Search NASA⌕ Search

SEARCH · Search NASA

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.

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

At least 1,261 records · Page 70

Multi-stage preconditioners for thermal–compositional–reactive flow in porous media

We present a family of multi-stage preconditioners for coupled thermal-compositional-reactive reservoir simulation problems. The most common preconditioner used in industrial practice, the Constrained Pressure Residual (CPR) method, was designed for isothermal models and does not offer a specific strategy for the energy equation. For thermal simulations, inadequate treatment of the temperature unknown can cause severe conver-gence degradation. When strong thermal diffusion is present, the energy equation exhibits significant elliptic behavior that cannot be accurately corrected by CPR's second stage. In this work, we use Schur-complement decompositions to extract a temperature subsystem and apply an Algebraic MultiGrid (AMG) approximation as an additional preconditioning stage to improve the treatment of the energy equation. We present results for several two-dimensional hot air injection problems using an extra heavy oil, including challenging reactive In-Situ Combustion (ISC) cases. We show improved performance and robustness across different thermal regimes, from advection dominated (high Péclet number) to diffusion dominated (low Péclet number). The number of linear iterations is reduced by 40–85% compared to standard CPR for both homogeneous and heterogeneous media, and the new methods exhibit almost no sensitivity to the thermal regime.

42 ENGINEERING↗

Dynamic response of shock waves in transonic diffuser and supersonic inlet - An analysis with the Navier-Stokes equations and adaptive grid

An existing method which solves the multi-dimensional ensemble-averaged compressible time-dependent Navier-Stokes equations in conjunction with mixing length turbulence model and shock capturing technique has been extended to include the shock-tracking adaptive grid systems. The numerical scheme for solving the governing equations is based on a linearized block implicit approach. The effects of grid-motion and grid-distribution on the calculated flow solutions have been studied in relative detail and this is carried out in the context of physically steady, shocked flows computed with non-stationary grids. Subsequently, the unsteady dynamics of the flows occurring in a supercritically operated transonic diffuser and a mixed compression supersonic inlet have been investigated with the adaptive grid systems by solving the Navier-Stokes equations.

Liu, N.-S.↗

A molecular dynamics study of intramolecular proton transfer reaction of malonaldehyde in solutions based upon mixed quantum-classical approximation. I. Proton transfer reaction in water

In order to investigate proton transfer reaction in solution, mixed quantum-classical molecular dynamics calculations have been carried out based on our previously proposed quantum equation of motion for the reacting system [A. Yamada and S. Okazaki, J. Chem. Phys. 128, 044507 (2008)]. Surface hopping method was applied to describe forces acting on the solvent classical degrees of freedom. In a series of our studies, quantum and solvent effects on the reaction dynamics in solutions have been analysed in detail. Here, we report our mixed quantum-classical molecular dynamics calculations for intramolecular proton transfer of malonaldehyde in water. Thermally activated proton transfer process, i.e., vibrational excitation in the reactant state followed by transition to the product state and vibrational relaxation in the product state, as well as tunneling reaction can be described by solving the equation of motion. Zero point energy is, of course, included, too. The quantum simulation in water has been compared with the fully classical one and the wave packet calculation in vacuum. The calculated quantum reaction rate in water was 0.70 ps{sup −1}, which is about 2.5 times faster than that in vacuum, 0.27 ps{sup −1}. This indicates that the solvent water accelerates the reaction. Further, the quantum calculation resulted in the reaction rate about 2 times faster than the fully classical calculation, which indicates that quantum effect enhances the reaction rate, too. Contribution from three reaction mechanisms, i.e., tunneling, thermal activation, and barrier vanishing reactions, is 33:46:21 in the mixed quantum-classical calculations. This clearly shows that the tunneling effect is important in the reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Chemical potential effects on neutrino diffusion in supernovae

The validity of imposing a zero chemical potential for neutrinos in hydrodynamic calculations of collapsing supernovae is investigated in the diffusion approximation of neutrino transport. A coupled system of equations is solved for neutrino and energy diffusion fluxes as well as lepton diffusion in a collapsing supernovae ambient medium, and the results indicate a substantial growth in the neutrino chemical potential for densities greater than 10 to the 12th power gm/cu cm. The rate of energy transport is shown to be significantly affected by increases in Fermi integrals and chemical-potential gradients accompanied by decreases in temperature, and the extent of neutrino particle/antiparticle reactions is found also to affect energy diffusion rates. It is concluded that the photon-like behavior usually assumed for neutrinos may be incorrect and that an extension of the Sn transport approximation to include lepton characteristics is necessary for a definitive answer to the question of neutrino transport in supernovae.

