Search NASA⌕ Search

SEARCH · Search NASA

Results for “fractional 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.

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

At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Modeling and Simulation of Porosity in Spray Deposition

Numerical models, consisting of interstitial porosity model and gas porosity model, have been developed to predict the porosity in the spray deposition process. The interstitial porosity model is based on the assumption of liquid feeding in the porous mushy layer of the deposit. The porosity fraction is related to the particle packing density and the amount of the feeding flow during solidification. The gas porosity model is based on the diffusion kinetics of gas pore formation. A numerical simulation of spray deposition for a billet was carried out by coupling the porosity model with the shape and heat-transfer models. The volume fraction and distribution of the porosity were investigated. As a result of the experimental verification, the simulation results showed good agreement with the experimental data. As applications, the models were used to investigate the influence of spray process parameters on porosity formation. The investigation demonstrated that the porosity is substantially influenced by the temperature of the impinging layer and the preheating of the substrate.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Origin of the $ν$ = 1/2 fractional quantum Hall effect in wide quantum wells

The nature of the fractional quantum Hall effect at ν = 1/2, observed in wide quantum wells al- most three decades ago, is still under debate. Previous studies have investigated it by the variational Monte Carlo method, which assumes that the transverse wave function and the gap between the symmetric and antisymmetric subbands obtained in a local density approximation at zero magnetic field remain valid even at high perpendicular magnetic fields; this method also ignores the effect of Landau level mixing. We develop in this work a three-dimensional fixed phase diffusion Monte Carlo method, which gives, in a single framework, the total energies of various candidate states in a finite width quantum well, including Landau level mixing, directly in a large magnetic field. This method can be applied to one-component states, and also to two-component states in the limit where the symmetric and antisymmetric bands are nearly degenerate. Our three-dimensional fixed-phase diffusion Monte Carlo calculations find that the one-component composite-fermion Fermi sea and the one-component Pfaffian states are very close in energy for a range of quantum well widths and densities, suggesting that the observed 1/2 fractional quantum Hall state in wide quantum wells is likely to be the one-component Pfaffian state. Furthermore, we hope that this will motivate further experimental studies of this state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2007

An Experimental Investigation of the Laminar Flamelet Concept for Soot Properties

The soot properties of round, nonbuoyant, laminar jet diffusion flames are described, based on experiments at microgravity carried out on orbit during three flights of the Space Shuttle Columbia, (Flights STS-83, 94 and 107). Experimental conditions included ethylene- and propane-fueled flames burning in still air at an ambient temperature of 300 K and ambient pressures of 35-100 kPa. Measurements included soot volume fraction distributions using deconvoluted laser extinction imaging, and soot temperature distributions using deconvoluted multiline emission imaging. Flowfield modeling based on the work of Spalding is presented. The present work explores whether soot properties of these flames are universal functions of mixture fraction, i.e., whether they satisfy soot state relationships. Measurements are presented, including radiative emissions and distributions of soot temperature and soot volume fraction. It is shown that most of the volume of these flames is bounded by the dividing streamline and thus should follow residence time state relationships. Most streamlines from the fuel supply to the surroundings are found to exhibit nearly the same maximum soot volume fraction and temperature. The radiation intensity along internal streamlines also is found to have relatively uniform values. Finally, soot state relationships were observed, i.e., soot volume fraction was found to correlate with estimated mixture fraction for each fuel/pressure selection. These results support the existence of soot property state relationships for steady nonbuoyant laminar diffusion flames, and thus in a large class of practical turbulent diffusion flames through the application of the laminar flamelet concept.

