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A survey of the core-congruential formulation for geometrically nonlinear TL finite elements

This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.

Felippa, Carlos A.↗

Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

Casarin, Mario↗

Improved Finite Element Modeling of the Turbofan Engine Inlet Radiation Problem

Improvements have been made in the finite element model of the acoustic radiated field from a turbofan engine inlet in the presence of a mean flow. The problem of acoustic radiation from a turbofan engine inlet is difficult to model numerically because of the large domain and high frequencies involved. A numerical model with conventional finite elements in the near field and wave envelope elements in the far field has been constructed. By employing an irrotational mean flow assumption, both the mean flow and the acoustic perturbation problem have been posed in an axisymmetric formulation in terms of the velocity potential; thereby minimizing computer storage and time requirements. The finite element mesh has been altered in search of an improved solution. The mean flow problem has been reformulated with new boundary conditions to make it theoretically rigorous. The sound source at the fan face has been modeled as a combination of positive and negative propagating duct eigenfunctions. Therefore, a finite element duct eigenvalue problem has been solved on the fan face and the resulting modal matrix has been used to implement a source boundary condition on the fan face in the acoustic radiation problem. In the post processing of the solution, the acoustic pressure has been evaluated at Gauss points inside the elements and the nodal pressure values have been interpolated from them. This has significantly improved the results. The effect of the geometric position of the transition circle between conventional finite elements and wave envelope elements has been studied and it has been found that the transition can be made nearer to the inlet than previously assumed.

Roy, Indranil Danda↗

Investigating the Partitioning of Inorganic Elements Consumed by Humans between the Various Fractions of Human Wastes: An Alternative Approach

The elemental composition of food consumed by astronauts is well defined. The major elements carbon, hydrogen, oxygen, nitrogen and sulfur are taken up in large amounts and these are often associated with the organic fraction (carbohydrates, proteins, fats etc) of human tissue. On the other hand, a number of the elements are located in the extracellular fluids and can be accounted for in the liquid and solid waste fraction of humans. These elements fall into three major categories - cationic macroelements (e.g. Ca, K, Na, Mg and Si), anionic macroelements (e.g. P, S and Cl and 17 essential microelements, (e.g. Fe, Mn, Cr, Co, Cu, Zn, Se and Sr). When provided in the recommended concentrations to an adult healthy human, these elements should not normally accumulate in humans and will eventually be excreted in the different human wastes. Knowledge of the partitioning of these elements between the different human waste fractions is important in understanding (a) developing waste separation technologies, (b) decision-making on how these elements can be recovered for reuse in space habitats, and (c) to developing the processors for waste management. Though considerable literature exists on these elements, there is a lack of understanding and often conflicting data. Two major reasons for these problems include the lack of controlled experimental protocols and the inherently large variations between human subjects (Parker and Gallagher, 1988). We have used the existing knowledge of human nutrition and waste from the available literature and NASA documentation to build towards a consensus to typify and chemically characterize the various human wastes. It is our belief, that this could be a building block towards integrating a human life support and waste processing in a closed system.

Wignarajah, Kanapathipillai↗

Partitioning of Inorganic Elements Consumed by Humans Between the Various Fractions of Human Wastes: A Review and Analysis of Existing Literature

The nutritional requirements of humans and astronauts are well defined and show consistency, but the same cannot be said of human wastes. Nutrients taken up by humans can be considered to fall into two major categories - organic and inorganic fractions. Carbon, hydrogen, oxygen, nitrogen and sulfur are elements that are associated with the organic fraction. These elements are taken up in large amounts by humans and when metabolized released in wastes often in gaseous forms or as water. On the other hand, a large number of the elements are simply exchanged and can be accounted for in the liquid and solid wastes of humans. These elements fall into three major categories - cationic macroelements (e.g. Ca, K, Na, Mg and Si), anionic macroelements (e.g P, S and Cl), 17 essential microelements, (e.g. Fe, Mn, Cr, Co, Cu, Zn, Se and Sr). When provided in the recommended concentrations to an adult human, these elements should not normally accumulate in humans, but will be excreted in the different human wastes. Knowledge of the partitioning of these elements between the different human waste fractions is fundamental to understanding (a) how these elements can be recovered for reuse in space habitats, and (b) to developing the processors for waste management. The current literature is exhaustive but sometimes also conflicting. We have used the existing knowledge of nutrition and waste from medical literature and NASA documentation to develop a consensus to typify and chemically characterize the various human wastes. The partitioning of these elements has been developed into a functional model.

Wignarajah, K.↗

Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element

Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and finite element results.