Mazurek, T. J.↗

A new least-squares transport equation compatible with voids

We define a new least-squares transport equation that is applicable in voids, can be solved using source iteration with diffusion-synthetic acceleration, and requires only the solution of an independent set of second-order self-adjoint equations for each direction during each source iteration. We derive the equation, discretize it using the S{sub n} method in conjunction with a linear-continuous finite-element method in space, and computationally demonstrate various of its properties. (authors)

97 MATHEMATICS AND COMPUTING↗

Plasma equilibrium in a semiclassical plasma due to non-resonant wave particle interactions

A nonresonant perturbative approach has been utilized to probe the modification of the equilibrium plasma distribution function due to plasma interaction with externally launched high-frequency large-amplitude RF waves in the presence of quantum effects. The quantum distribution function from the complete Wigner equation has been obtained for a high-frequency wave with constant amplitude. For waves with weak spatial or temporal modulation, the equilibrium distribution function has been obtained by solving the Wigner equation as an initial or boundary-value problem and retaining only lowest-order quantum effects. In the dipole approximation, a higher order diffusion has been identified in addition to quantum modified ponderomotive and quasilinear diffusion effects. Additional terms of the Wigner equation give the impression of higher order diffusion effects in the system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Classical non-Markovian Boltzmann equation

The modeling of particle transport involves anomalous diffusion, (x²(t) ) ∝ t{sup α} with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

CMB spectral distortions as solutions to the Boltzmann equations

We propose to re-interpret the cosmic microwave background spectral distortions as solutions to the Boltzmann equation. This approach makes it possible to solve the second order Boltzmann equation explicitly, with the spectral y distortion and the momentum independent second order temperature perturbation, while generation of μ distortion cannot be explained even at second order in this framework. We also extend our method to higher order Boltzmann equations systematically and find new type spectral distortions, assuming that the collision term is linear in the photon distribution functions, namely, in the Thomson scattering limit. As an example, we concretely construct solutions to the cubic order Boltzmann equation and show that the equations are closed with additional three parameters composed of a cubic order temperature perturbation and two cubic order spectral distortions. The linear Sunyaev-Zel'dovich effect whose momentum dependence is different from the usual y distortion is also discussed in the presence of the next leading order Kompaneets terms, and we show that higher order spectral distortions are also generated as a result of the diffusion process in a framework of higher order Boltzmann equations. The method may be applicable to a wider class of problems and has potential to give a general prescription to non-equilibrium physics.

79 ASTRONOMY AND ASTROPHYSICS↗

Quantum diffusion during inflation and primordial black holes

We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-δ N formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. In the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than ∼ 1 e -fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples.

79 ASTRONOMY AND ASTROPHYSICS↗

CONDUCTION IN LOW MACH NUMBER FLOWS. I. LINEAR AND WEAKLY NONLINEAR REGIMES

Thermal conduction is an important energy transfer and damping mechanism in astrophysical flows. Fourier's law, in which the heat flux is proportional to the negative temperature gradient, leading to temperature diffusion, is a well-known empirical model of thermal conduction. However, entropy diffusion has emerged as an alternative thermal conduction model, despite not ensuring the monotonicity of entropy. This paper investigates the differences between temperature and entropy diffusion for both linear internal gravity waves and weakly nonlinear convection. In addition to simulating the two thermal conduction models with the fully compressible Navier-Stokes equations, we also study their effects in the reduced ''soundproof'' anelastic and pseudoincompressible (PI) equations. We find that in the linear and weakly nonlinear regime, temperature and entropy diffusion give quantitatively similar results, although there are some larger errors in the PI equations with temperature diffusion due to inaccuracies in the equation of state. Extrapolating our weakly nonlinear results, we speculate that differences between temperature and entropy diffusion might become more important for strongly turbulent convection.