Diez, F. J.↗
NASA NTRS1998

Orbital Processing of Eutectic Rod-Like Arrays

The eutectic is one of only three solidification classes that exist. The others are isostructural and peritectic-class reactions, respectively. Simplistically, in a binaryeutectic phase diagram, a single liquid phase isothermally decomposes to two solid phases in a cooperative manner. The melting point minimum at the eutectic composition, isothermal solidification temperature, near-isocompositional solidification and refined solidification microstructure lend themselves naturally to such applications as brazing and soldering; industries that eutectic alloys dominate. Interest in direct process control of microstructures has led, more recently, to in-situ eutectic directional solidification with applications in electro-magnetics and electro-optics. In these cases, controlled structural refinement and the high aspect ratio and regularity of the distributed eutectic phases is highly significant to the fabrication and application of these in-situ natural composites. The natural pattern formation and scaling of the dispersed phase on a sub-micron scale has enormous potential application, since fabricating bulk materials on this scale mechanically has proven to be particularly difficult. It is thus of obvious importance to understand the solidification of eutectic materials since they are of great commercial significance. The dominant theory that describes eutectic solidification was derived for diffusion-controlled growth of alloys where both solid eutectic phases solidify metallically, i.e. without faceting at the solidification interface. Both high volume fraction (lamellar) and low volume fraction (rod-like) regular metallic arrays are treated by this theory. Many of the useful solders and brazements, however, and most of the regular in-situ composites are characterized by solidification reactions that are faceted/non-faceted in nature, rather than doubly non-faceted (metallic). Further, diffusion-controlled growth conditions are atypical terrestrially since gravitationally-driven convection is pervasive. As a consequence, it is important to determine whether these faceted/non-faceted composites behave in the same manner as their doubly non-faceted counterparts, particularly in the presence of convection. Prior analytical convective sensitivity testing of this theory predicted insensitivity. Prior experimental testing of this theory offered broad-based agreement between theory and experiment, though most results were for high volume fraction lamellar eutectics that solidified without faceting at the solidification interface. Directional solidification experiments of low volume fraction rod eutectics under damped (microgravity or magnetic field) conditions, however, have demonstrated significant sensitivity, challenging this fundamental theory. More recent theories have been proposed which introduce kinetic undercooling, faceting, fluid shear of the solute redistribution zone and the possibility that the interface composition is not the same as the bulk liquid composition. This program tests the established and proposed analytical theories and addresses the origins of discrepancies between the experimental and analytical results.

Larson, David J., Jr.↗
NASA NTRS2004

Evaporation and Accompanying Isotopic Fractionation of Sulfur from FE-S Melt During Shock Wave Heating

Chondrules probably formed by melting and subsequent cooling of solid precursors. Evaporation during chondrule melting may have resulted in depletion of volatile elements in chondrules. It is known that kinetic evaporation, especially evaporation from a melt, often leads to enrichment of heavy isotopes in an evaporation residue. However, no evidence for a large degree of heavy-isotope enrichment has been reported in chondrules for K, Mg, Si, and Fe (as FeO). The lack of isotopic fractionation has also been found for sulfur in troilites (FeS) within Bishunpur (LL3.1) and Semarkona (LL3.0) chondrules by an ion microprobe study. The largest fractionation, found in only one grain, was 2.7 +/- 1.4 %/amu, while all other troilite grains showed isotopic fractionations of <1 %/amu. The suppressed isotopic fractionation has been interpreted as results of (i) rapid heating of precursors at temperatures below the silicate solidus and (ii) diffusion-controlled evaporation through a surrounding silicate melt at temperatures above the silicate solidus. The kinetic evaporation model suggests that a rapid heating rate of >10(exp 4)-10(exp 6) K/h for a temperature range of 1000-1300 C is required to explain observed isotopic fractionations. Such a rapid heating rate seems to be difficult to be achieved in the X-wind model, but can be achieved in shock wave heating models. In this study, we have applied the sulfur evaporation model to the shock wave heating conditions of to evaluate evaporation of sulfur and accompanying isotopic fractionation during shock wave heating at temperatures below the silicate solidus.

Tachibana, S.↗
DOE OSTI2017

Search for photons with energies above 10 18 eV using the hybrid detector of the Pierre Auger Observatory

