at electroneutral scales

At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations. However, at length and time scales larger than the Debye scales, electrolytes are effectively electroneutral, and the charged-fluid PNP equations become too stiff to solve numerically. Here we formulate the isothermal incompressible equations of fluctuating hydrodynamics for reactive multispecies mixtures involving charged species in the electroneutral limit, and design a numerical algorithm to solve these equations. Our model does not assume a dilute electrolyte solution but rather treats all species on an equal footing, accounting for cross-diffusion and non-ideality using Maxwell-Stefan theory. By enforcing local electroneutrality as a constraint, we obtain an elliptic equation for the electric potential that replaces the Poisson equation in the fluctuating PNP equations. We develop a second-order midpoint predictor-corrector algorithm to solve either the charged-fluid or electroneutral equations with only a change of the elliptic solver. We use the electroneutral algorithm to study a gravitational fingering instability, triggered by thermal fluctuations, at an interface where an acid and base react to neutralize each other. Our results demonstrate that, because the four ions diffuse with very different coefficients, one must treat each ion as an individual species, and cannot treat the acid, base, and salt as neutral species. This emphasizes the differences between electrodiffusion and classical Fickian diffusion, even at electroneutral scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Mathematical Modeling of Decarburization in Levitated Fe-Cr-C Droplets

Using carbon dioxide to replace oxygen as an alternative oxidant gas has proven to be a viable solution in the decarburization process, with potential for industrial applications. In a recent study, the transport phenomena governing the carbon dioxide decarburization process through the use of electromagnetic levitation (EML) was examined. CO{sub 2}/CO mass transfer was found to be the principal reaction rate control step, as a result gas diffusion has gained significant attention. In the present study, gas diffusion during decarburization process was investigated using computational fluid dynamics (CFD) modeling coupled with chemical reactions. The resulting model was verified through experimental data in a published paper, and employed to provide insights on phenomena typically unobservable through experiments. Based on the results, a new correction of the Frössling equation was presented which better represents the mass transfer phenomena at the metal-gas interface within the range of this research.

36 MATERIALS SCIENCE↗

NASA NTRS2022

Prediction of Turbulent Diffusing Flows Using FUN3D

The FUN3D code was used to perform Reynolds-averaged Navier-Stokes (RANS) simulations to compute subsonic flow in an S-duct diffuser and transonic flow in a two-dimensional diffuser using the Speziale-Sarkar-Gatski/Launder-Rodi-Reece (SSG/LRR) Reynolds stress model (RSM). For comparison purposes, additional simulations were run with the one-equation Spalart-Allmaras (SA) and the two-equation Menter Shear-Stress Transport (SST) turbulence models. Each model was run with and without the quadratic constitutive relation (QCR) for computing the turbulent stresses. It was shown that the simulations that utilized the RSM had better overall predictions of the diffusive flow fields compared to the simulations that utilized the one and two equation turbulence models.

Inlet Distortion↗

DOE OSTI2024

High-accuracy method for modeling nucleation and growth of particles

State-of-the-art numerical models describing the kinetics of aerosol particle nucleation and growth from a cooling vapor primarily use a nodal method, in which particles that are smaller than the critical size are omitted from consideration because they are thermodynamically unfavorable. This omission is based on the assumption that most newly formed particles are above the critical size, so that subcritical-size particles are not important to take into account. Due to the nature of the nodal method, it suffers from numerical diffusion, which can cause an artificial broadening of the cluster size distribution leading to a significant overestimation of the number of large-size particles. To address these issues, we propose a more accurate numerical method that explicitly models particles of all sizes, and uses a special numerical scheme that substantially reduces the numerical diffusion and provides high solution accuracy and numerical stability. We extensively compare this novel method to the commonly used nodal solver of the general dynamic equation (GDE) for particle growth and demonstrate that it offers GDE solutions with higher accuracy with low numerical diffusion. Incorporating small subcritical clusters into the solution is crucial for: 1) more precise determination of the entire particle size distribution function and 2) wider applicability of the model to experimental studies with non-monotonic temperature variations leading to particle evaporation. The computational code implementing this numerical method in Python is available upon request.

42 ENGINEERING↗

DOE OSTI2026

High-Fidelity, Low-Dissipation/Symmetry-Preserving Numerical Scheme for Solving the Euler Equations with Unstructured, Metric-Based Mesh Adaptation

This work presents an overview of a high-fidelity compressible Euler solver that utilizes the continuous Galerkin (CG) method with added artificial numerical diffusion for stabilization to solve a variety of unsteady and steady benchmark inviscid flow problems. This work shows that discretizing the Euler equations with this CG approach and first order basis functions produces a cost-effective stencil as well as simple well-posed boundary conditions. We show through convergence testing with manufactured solutions that the reduced stencil of CG, combined with the low amount of artificial diffusion required when using the stabilization method outlined in this work, leads to stable and highly accurate results for a variety of unsteady and steady applications. When combined with the adaptive mesh refinement approach used for many of the cases in this work, our results show that the flow solver achieves even more accurate results. A variety of inviscid flow cases are presented in this work, including transient 2D cases with complex shock structures and several steady 3D airfoils sections with a constant span.

