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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Carbon Isotope Fractionations Associated with Methanotrophic Growth with the Soluble and Particulate Methane Monooxygenases

Growth experiments with the RuMP-type methanotroph, Methylococcus capsulatus (Bath), have demonstrated that biomass and lipid biomarkers are significantly depleted in C-13 compared to the substrate methane and that the extent of fractionation is dependent on whether cells express the soluble (s) or particulate (p) methane monooxygenase (MMO). The presence or absence of the characteristic sMMO subunits was monitored using SDS-polyacrylamide gels. In M. capsulatus grown with no Cu supplementation, the characteristic sMMO subunits were observed in the soluble fraction throughout the entire growth period and biomass was depleted in C-13 by approximately 14,700 relative to substrate methane. In cells grown with 5uM Cu, no sMMO bands were observed and a greater fractionation of approximately 27,700 in resultant biomass was obtained. Methanol growth experiments with M. capsulatus and with a RuMP methylotroph, Methylophilus methylotrophus, in which biomass measurements yielded depletions in C-13 of 9 and 5%(sub o), respectively, suggest that oxidation of methane is the major fractionation step. Growth of M. capsulatus at a low level of oxygen, approximately 0.5%, had no significant effect on carbon isotope fractionation by either sMMO or pMMO. These observations are significant for identification of molecular biomarkers; and methanotrophic contributions to carbon isotope composition in natural environments.

Jahnke, Linda L.↗
NASA NTRS2002

Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

Lorenzo, Carl F.↗
NASA NTRS2004

Modeling of Isotope Fractionation in Stratospheric CO2, N2O, CH4, and O3: Investigations of Stratospheric Chemistry and Transport, Stratosphere-Troposphere Exchange, and Their Influence on Global Isotope Budgets

We investigated the isotopic fractionation of CH4 and hydrogen (H2) in the stratosphere by incorporating isotope-specific rate coefficients into the Lawrence Livermore National Laboratory (LLNL) 2D model and comparing the model results with new observations from the NASA ER-2 aircraft (funded through a separate task under the Upper Atmosphere Research Program). The model results reveal that fractionation which occurs in the stratosphere has a significant influence on isotope compositions in the free troposphere, an important point which had previously been ignored, unrecognized or unquantified for many long-lived trace gases, including CH4 and H2 which we have focused our efforts on to date. Our analyses of the model results and new isotope observations have also been used to test how well the kinetic isotope effects are known, at least to within the uncertainties in model chemistry and transport. Overall, these results represent an important step forward in our understanding of isotope fractionation in the atmosphere and demonstrate that stratospheric isotope fractionation cannot be ignored in modeling studies which use isotope observations in the troposphere to infer the global budgets of CH4 (an important greenhouse gas) and of H2 (a gas whose atmospheric budget must be better quantified, particularly before a large human perturbation from fuel cell use is realized). Our analyses of model results and observations from the NASA ER-2 aircraft are briefly summarized separately below for CH4, H2, and H2O and for the contribution of these modeling studies to date to our understanding of isotope fractionation for N2O, CO2, and O3 as well.

Boering, Kristie A.↗
NASA NTRS2011

Attitude Estimation in Fractionated Spacecraft Cluster Systems

An attitude estimation was examined in fractioned free-flying spacecraft. Instead of a single, monolithic spacecraft, a fractionated free-flying spacecraft uses multiple spacecraft modules. These modules are connected only through wireless communication links and, potentially, wireless power links. The key advantage of this concept is the ability to respond to uncertainty. For example, if a single spacecraft module in the cluster fails, a new one can be launched at a lower cost and risk than would be incurred with onorbit servicing or replacement of the monolithic spacecraft. In order to create such a system, however, it is essential to know what the navigation capabilities of the fractionated system are as a function of the capabilities of the individual modules, and to have an algorithm that can perform estimation of the attitudes and relative positions of the modules with fractionated sensing capabilities. Looking specifically at fractionated attitude estimation with startrackers and optical relative attitude sensors, a set of mathematical tools has been developed that specify the set of sensors necessary to ensure that the attitude of the entire cluster ( cluster attitude ) can be observed. Also developed was a navigation filter that can estimate the cluster attitude if these conditions are satisfied. Each module in the cluster may have either a startracker, a relative attitude sensor, or both. An extended Kalman filter can be used to estimate the attitude of all modules. A range of estimation performances can be achieved depending on the sensors used and the topology of the sensing network.