A search for ultra-high energy photons with energies above 1 EeV is performed using nine years of data collected by the Pierre Auger Observatory in hybrid operation mode. An unprecedented separation power between photon and hadron primaries is achieved by combining measurements of the longitudinal air-shower development with the particle content at ground measured by the fluorescence and surface detectors, respectively. Only three photon candidates at energies 1 - 2 EeV are found, which is compatible with the expected hadron-induced background. Upper limits on the integral flux of ultra-high energy photons of 0.027, 0.009, 0.008, 0.008 and 0.007 km$^{-2}$ sr$^{-1}$ yr$^{-1}$ are derived at 95% C.L. for energy thresholds of 1, 2, 3, 5 and 10 EeV. These limits bound the fractions of photons in the all-particle integral flux below 0.1%, 0.15%, 0.33%, 0.85% and 2.7%. For the first time the photon fraction at EeV energies is constrained at the sub-percent level. The improved limits are below the flux of diffuse photons predicted by some astrophysical scenarios for cosmogenic photon production. Here, the new results rule-out the early top-down models $-$ in which ultra-high energy cosmic rays are produced by, e.g., the decay of super-massive particles $-$ and challenge the most recent super-heavy dark matter models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2004

The Liquid-Water Oscillation in Modeling Boundary-Layer Cumuli with Third-Order Turbulence Closure Models

A hierarchy of third-order turbulence closure models are used to simulate boundary-layer cumuli in this study. An unrealistically strong liquid-water oscillation (LWO) is found in the fully prognostic model, which predicts all third moments. The LWO propagates from cloud base to cloud top with a speed of 1 m/s. The period of the oscillation is about 1000 s. Liquid-water buoyancy terms in the third-moment equations contribute to the LWO. The LWO mainly affects the vertical profiles of cloud fraction, mean liquid-water mixing ratio and the fluxes of liquid-water potential temperature and total water, but has less impact on the vertical profiles of other second-moments and third-moments. In order to minimize the LWO, a moderate large diffusion coefficient and a large turbulent dissipation at its originating level are needed. However, this approach distorts the vertical distributions of cloud fraction and liquid-water mixing ratio. A better approach is to parameterize liquid-water buoyancy more reasonably. A minimally prognostic model, which diagnoses all third moments except for vertical velocity, is shown to produce better results, compared to a fully prognostic model.

Cheng, A.↗
NASA NTRS1994

Loss of solar He and Ne from IDPS in subducting sediment: Diffusion and the effect of phase changes

The results of the diffusion experiment for solar He and Ne in IDP's in a magnetic separate from Pacific Ocean sediment suggest that solar He and Ne would be easily released from IDP grains and hence lost from subducting slabs at shallow depths. However, since the diffusion experiments was conducted under high vacuum, there may be a possibility that magnetite grains, which are supposedly the main constituent of the magnetic fraction, might be partly reduced to form a metal phase due to low oxygen fugacity in the experimental condition. If this is the case, such a phase change might affect the gas release and hence the results of the diffusion coefficients. In order to examine whether or not such a phase change really occurred in the condition of the diffusion experiment, I conducted a heating experiment for a magnetic separate from Pacific Ocean sediment. In the same condition as in the diffusion experiment, and the run products were examined with an x ray diffraction method. Three samples were prepared: they were wrapped with platinum foil, put in a vacuum line, and heated in a molybdenum crucible for two hours at 500 C, 800 C,and 950 C, respectively. After cooling the furnace, the samples were taken out from the crucible and analyzed with an x ray diffraction method.

Hiyagon, H.↗
DOE OSTI2021

The response of the Amazon ecosystem to the photosynthetically active radiation fields: integrating impacts of biomass burning aerosol and clouds in the NASA GEOS Earth system model

The Amazon experiences fires every year, and the resulting biomass burning aerosols, together with cloud particles, influence the penetration of sunlight through the atmosphere, increasing the ratio of diffuse to direct photosynthetically active radiation (PAR) reaching the vegetation canopy and thereby potentially increasing ecosystem productivity. In this study, we use the NASA Goddard Earth Observing System (GEOS) model with coupled aerosol, cloud, radiation, and ecosystem modules to investigate the impact of Amazon biomass burning aerosols on ecosystem productivity, as well as the role of the Amazon's clouds in tempering this impact. The study focuses on a 7-year period (2010–2016) during which the Amazon experienced a variety of dynamic environments (e.g., La Niña, normal years, and El Niño). The direct radiative impact of biomass burning aerosols on ecosystem productivity – called here the aerosol diffuse radiation fertilization effect – is found to increase Amazonian gross primary production (GPP) by 2.6 % via a 3.8 % increase in diffuse PAR (DFPAR) despite a 5.4 % decrease in direct PAR (DRPAR) on multiyear average during burning seasons. On a monthly basis, this increase in GPP can be as large as 9.9 % (occurring in August 2010). Consequently, the net primary production (NPP) in the Amazon is increased by 1.5 %, or ~92 Tg C yr -1 – equivalent to ~37 % of the average carbon lost due to Amazon fires over the 7 years considered. Clouds, however, strongly regulate the effectiveness of the aerosol diffuse radiation fertilization effect. The efficiency of this fertilization effect is the highest in cloud-free conditions and linearly decreases with increasing cloud amount until the cloud fraction reaches ~0.8, at which point the aerosol-influenced light changes from being a stimulator to an inhibitor of plant growth. Nevertheless, interannual changes in the overall strength of the aerosol diffuse radiation fertilization effect are primarily controlled by the large interannual changes in biomass burning aerosols rather than by changes in cloudiness during the studied period.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2021