Doetsch, Kevin [ORNL] (ORCID:0000000267051705)↗

DOE OSTI2018

Neoclassical Diffusion of Radiation-Belt Electrons Across Very Low L -shells

In the presence of drift-shell splitting intrinsic to the IGRF magnetic field model, pitch-angle scattering from Coulomb collisions experienced by radiation-belt electrons in the upper atmosphere and ionosphere produces extra radial diffusion, a form of neoclassical diffusion. The strength of the neoclassical radial diffusion at L < 1.2 exceeds that expected there from radial-diffusion mechanisms traditionally considered, and decreases with increasing L-shell. In this study we construct a numerical model for this coupled (radial and pitch-angle) collisional diffusion process and apply it to simulate raw count-rate data observed aboard the Gemini spacecraft for several years after the 1962 Starfish nuclear detonation. The data show apparent lifetimes 10-100 times as long as would have been expected from collisional pitch-angle diffusion and Coulomb drag alone. Our model reproduces apparent lifetimes for >0.5-MeV electrons in the region 1.14 < L < 1.26 to within a factor of two (comparable to the uncertainty quoted for the observations). We conclude that neoclassical radial diffusion (resulting from drift-shell splitting intrinsic to IGRF's azimuthal asymmetries) mitigates the decay expected from collisional pitch-angle diffusion and inelastic energy loss alone and thus contributes importantly to the long apparent lifetimes observed at these low L-shells.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2002

Dynamics of Diffusion Flames in von Karman Swirling Flows Studied

Von Karman swirling flow is generated by the viscous pumping action of a solid disk spinning in a quiescent fluid media. When this spinning disk is ignited in an oxidizing environment, a flat diffusion flame is established adjacent to the disk, embedded in the boundary layer (see the preceding illustration). For this geometry, the conservation equations reduce to a system of ordinary differential equations, enabling researchers to carry out detailed theoretical models to study the effects of varying strain on the dynamics of diffusion flames. Experimentally, the spinning disk burner provides an ideal configuration to precisely control the strain rates over a wide range. Our original motivation at the NASA Glenn Research Center to study these flames arose from a need to understand the flammability characteristics of solid fuels in microgravity where slow, subbuoyant flows can exist, producing very small strain rates. In a recent work (ref. 1), we showed that the flammability boundaries are wider and the minimum oxygen index (below which flames cannot be sustained) is lower for the von Karman flow configuration in comparison to a stagnation-point flow. Adding a small forced convection to the swirling flow pushes the flame into regions of higher strain and, thereby, decreases the range of flammable strain rates. Experiments using downward facing, polymethylmethacrylate (PMMA) disks spinning in air revealed that, close to the extinction boundaries, the flat diffusion flame breaks up into rotating spiral flames (refs. 2 and 3). Remarkably, the dynamics of these spiral flame edges exhibit a number of similarities to spirals observed in biological systems, such as the electric pulses in cardiac muscles and the aggregation of slime-mold amoeba. The tail of the spiral rotates rigidly while the tip executes a compound, meandering motion sometimes observed in Belousov-Zhabotinskii reactions.

Nayagam, Vedha↗

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 OSTI2019

Entropy-based closure for probabilistic learning on manifolds

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization from a non-Gaussian random vector. The manifold structure is learned using diffusion manifolds and the statistical sample generation is accomplished using a projected Itˆo stochastic differential equation. This probabilistic learning approach has been extended to polynomial chaos representation of databases on manifolds and to probabilistic nonconvex constrained optimization with a fixed budget of function evaluations. The methodology introduces an isotropic-diffusion kernel with hyperparameter ". Currently, " is more or less arbitrarily chosen. In this paper, we propose a selection criterion for identifying an optimal value of ", based on a maximum entropy argument. The result is a comprehensive, closed, probabilistic model for characterizing data sets with hidden constraints. This entropy argument ensures that out of all possible models, this is the one that is the most uncertain beyond any specified constraints, which is selected. Applications are presented for several databases.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first showthat the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient finite element assembly.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1973

Reflectance and unsteady temperature distribution of diffuse reflectors

The applicability of a previously derived solution of the Kubelka-Munk differential equations for the reflectance of an absorbing and scattering material for the case of a zero absorption coefficient to the description of the reflectance of a weakly absorbing, highly scattering material is examined. A solution for the transient heating of a one-dimensional volume reflector is obtained, and the error incurred in the use of the zero absorption coefficient solution is assessed for early times appropriate to the entry heat protection system application. It is found that the small difference in reflectance causes a significant difference in internal temperature.