Hadaegh, Fred Y.↗
NASA NTRS2009

A Simple Mechanism for Fractionating Oxygen Isotopes in the Solar Nebula

Lightning in the Solar Nebula is caused by the tribo-electric charging of dust grains carried by massive turbulent flows and driven by the accretion energy in the disk: it has long been one agent assumed responsible for the formation of chondrules. The degree to which charge separation can occur is dependent upon a number of factors, including the concentration of radioactive sources and the total level of ionization in the nebula, and these factors determine the maximum energy likely to be released by a single bolt. While chondrule formation requires a massive discharge, even a small lightning bolt can vaporize grains in the ionized discharge channel. Experimental studies have shown that silica, iron silicate and iron oxide grains formed from a high voltage discharge in hydrogen rich gas containing some oxygen produces solids that are enriched in O-17 and O-18 relative to the composition of the starting gas. Vaporization of silicates produces SiO, metal and free oxygen atoms in each discharge and these species will immediately begin to recondense from the hot plasma. Freshly condensed grains are incrementally enriched in heavy oxygen while the gas is enriched in O-16. Repeated evaporation and condensation of silicates in continuously occurring lightning discharges will monotonically increase the fractionation of oxygen isotopes between the O-17 and O-18 rich dust and the O-16 rich gas. The first mass independently fractionated refractory oxide particles were produced in the lab following the condensation of a flowing gas mixture containing variable amounts of hydrogen, silane, pentacarbonyl iron and oxygen that passed through a high voltage discharge powered by a Tesla coil. While the exact chemical pathway is still uncertain, the most probable reaction mechanisms involve oxidation of the growing refractory clusters by O3, OH or O atoms. This model has some interesting consequences for chemical processes in the early solar nebula. Chemical fractionation of recondensed dust evaporated via lightning discharges should be strongly time dependent. At earlier times, the accretion rate is maximal, thus driving strong turbulence, energetic grain-grain collisions, tribo-electric charging and charge separation, leading to frequent, powerful lightning discharges. As the accretion rate diminishes, turbulence decreases and lightning discharges will become both less powerful and less frequent, thus decreasing the rate of dust-gas fractionation. The most rapid increase in the formation of O-16 poor dust will occur early in nebular history. Generation of fractionated dust should be distributed throughout the inner disk. Once condensed, grain dispersal would average out any significant isotopic anomalies within the inner disk.

Nuth, Joseph A., III↗
NASA NTRS2011

Observations of Nitrogen Isotope Fractionation in Prestellar Cores

Isotopically fractionated material is found in many solar system objects, including meteorites and comets [1]. It is considered, in some cases, to trace interstellar material that was incorporated into the solar system without undergoing significant processing, thus preserving the fractionation. In interstellar molecular clouds, ion-molecule chemistry continually cycles nitrogen between the two main reservoirs - Nand N2 - leading to only minor N-15 enrichments [2]. Charnley and Rodgers [3,4] showed that depletion of CO removes oxygen from the gas and weakens this cycle such that significant N-15 fractionation can occur for N2 and other N-bearing species in such cores. Observations are being conducted at millimeter and submillimeter wavelengths employing various facilities in order to both spatially and spectrally, resolve emission from these cores. A preliminary study to obtain the N-14/N-15 ratio in nitriles was conducted at the Arizona Radio Observatory's 12m telescope on Kitt Peak, AZ. Spectra were obtained at high resolution (0.08 km/s) in order to resolve dynamic properties of each source as well as to resolve hyperfine structure present in certain isotopologues. This study included four dark cloud cores, observed to have varying levels of molecular depletion: Ll521E, Ll498, Ll544, and Ll521F. Previous studies of the N-14/N-15 ratio towards Ll544 were obtained with N2H(+) and NH3 yielding ratios of 446 and greater than 700, respectively [5,6]. The discrepancy observed in these two measurements suggests a strong chemical dependence on the fractionation of nitrogen. Ratios (C,N, and D) obtained from isotopologues for a particular molecule are likely tracing the same chemical heritage and are directly comparable within a given source. Results and comparisons between the protostellar evolutionary state and isomer isotope fractionation as well as between other N-bearing species will be presented.