The Response of the Amazon Ecosystem to the Photosynthetically Active Radiation Fields: Integrating Impacts of Biomass Burning Aerosol and Clouds in the NASA GEOS Earth System Model

The Amazon experiences fires every year, and the resulting biomass burning aerosols, together with cloud particles, influence the penetration of sunlight through the atmosphere, increasing the ratio of diffuse to direct photosynthetically active radiation (PAR) reaching the vegetation canopy and thereby potentially increasing ecosystem productivity. In this study, we use the NASA Goddard Earth Observing System (GEOS) model with coupled aerosol, cloud, radiation, and ecosystem modules to investigate the impact of Amazon biomass burning aerosols on ecosystem productivity, as well as the role of the Amazon’s clouds in tempering this impact. The study focuses on a seven-year period (2010-2016) during which the Amazon experienced a variety of dynamic environments (e.g., La Niña, normal years, and El Niño). The direct radiative impact of biomass burning aerosols on ecosystem productivity—called here the aerosol diffuse radiation fertilization effect —is found to increase Amazonian Gross Primary Production (GPP) by 2.6% via a 3.8% increase in diffuse PAR (DFPAR) despite a 5.4% decrease in direct PAR (DRPAR) on multiyear average during burning seasons. On a monthly basis, this increase in GPP can be as large as 9.9% (occurring in August 2010). Consequently, the net primary production (NPP) in Amazon is increased by 1.5%, or ~92 Tg C a-1– equivalent to ~37% of the average carbon lost due to Amazon fires over the seven years considered. Clouds, however, strongly regulate the effectiveness of the aerosol diffuse radiation fertilization effect. The efficiency of this fertilization effect is the highest in cloud-free conditions and linearly decreases with increasing cloud amount until the cloud fraction reaches ~0.8, at which point the aerosol-influenced light changes from being a stimulator to an inhibitor of plant growth. Nevertheless, interannual changes in the overall strength of the aerosol diffuse radiation fertilization effect are primarily controlled by the large interannual changes in biomass burning aerosols rather than by changes in cloudiness during the studied period.

biomass burning aerosols on ecosystem productivity↗
DOE OSTI2014

Effect of cold drawing ratio on γ′ precipitation in Inconel X-750

Inconel X-750 is a Ni-based precipitation-hardened superalloy having large tensile and fracture strengths. In the study, X-750 wires were cold drawn to different extents. Small angle neutron scattering was employed to quantitatively measure the size and volume fraction of the γ′ phase as a function of the cold drawing ratio (DR) and aging temperature. The presence and size of γ′ precipitates were confirmed by transmission electron microscopy. The drawing ratio had an important effect on the volume fraction of the γ′ precipitates. However, the size of the precipitates was independent on the drawing ratio. The specimen with the minimum drawing ratio (DR0) produced the largest volume fraction of γ′ as compared with large drawing ratio (DR) specimens such as DR17 and DR42. The small volume fraction of the γ′ phase for a sizeable drawing ratio was associated with the large amount of nucleation sites for secondary carbides, M{sub 23}C{sub 6}, and the fast diffusion path, i.e., dislocation, needed to form M{sub 23}C{sub 6}. A Cr depletion zone around the secondary carbides raised the solubility of γ′. Therefore, the significant drawing ratio contributing to the large volume fraction of the secondary carbides decreased the volume fraction of the γ′ precipitates in Inconel X-750. - Highlights: • The volume fraction of secondary carbides increased with the drawing ratio. • The volume fraction of γ′ decreased as the drawing ratio increased. • The drawing ratio affected the γ′ volume fraction with no variation of the γ' size. • The volume fraction of γ′ was affected by the secondary carbide volume fraction.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Development of a Novel Equilibrium Passive Sampling Device for Methylmercury in Sediment and Soil Porewaters