Weston, K. C.↗

NASA NTRS1990

Improved Analysis Of Heat-Pulse Data

Equations derived to improve analysis of experimental data in flash method for measurement of thermal diffusivity and heat capacity. In flash method, pulse of radiant energy from flashlamp or other source deposited on front face of small, thin specimen, and temperature of rear face monitored as function of time. New equations account for both losses and exponentially decaying pulses.

Vining, C. B.↗

DOE OSTI2016

Finite element formulation of fluctuating hydrodynamics for fluids filled with rigid particles using boundary fitted meshes

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Resolving turbulent magnetohydrodynamics: a hybrid operator-diffusion framework

We present a hybrid machine learning framework that combines physics-informed neural operators (PINOs) with score-based generative diffusion models to simulate the full spatio-temporal evolution of two-dimensional, incompressible, resistive magnetohydrodynamic turbulence across a broad range of Reynolds numbers (Re). The framework leverages the equation-constrained generalization capabilities of PINOs to predict coherent, low-frequency dynamics, while a conditional diffusion model stochastically corrects high-frequency residuals, enabling accurate modeling of fully developed turbulence. Trained on a comprehensive ensemble of high-fidelity simulations with Re ϵ {100, 250, 500, 750, 1000, 3000, 10000}, the approach achieves state-of-the-art accuracy in regimes previously inaccessible to deterministic surrogates. At Re = 1000 and 3000, the model faithfully reconstructs the full spectral energy distributions of both velocity and magnetic fields late into the simulation, capturing non-Gaussian statistics, intermittent structures, and cross-field correlations with high fidelity. At extreme turbulence levels (Re = 10 000), it remains the first surrogate capable of recovering the high-wavenumber evolution of the magnetic field, preserving large-scale morphology and enabling statistically meaningful predictions.

Diffusion-Integrated Neural Operators↗

DOE OSTI2016

Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport

The telegraph equation and its generalizations have been repeatedly considered in the models of diffusive cosmic-ray transport. Yet the telegraph model has well-known limitations, and analytical arguments suggest that a hyperdiffusion model should serve as a more accurate alternative to the telegraph model, especially on the timescale of a few scattering times. We present a detailed side-by-side comparison of an evolving particle density profile, predicted by the telegraph and hyperdiffusion models in the context of a simple but physically meaningful initial-value problem, compare the predictions with the solution based on the Fokker–Planck equation, and discuss the applicability of the telegraph and hyperdiffusion approximations to the description of strongly anisotropic particle distributions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRSDate not supplied

Prediction of Turbulent Diffusing Flows Using FUN3D

Inlet Distortion↗

NASA NTRS1975

Steady-state solutions of a diffusive energy-balance climate model and their stability

A diffusive energy-balance climate model, governed by a nonlinear parabolic partial differential equation, was studied. Three positive steady-state solutions of this equation are found; they correspond to three possible climates of our planet: an interglacial (nearly identical to the present climate), a glacial, and a completely ice-covered earth. Models similar to the main one are considered, and the number of their steady states was determined. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The stability under small perturbations of the main model's climates was investigated. A stability criterion is derived, and its application shows that the present climate and the deep freeze are stable, whereas the model's glacial is unstable. The dependence was examined of the number of steady states and of their stability on the average solar radiation.

Ghil, M.↗

DOE OSTI2019

The role of mid-gap phonon modes in thermal transport of transition metal dichalcogenides

We present a comprehensive theoretical study on thermal transport in monolayer transition metal dichalcogenides MX 2 (M: Mo, W; X: S, Se) with various sample sizes. An unusually high anharmonic scattering strength is found in MoSe 2 compared to the other three family members, which arises from its unique phonon band dispersion, specifically the mid-frequency phonon branches associated with the vibrations of Se atoms of MoSe 2 . The mid-frequency modes almost completely span the gap that exists between the high-frequency phonon branches and the acoustic ones, allowing the former to readily decay into the latter. The resultant high anharmonic scattering gives rise to a short mean free path which makes the room temperature in-plane thermal conductivity in MoSe 2 even lower than WSe 2 when the sample length is larger than 51.5 nm. With varying sample sizes, the ordering of thermal conductivity among the four materials changes as phonon transport transits from the ballistic to diffusive regime, driven by the competition between the phonon frequency spectrum range and the scattering strength. In conclusion, our work provides a microscopic picture of phonon transport in TMDs and guidance to tailor their thermal conductivities for electronic and thermoelectric applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