Milam, Stefanie N.↗
NASA NTRS2011

Isotope Fractionation Studies in Prestellar Cores: The Case of Nitrogen

Isotopically fractionated material is found in many solar system objects, including meteorites and comets. It is considered, in some cases, to trace interstellar material that was incorporated into the solar system without undergoing significant processing, thus preserving the fractionation. In interstellar molecular clouds, ion-molecule chemistry continually cycles nitrogen between the two main reservoirs - N and N2 - leading to only minor N-15 enrichments. Charnley and Rodgers showed that depletion of CO removes oxygen from the gas and weakens this cycle such that significant N-15 fractionation can occur for N2 and other N-bearing species in such cores. Observations are being conducted at millimeter and submillimeter wavelengths employing various facilities in order to both spatially and spectrally, resolve emission from these cores. A preliminary study to obtain the N-14/N-15 ratio in nitriles (HCN and HNC) was conducted at the Arizona Radio Observatory's 12m telescope on Kitt Peak, AZ. Spectra were obtained at high resolution (0.08 km/s) in order to resolve dynamic properties of each source as well as to resolve hyperfine structure present in certain isotopologues. This study included four dark cloud cores, observed to have varying levels of molecular depletion: L1521E, L1498, L1544, and L1521F. Previous studies of the N-14/N-15 ratio towards LI544 were obtained with N2H+ and NIH3, yielding ratios of 446 and >700, respectively. The discrepancy observed in these two measurements suggests a strong chemical dependence on the fractionation of nitrogen. Ratios (C,N, and D) obtained from isotopologues for a particular molecule are likely tracing the same chemical heritage and are directly comparable within a given source. Results and comparisons between the protostellar evolutionary state and isomer isotope fractionation as well as between other N-bearing species will be presented.

Milam, Stefanie N.↗
NASA NTRS2012

Observations of Carbon Isotopic Fractionation in Interstellar Formaldehyde

Primitive Solar System materials (e.g. chondrites. IDPs, the Stardust sample) show large variations in isotopic composition of the major volatiles (H, C, N, and O ) even within samples, witnessing to various degrees of processing in the protosolar nebula. For ex~ ample. the very pronounced D enhancements observed in IDPs [I] . are only generated in the cold. dense component of the interstellar medium (ISM), or protoplanetary disks, through ion-molecule reactions in the presence of interstellar dust. If this isotopic anomaly has an interstellar origin, this leaves open the possibility for preservation of other isotopic signatures throughout the form ation of the Solar System. The most common form of carbon in the ISM is CO molecules, and there are two potential sources of C-13 fractionation in this reservoir: low temperature chemistry and selective photodissociation. While gas-phase chemistry in cold interstellar clouds preferentially incorporates C-13 into CO [2], the effect of self-shielding in the presence of UV radiation instead leads to a relative enhancement of the more abundant isotopologue, 12CO. Solar System organic material exhibit rather small fluctuations in delta C-13 as compared to delta N-15 and delta D [3][1], the reason for which is still unclear. However, the fact that both C-13 depleted and enhanced material exists could indicate an interstellar origin where the two fractionation processes have both played a part. Formaldehyde (H2CO) is observed in the gas-phase in a wide range of interstellar environments, as well as in cometary comae. It is proposed as an important reactant in the formation of more complex organic molecules in the heated environments around young stars, and formaldehyde polymers have been suggested as the common origin of chondritic insoluable organic matter (IOM) and cometary refractory organic solids [4]. The relatively high gas-phase abundance of H2CO observed in molecular clouds (10(exp- 9) - 10(exp- 8) relative to H2) makes it feasible to observe its less common isotopologues. As a step in our investigation of C-13 fractionation patterns in the ISM, we here present comparisons between observations of the C-13 fraction in formaldehyde, and chemical fractionation models.

Wirstrom, E. S.↗
NASA NTRS2016

Coordinated Isotopic and Mineral Characterization of Highly Fractionated 18O-Rich Silicates in the Queen Alexandra Range 99177 CR3 Chondrite