In this work, we explored the concept of equilibrium passive sampling for methylmercury (MeHg) using the strategy developed for hydrophobic organic chemicals. Passive sampling should allow prediction of the concentration of the chemically labile fraction of MeHg in sediment porewaters based on equilibrium partitioning into the sampler, without modeling diffusion rates through the sampler material. Our goals were to identify sampler materials with the potential to mimic MeHg partitioning into animals and sediments and provide reversible sorption in a time frame appropriate for in situ samplers. Candidate materials tested included a range of polymers embedded with suitable sorbents for MeHg. The most promising were activated carbon (AC) embedded in agarose, thiol–self-assembled monolayers on mesoporous supports embedded in agarose, and cysteine-functionalized polyethylene terephthalate, which yielded log sampler–water partition coefficients of 2.8 to 5 for MeHgOH and MeHg complexed with dissolved organic matter (Suwannee River humic acid). Sampler equilibration time in sediments was approximately 1 to 2 wk. Investigation of the MeHg accumulation mechanism by AC embedded in agarose suggested that sampling was kinetically influenced by MeHg interactions with AC particles and not limited by diffusion through the gel for this material. Also, AC exhibited relatively rapid desorption of Hg and MeHg, indicating that this sorbent is capable of reversible, equilibrium measurements. In sediment:water microcosms, porewater concentrations made with isotherm-calibrated passive samplers agreed within a factor of 2 (unamended sediment) or 4 (AC-amended sediment) with directly measured concentrations. The present study demonstrates a potential new approach to passive sampling of MeHg.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Effects of Surgery and Proton Therapy on Cerebral White Matter of Craniopharyngioma Patients

Purpose: The purpose of this study was to determine radiation dose effect on the structural integrity of cerebral white matter in craniopharyngioma patients receiving surgery and proton therapy. Methods and Materials: Fifty-one patients (2.1-19.3 years of age) with craniopharyngioma underwent surgery and proton therapy in a prospective therapeutic trial. Anatomical magnetic resonance images acquired after surgery but before proton therapy were inspected to identify white matter structures intersected by surgical corridors and catheter tracks. Longitudinal diffusion tensor imaging (DTI) was performed to measure microstructural integrity changes in cerebral white matter. Fractional anisotropy (FA) derived from DTI was statistically analyzed for 51 atlas-based white matter structures of the brain to determine radiation dose effect. FA in surgery-affected regions in the corpus callosum was compared to that in its intact counterpart to determine whether surgical defects affect radiation dose effect. Results: Surgical defects were seen most frequently in the corpus callosum because of transcallosal resection of tumors and insertion of ventricular or cyst catheters. Longitudinal DTI data indicated reductions in FA 3 months after therapy, which was followed by a recovery in most white matter structures. A greater FA reduction was correlated with a higher radiation dose in 20 white matter structures, indicating a radiation dose effect. The average FA in the surgery-affected regions before proton therapy was smaller (P=.0001) than that in their non–surgery-affected counterparts with more intensified subsequent reduction of FA (P=.0083) after therapy, suggesting that surgery accentuated the radiation dose effect. Conclusions: DTI data suggest that mild radiation dose effects occur in patients with craniopharyngioma receiving surgery and proton therapy. Surgical defects present at the time of proton therapy appear to accentuate the radiation dose effect longitudinally. This study supports consideration of pre-existing surgical defects and their locations in proton therapy planning and studies of treatment effect.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2026

Thermal cycling-driven microstructural changes of eutectic Al–Si phase change materials in SS304 containers revealed by multi-modal imaging