Stapleton, Scott E.↗

Influence of Finite Element Size in Residual Strength Prediction of Composite Structures

The sensitivity of failure load to the element size used in a progressive failure analysis (PFA) of carbon composite center notched laminates is evaluated. The sensitivity study employs a PFA methodology previously developed by the authors consisting of Hashin-Rotem intra-laminar fiber and matrix failure criteria and a complete stress degradation scheme for damage simulation. The approach is implemented with a user defined subroutine in the ABAQUS/Explicit finite element package. The effect of element size near the notch tips on residual strength predictions was assessed for a brittle failure mode with a parametric study that included three laminates of varying material system, thickness and stacking sequence. The study resulted in the selection of an element size of 0.09 in. X 0.09 in., which was later used for predicting crack paths and failure loads in sandwich panels and monolithic laminated panels. Comparison of predicted crack paths and failure loads for these panels agreed well with experimental observations. Additionally, the element size vs. normalized failure load relationship, determined in the parametric study, was used to evaluate strength-scaling factors for three different element sizes. The failure loads predicted with all three element sizes provided converged failure loads with respect to that corresponding with the 0.09 in. X 0.09 in. element size. Though preliminary in nature, the strength-scaling concept has the potential to greatly reduce the computational time required for PFA and can enable the analysis of large scale structural components where failure is dominated by fiber failure in tension.

Satyanarayana, Arunkumar↗

Nuclear Thermal Rocket Element Environmental Simulator (NTREES) Upgrade Activities

Over the past year the Nuclear Thermal Rocket Element Environmental Simulator (NTREES) has been undergoing a significant upgrade beyond its initial configuration. The NTREES facility is designed to perform realistic non-nuclear testing of nuclear thermal rocket (NTR) fuel elements and fuel materials. Although the NTREES facility cannot mimic the neutron and gamma environment of an operating NTR, it can simulate the thermal hydraulic environment within an NTR fuel element to provide critical information on material performance and compatibility. The first phase of the upgrade activities which was completed in 2012 in part consisted of an extensive modification to the hydrogen system to permit computer controlled operations outside the building through the use of pneumatically operated variable position valves. This setup also allows the hydrogen flow rate to be increased to over 200 g/sec and reduced the operation complexity of the system. The second stage of modifications to NTREES which has just been completed expands the capabilities of the facility significantly. In particular, the previous 50 kW induction power supply has been replaced with a 1.2 MW unit which should allow more prototypical fuel element temperatures to be reached. The water cooling system was also upgraded to so as to be capable of removing 100% of the heat generated during. This new setup required that the NTREES vessel be raised onto a platform along with most of its associated gas and vent lines. In this arrangement, the induction heater and water systems are now located underneath the platform. In this new configuration, the 1.2 MW NTREES induction heater will be capable of testing fuel elements and fuel materials in flowing hydrogen at pressures up to 1000 psi at temperatures up to and beyond 3000 K and at near-prototypic reactor channel power densities. NTREES is also capable of testing potential fuel elements with a variety of propellants, including hydrogen with additives to inhibit corrosion of certain potential NTR fuel forms. Additional diagnostic upgrades included in the present NTREES set up include the addition of a gamma ray spectrometer located near the vent filter to detect uranium fuel particles exiting the fuel element in the propellant exhaust stream to provide additional information any material loss occurring during testing. Other aspects of the upgrade included reworking NTREES to reduce the operational complexity of the system despite the increased complexity of the induction heating system. To this end, many of the controls were consolidated on fewer panels. As part of this upgrade activity, the Safety Assessment (SA) and the Standard Operating Procedures (SOPs) for NTREES were extensively rewritten. The new 1.2 MW induction heater consists of three physical units consisting of a transformer, rectifier, and inverter. This multiunit arrangement facilitated increasing the flexibility of the induction heater by more easily allowing variable frequency operation. Frequency ranges between 20 and 60 kHz can be accommodated in the new induction heater allowing more representative power distributions to be generated within the test elements.