Carbonaceous chondrites contain a mixture of solar system condensates, pre-solar grains, and primitive organic matter. Each of these materials record conditions and processes in different regions of the solar nebula, on the meteorite parent body, and beyond the solar system. Oxygen isotopic studies of meteorite components can trace interactions of distinct oxygen isotopic reservoirs in the early solar system and secondary alteration processes. The O isotopic compositions of the earliest solar system condensates fall along a carbonaceous chondrite anhydrous mineral (CCAM) line of slope approximately 1 in a plot of delta 17O against delta 18O. This trend is attributed to mixing of material from 16O-poor and 16O-rich reservoirs. Secondary processing can induce mass-dependent fractionation of the O isotopes, shifting these compositions along a line of slope approximately 0.52. Substantial mass-dependent fractionation of O isotopes has been observed in secondary minerals in CAIs, calcite, and FUN inclusions. These fractionations were caused by significant thermal or aqueous alteration. We recently reported the identification of four silicate grains with extremely fractionated O isotopic ratios (delta 18O equals 37 - 55 per mille) in the minimally altered CR3 chondrite QUE 99177. TEM analysis of one grain indicates it is a nebular condensate that did not experience substantial alteration. The history of these grains is thus distinct from those of the aforementioned fractionated materials. To constrain the origin of the silicate grains, we conducted further Mg and Fe isotopic studies and TEM analyses of two grains.

Nguyen, A. N.↗
NASA NTRS2017

Revised Models of Interstellar Nitrogen Isotopic Fractionation

Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom-molecular ion and ion-molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirstrom et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral-neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of >2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.

Wirstrom, E. S.↗
NASA NTRS2014

Xenon Fractionation, Hydrogen Escape, and the Oxidation of the Earth

Xenon in Earth's atmosphere is severely mass fractionated and depleted compared to any plausible solar system source material, yet Kr is unfractionated. These observations seem to imply that Xe has escaped from Earth. But to date no process has been identified that can cause Xe, which is heavier than Kr, to escape while Kr does not. Vigorous hydrodynamic hydrogen escape can produce mass fractionation in heavy gases. The required hydrogen flux is very high but within the possible range permitted by solar Extreme Ultraviolet radiation (EUV, which here means radiation at wavelengths short enough to be absorbed efficiently by hydrogen) heating when Earth was on the order of 100 Myrs old or younger. However this model cannot explain why Xe escapes but Kr does not. Recently, what appears to be ancient atmospheric xenon has been recovered from several very ancient (3-3.5 Ga) terrestrial hydrothermal barites and cherts. What is eye-catching about this ancient Xe is that it is less fractionated that Xe in modern air. In other words, it appears that a process was active on Earth some 3 to 3.5 billion years ago that caused xenon to fractionate. By this time the Sun was no longer the EUV source that it used to. If xenon was being fractionated by escape — currently the only viable hypothesis — it had to be in the less unfamiliar context of Earth’s Archean atmosphere and under rather modest levels of EUV forcing. This requires a new model. Here we address the circumstances in which Xe, but not Kr, could escape from Earth as an ion. In a hydrodynamically escaping hydrogen wind the hydrogen is partially photo-ionized. The key concepts are that ions are much more strongly coupled to the escaping flow than are neutrals (so that a relatively modest flow of H and H+ to space could carry Xe+ along with it), and that xenon alone among the noble gases is more easily ionized than hydrogen. This sort of escape is possible if not prevented by a planetary magnetic field. The best prospects for Earth are therefore escape along the polar field lines, although a very weak or absent magnetic field would likely work as well. As applied to the Archean Earth the discussion will be constrained by diffusion-limited hydrogen escape. The extended history of hydrogen escape implicit in Xe escape in the Archean is consistent with suggestions that hydrogen escape from the anoxic Archean atmosphere was considerable, because biogenic methane is expected to have been rather abundant. Hydrogen escape plausibly played the key role in creating oxidizing condition at the surface of the Earth and setting the stage for the creation of an O2 atmosphere.

photo-ionized gases↗
NASA NTRS2017

Revised Models of Interstellar Nitrogen Isotopic Fractionation

Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom–molecular ion and ion–molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirström et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral–neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of >2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.

astrochemistry – molecular processes – comets: gen↗
NASA NTRS2017

Revised Models of Interstellar Nitrogen Isotopic Fractionation

Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom–molecular ion and ion–molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirström et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral–neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of >2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.

astrochemistry – molecular processes – comets: gen↗
NASA NTRS2017

Revised Models of Interstellar Nitrogen Isotopic Fractionation

Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of (15)N enrichments found in comets and meteorites. Chemical model calculations indicate that atom-molecular ion and ion-molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense loud chemistry show that the revised (15)N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirstrom et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included (15)N fractionation of CN in neutral-neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing (15)N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching (14)N/(15)N ratios of > 2000. Taking the updated nitrogen chemistry into account, no sigificant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the (14)N/(15)N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk (15)N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.