79 ASTRONOMY AND ASTROPHYSICS↗

A computational thrombus formation model: application to an idealized two-dimensional aneurysm treated with bare metal coils

Cardiovascular implantable devices alter the biofluid dynamics and biochemistry of the blood in which they are placed. These perturbations can lead to thrombus formation which may or may not be desired, depending on the application. In this work, a computational model is developed that couples biofluid dynamics and biochemistry to predict the clotting response of blood to such devices. The model consists of 28 advection–diffusion–reaction partial differential equations to track proteins in the blood involved in clotting and utilizes boundary flux terms to model the initiation of the intrinsic clotting pathway at thrombogenic device surfaces. We use this model to simulate the transient clot growth within a 2D idealized bifurcation aneurysm filled with various distributions of bare metal coils with similar packing densities. The clot model predicts initial clot formation to occur in areas along coil surfaces where flow is minimal and where time-averaged shear rates are the smallest. Among the six coil-filled aneurysm cases simulated, maximum thrombus occlusion ranged between 80.8 and 92.2% of the post-treatment aneurysm volume and was achieved 325–450 s after treatment. Finally, with further refinement and validation, the computational clotting model will be a valuable engineering tool for evaluating and comparing the relative performance of cardiovascular implantable devices.

60 APPLIED LIFE SCIENCES↗

Continuous Fluorescence Depletion Anisotropy Measurement of Protein Rotation

Protein rotation in viscous environments can be measured by fluorescence depletion anisotropy (FDA) which combines long lifetimes of chromophore triplet states with the sensitivity of fluorescence excitation and detection. FDA achieves sensitivity well beyond that attainable by the more common technique of time-resolved phosphorescence anisotropy (TPA). We have now combined benefits of both time-domain and frequency-domain FDA into a single continuous technique (CFDA). Intensity and polarization of a single laser beam are modulated continuously according to a complex, repeating waveform. Fluorescence signals excited from triplet-forming fluorescent probes are digitized over recurring waveform periods by a high-speed signal averager. CFDA experiments typically involve substantial ground state depletion. Thus signals, unlike those of TPA, are not linear in the exciting light intensity and simple data analysis based on such linearity is not appropriate. An exact solution of the coupled diffusion and triplet production/decay equation describing CFDA within individual data points has been combined with simulated annealing optimization to extract triplet and anisotropy decay kinetics from experimental data. Related calculations compare possible excitation waveforms with respect to rotational information provided per fluorescence photon. We present CFDA results for the model system of eosin conjugates of carbonic anhydrase, BSA and immunoglobulin G in 90% glycerol at various temperatures and initial cellular results on eosin-IgE bound to 2H3 cell Type I Fcε receptors. We explore how CFDA reflects rotational parameters of heterogeneous systems and discuss challenges of extending this method to single cell microscopic measurements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Experimental and Modeling Studies for the Removal of Crystal Violet Dye from Aqueous Solutions using Eco-friendly Gracilaria corticata Seaweed Activated Carbon/Zn/Alginate Polymeric Composite Beads

This research article describes, an eco-friendly activated carbon prepared from the Gracilaria corticata seaweeds which was employed for the preparation of biodegradable polymeric beads for the efficient removal of crystal violet dye in an aqueous solution. The presence of chemical functional groups in the adsorbent material was detected using FTIR spectroscopy. The morphology and physical phases of the adsorbent materials were analyzed using SEM and XRD studies respectively. Batch mode dye adsorption behavior of the activated carbon/Zn/alginate polymeric beads was investigated as a function of dosage, solution pH, contact time, initial dye concentration and temperature. Maximum dye removal was observed at a pH of 5.0, 1 g of adsorbent dosage with 60 mg/L dye concentration, 50 min of contact time and at 30 °C. The equilibrium modeling studies were analyzed with Freundlich and Langmuir adsorption isotherms and the adsorption dynamics was predicted with Lagergren’s pseudo-first order, pseudo-second order equations and intra particle diffusion models. The process of dye removal followed a pseudo second-order kinetics rather than pseudo first order. The thermodynamic parameters like standard Gibbs free energy change (ΔG°), enthalpy change (ΔH°) and entropy change (ΔS°) were determined and the results imply that the adsorption process was spontaneous, endothermic and increases the randomness between the adsorbent and adsorbate. The results from the experimental and correlation data reveal that the Gracilaria corticata activated carbon/Zn/alginate polymeric beads have proved to be an excellent adsorbent material for the removal of CV dye.