Aluminum-based Al–Si alloys are widely used as phase change materials (PCMs) in thermal energy storage (TES) systems owing to their high volumetric latent heat and superior thermal conductivity. However, their long-term reliability is limited by degradation processes that remain insufficiently understood. In this work, we employ a multimodal, correlative characterization framework to systematically resolve the degradation behavior of eutectic Al–Si PCMs in contact with SS304 containers under repeated thermal cycling. By integrating high-resolution electron microscopy, three-dimensional X-ray fluorescence (3D XRF) imaging, and differential scanning calorimetry (DSC), we directly link spatially resolved compositional and microstructural evolution to changes in thermophysical properties. The correlative analysis reveals that elemental leaching of Fe, Cr, and Ni from the stainless-steel container into the PCM drives the formation of intermetallic compounds (IMCs) both at the interface and within the bulk PCM, leading to pronounced compositional heterogeneity. These interfacial reactions and diffusion-induced transformations progressively destabilize the Al–Si eutectic, reducing the effective phase-transforming fraction. Consistent with these observations, DSC measurements show a decrease in melting temperature and latent heat of fusion with thermal cycling. These results underscore the critical influence of interfacial reactions and material compatibility on the stability, durability, and overall performance of Al–Si-based TES systems.

25 ENERGY STORAGE↗
DOE OSTI2016

Local Structural Investigations, Defect Formation, and Ionic Conductivity of the Lithium Ionic Conductor Li 4 P 2 S 6

Glassy, glass–ceramic, and crystalline lithium thiophosphates have attracted interest in their use as solid electrolytes in all-solid-state batteries. Despite similar structural motifs, including PS 4 3– , P 2 S 6 4– , and P 2 S 7 4– polyhedra, these materials exhibit a wide range of possible compositions, crystal structures, and ionic conductivities. Here, we present a combined approach of Bragg diffraction, pair distribution function analysis, Raman spectroscopy, and 31 P magic angle spinning nuclear magnetic resonance spectroscopy to study the underlying crystal structure of Li 4 P 2 S 6 . In this work, we show that the material crystallizes in a planar structural arrangement as a glass ceramic composite, explaining the observed relatively low ionic conductivity, depending on the fraction of glass content. Calculations based on density functional theory provide an understanding of occurring diffusion pathways and ionic conductivity of this Li + ionic conductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

A 'nu' look at gravitational waves: the black hole birth rate from neutrinos combined with the merger rate from LIGO

We make projections for measuring the black hole birth rate from the diffuse supernova neutrino background (DSNB) by future neutrino experiments, and constrain the black hole merger fraction ε, when combined with information on the black hole merger rate from gravitational wave experiments such as LIGO. The DSNB originates from neutrinos emitted by all the supernovae in the Universe, and is expected to be made up of two components: neutrinos from neutron-star-forming supernovae, and a sub-dominant component at higher energies from black-hole-forming 'unnovae'. We perform a Markov Chain Monte Carlo analysis of simulated data of the DSNB in an experiment similar to Hyper-Kamiokande, focusing on this second component. Since all knowledge of the neutrino emission from unnovae comes from simulations of collapsing stars, we choose two sets of priors: one where the unnovae are well-understood and one where their neutrino emission is poorly known. By combining the black hole birth rate from the DSNB with projected measurements of the black hole merger rate from LIGO, we show that the fraction of black holes which lead to binary mergers observed today ε could be constrained to be within the range 2 ⋅ 10{sup −4} ≤ ε ≤ 3 ⋅ 10{sup −2} at 3 σ confidence, after ten years of running an experiment like Hyper-Kamiokande.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

MFiX: Fractional-Step Method Implementation

A comprehensive, multiphase computational fluid dynamics (CFD) simulation solves several coupled transport equations including continuity, momentum, species, and energy. Chemical reactions further couple these equations through heats of reaction and rates of formation of products and rates of destruction of reactants. A fractional-step method separates changes attributed to chemical reactions from transport phenomena like convection and diffusion. When the governing equations are split into the transport and reacting components, efficient and independent methodologies can be exploited to solve the different systems. Specifically, discretization of field variable transport equations results in large, sparse matrices which are loosely coupled. These systems are solved in succession using iterative techniques that take advantage of the matrix structure. In contrast, chemical reactions tightly couple field variables locally within the domain (e.g., within a single computational cell) resulting in low dimensional but dense, nonlinear systems that are better solved using direct integration techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