Astrochemistry↗
NASA NTRS2017

Revised Models of Interstellar Nitrogen Isotopic Fractionation

Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom-molecular ion and ion-molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modfications on the chemical model of Wirstrom et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral-neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of > 2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.

astrochemistry – molecular processes – comets: gen↗
DOE OSTI2026

Flow pattern and void fraction characterization in nitrogen/water flows through a diamond-type triply periodic minimal surface lattice

Here, this study presents, to the authors knowledge, the first experimental investigation on the void fraction and flow patterns in two-phase flows through a diamond-type Triply Periodic Minimal Surface (TPMS) lattice. An additively manufactured TPMS structure was tested under upward co-current flow of a water/nitrogen mixture. Superficial velocities varied for a total of 42 test conditions (gas: 0.01–2.4 m/s; liquid: 0.01–2.4 m/s; mass flux: 20–2370 kg/m 2 ·s). High-speed video and X-ray imaging enabled time-averaged void fraction measurements and identified six distinct flow regimes which were used to develop a flow pattern map. Comparison of the void fraction data with correlations from literature demonstrated the Rouhani and Axelsson (1970) [49] correlation modified by Steiner (1993) [52] provided the best agreement, which was improved with empirically fit coefficients. This approach predicted the void fraction with errors < ±20% for 64% of the data, with a mean absolute percent deviation (MAPD) of 23%. The measured frictional pressure drop was compared to correlations from literature which captured the observed trends but did not provide good accuracy. The best agreement was found after optimizing the empirical coefficients of the Muller-Steinhagen & Heck (1986) [56] correlation; this approach captured 33% of the data within ±20% with a MAPD of 46% over the full range and captured 71% of the data within ±20% a MAPD of 13.3% at mass fluxes >1100 kg/m 2 -s. These results provide foundational insight into TPMS two-phase flow behavior and inform modeling and design of advanced heat exchange components incorporating TPMS geometries.

42 - ENGINEERING↗
DOE OSTI2025

Generalized fractional approach to solving partial differential equations with arbitrary dispersion relations

The dynamics of physical systems are typically modeled by partial differential equations (PDEs). Because of the complexity in physical systems, PDE models rely on approximations or limiting cases. To model the full complexity of physical systems, it is necessary to use multiscale approaches where appropriate models are used at each level. Alternatively, complexity can be directly tackled by fractional integrodifferential equations that must be derived for each system. Here, we argue that complexity can be restored in PDEs by describing them from a fractional calculus perspective. Rather than deriving a fractional integrodifferential equation, we reinterpret the dispersion relation of the system by use of the Riesz definition, which contains the required information relating the energy and momentum space of the system and thus fully describes their dynamics. The approach is demonstrated by two examples: the Landau–Lifshitz equation in a 1D ferromagnetic chain and a modified KdV equation supporting surface gravity waves or Euler dispersion. The presented approach is applicable to fluids, soft matter, and solid-state matter and can be readily generalized to higher dimensions and more complex systems. While numerical calculations are needed to determine the fractional operator, the approach is analytical and can be utilized to determine analytical solutions and investigate nonlinear problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Assessing the accuracy of time-fraction and ductility exhaustion approaches for creep-fatigue damage prediction through feature-test validation

Determining creep-fatigue damage formation is critical for elevated temperature components integrity. This study evaluates creep-fatigue assessments with emphasis on differences between creep damage models. Evaluated are the time-fraction model and the classical and stress-modified ductility exhaustion creep damage models. This work extends the domain of stress-modified ductility exhaustion models by introducing and validating such formalism to Ni-based alloys. The fidelity of the assessments was benchmarked against uniaxial creep-fatigue and multiaxial feature tests of Alloy 617. For uniaxial specimens, best estimate predictions rank ductility exhaustion as the most accurate and precise and time-fraction as markedly conservative. For feature tests, ductility exhaustion predictions are within < 4.0 times difference, whereas time-fraction underpredicts life by factors of 7–14. The observations suggest ductility exhaustion models as alternative to time-fraction models in design codes for situations requiring characterization of the design margin. Further work in employing such models to assess other relevant phenomena (e.g., stress relaxation cracking) is discussed.

creep-fatigue↗