36 MATERIALS SCIENCE↗

Diffusion-driven GaInP/GaAs light-emitting diodes enhanced by modulation doping

Diffusion-driven charge transport (DDCT) in III–V light-emitting diodes (LEDs) can enable unconventional optoelectronic devices and functionality by fundamentally changing device design and the current injection principle. In our recent study, an AlGaAs/GaAs DDCT–LED consisting of an array of lateral heterojunctions was studied for large-area applications at high powers. Here, we investigate the current spreading and recombination uniformity of a modulation doped GaInP/GaAs DDCT–LED. In particular, we analyze how the background doping of the lower GaInP cladding layer (CL) and the GaAs substrate changes the carrier distribution within the active region of the device. Our charge transport simulations based on the drift-diffusion current and continuity equations predict that modulation doping by a p-doped CL provides much higher recombination uniformity at high powers compared to an n-doped CL. Most importantly, improved current spreading is achieved while maintaining excellent device performance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Exploring the impact of hydro-mechanical coupling on compaction localization

In deep subsurface environments, where porous rocks are saturated with fluids, hydromechanical coupling plays a critical role in the formation and propagation of localized deformation zones, such as compaction bands. In this study, we numerically investigate the influence of fluid-rock interactions on the development of compaction localization in fluid-saturated rocks. For this purpose, it uses a numerical framework that adapts the heat equation to model the diffusion of pore pressure caused by deformation. This is achieved with specialized subroutines for material behavior and heat transfer formulated within the ABAQUS platform and by allowing changes in rock permeability during strain localization. The results highlight that hydromechanical coupling significantly alters the compaction behavior compared to dry conditions. Under high confining stress, excess pore pressure inhibits the progression of compaction fronts, while in time-dependent processes like rock creep, pore pressure transients accelerate deformation by creating feedback loops between mechanical forces and fluid flow. These findings underscore the importance of saturation in controlling the dynamics of compaction localization and provide insights into the interplay between pore pressure, deformation, and permeability. The implications of this study extend to applications in geological storage, resource extraction, and subsurface geomechanics, offering a deeper understanding of coupled hydromechanical processes in porous rocks.

58 GEOSCIENCES↗

The effects of turbulence on the flame structure and NO formation of ammonia turbulent premixed combustion at various equivalence ratios

Ammonia is carbon-free and is regarded as a potential fuel to address global warming issues. Here, in this work, three-dimensional direct numerical simulations (DNS) of ammonia/air turbulent premixed flames were performed to explore the influence of turbulence and equivalence ratio on the flame structure and NO formation characteristics. Two equivalence ratios were considered, i.e. Φ=0.9 and Φ=1.1. The general flame structures were presented and species distributions were examined. The NO mass fraction was found to be the highest in the product for the lean case and in the reaction zone for the rich case. The conditional mean values of species mass fractions and reaction rates were compared with those of the unstrained and strained laminar premixed flames to explore how well the laminar flame structures can approach those of the turbulent flame. The budget analysis of the species transport equations showed that turbulent diffusion plays an important role in species transport. The turbulent diffusivity D T was estimated using the gradient hypothesis based on the DNS data. Various laminar flame simulations with different diffusivities were carried out. It was shown that the conditional means of the DNS agree well with those of the laminar flames including D T in the transport property calculation. The global and local NO formation characteristics were investigated. It was found that the mean NO production conditioned on the progress variable is lower compared with the corresponding laminar flame in the rich case. However, the relative contributions from various NO pathways are rarely affected by turbulence. The NO mass fraction is higher in negative curvature regions compared with positive curvature regions of the flame surface for the rich case, which is due to the preferential diffusion of H 2 and other radicals and the enhanced NO pathways in negatively curved regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reactive particle-tracking solutions to a benchmark problem on heavy metal cycling in lake sediments

Geochemical systems are known to exhibit highly variable spatiotemporal behavior. This may be observed both in non-smooth concentration curves in space for a single sampling time and also in variability between samples taken from the same location at different times. However, most models that are designed to simulate these systems provide only single-solution smooth curves and fail to capture the noise and variability seen in the data. We apply a recently developed reactive particle-tracking method to a system that displays highly complex geochemical behavior. When the method is made to most closely resemble a corresponding Eulerian method, in its unperturbed form, we see near-exact match between solutions of the two models. More importantly, we consider two approaches for perturbing the model and find that the spatially-perturbed condition is able to capture a greater degree of the variability present in the data. This method of perturbation is a task to which particle methods are uniquely suited and Eulerian models are not well-suited. Additionally, because of the nature of the algorithm, noisy spatial gradients can be highly resolved by a large number of mobile particles, and this incurs negligible computational cost, as compared to expensive chemistry calculations.

54 ENVIRONMENTAL SCIENCES↗