Emrich, William J., Jr.↗

Measuring Surface Bulk Elemental Composition on Venus

The extreme surface environment (462 C, 93 bars pressure) of Venus makes subsurface measurements of its bulk elemental composition extremely challenging. Instruments landed on the surface of Venus must be enclosed in a pressure vessel. The high surface temperatures also require a thermal control system to keep the instrumentation temperatures within their operational range for as long as possible. Since Venus surface probes can currently operate for only a few hours, it is crucial that the lander instrumentation be able to make statistically significant measurements in a short time. An instrument is described that can achieve such a measurement over a volume of thousands of cubic centimeters of material by using high energy penetrating neutron and gamma radiation. The instrument consists of a Pulsed Neutron Generator (PNG) and a Gamma-Ray Spectrometer (GRS). The PNG emits isotropic pulses of 14.1 MeV neutrons that penetrate the pressure vessel walls, the dense atmosphere and the surface rock. The neutrons induce nuclear reactions in the rock to produce gamma rays with energies specific to the element and nuclear process involved. Thus the energies of the detected gamma rays identify the elements present and their intensities provide the abundance of each element. The GRS spectra are analyzed to determine the Venus elemental composition from the spectral signature of individual major, minor, and trace radioactive elements. As a test of such an instrument, a Schlumberger Litho Scanner oil well logging tool was used in a series of experiments at NASA's Goddard Space Flight Center. The Litho Scanner tool was mounted above large (1.8 m x 1.8 m x.9 m) granite and basalt monuments and made a series of one-hour elemental composition measurements in a planar geometry more similar to a planetary lander measurement. Initial analysis of the results shows good agreement with target elemental assays

Venus↗

Elemental Variation and Petrogenesis of Pyroxenes in HED Meteorites by Multivariable Discriminant Analysis Method

HED (Howardite, Eucrite and Diogenite) are meteorites with mafic and ultramafic igneous composition. Previous studies suggested HED came from asteroid (4) Vesta and they were generated by magmatic melting followed by differentiation crystallization, metamorphic, and impact. Uniform oxygen isotopic composition of HED samples favors global magma ocean for (4) Vesta. However, the petrological diversity of HED may indicate more complex magma processes in the meteorites. In general, most of the geochemical studies are using traditional methods (e.g. element to element or ratio to ratio plots) to classify the different rock type and groups. With the traditional methods, only limited elements can be shown in a figure. As such, some meteorites may have been identified as HED by a traditional method but found different either in isotopic composition or other elemental characteristic. These anomalous HED meteorites may or may not come from asteroid (4) Vesta. In fact, magma is a unit system where any elemental change should affect to all other elements as a whole, it would be reasonable to consider all elements together to look for the systematical changes. Using multivariable discriminant analysis (MDA) method is one of such testing for their geochemical variation. The method may be able to help us to better understand the petrologic processes and the relationship among elements. This study is to test the MDA method by focus mainly on pyroxene composition of eucrite and diogenite.

Peng, Z. X.↗

Computationally Efficient Beam Elements for Accurate Stresses in Sandwich Laminates and Laminated Composites with Delaminations

Laminated composites are prone to delamination failure due to the lack of reinforcement through the thickness. Therefore, during the design process the initiation and propagation of delaminations should be accounted for as early as possible. This paper presents computationally efficient nine degree-of-freedom (dof) and eight-dof shear locking-free beam elements using the mixed form of the refined zigzag theory (RZT(sup(m))). The corresponding nine-dof and eight-dof elements use the anisoparametric and constrained anisoparametric interpolation schemes, respectively, to eliminate shear locking in slender beams. The advantage of the present element over previous RZT beam elements is that no post-processing is required to accurately model the transverse shear stress while maintaining the computational efficiency of a low-order beam element. Comparisons with high-fidelity finite element models and three-dimensional elasticity solutions show that the elements can robustly and accurately predict the displacement field, axial stress and transverse shear stress through the thickness of a sandwich beam or a composite laminate with an embedded delamination. In fact, the accuracy and computational efficiency of predicting stresses in laminates with embedded delaminations make the present elements attractive choices for RZT-based delamination initiation and propagation methodologies available in the literature.

R. M. J. Groh↗

Trace Elemental Abundances in Calcium-Aluminum-Rich Inclusions in CV Chondrites

Introduction: Calcium-aluminum-rich inclusions (CAIs), are the first formed solids that define the age of the Solar System [1,2]. CAIs are thought to have condensed from nebular gas [3,4] within the first <1 Ma of Solar System formation [5,6]. CAIs have experienced numerous early Solar System processes including condensation, evaporation, melting, recrystallization, and aqueous alteration [e.g., 7]. The chemical, mineralogical, and textural diversity among CAIs results from a range of chemical and physical processes recorded during nebular and parent body epoch. This study aims to explore the mineralogical, textural, and chemical compositions of CAIs including the trace elemental abundances in CAI phases to determine the early Solar System processes recorded in them. Samples and Analytical Methods: We analyzed one CAI each from CV3 chondrites Northwest Africa (NWA) 5508 designated as ‘Saguaro’, and Northwest Africa (NWA) 12772 designated as ‘Hoopoe’. Back-scatter electron (BSE) images were collected using a Phenom XL scanning electron microscope (SEM) at the Lunar and Planetary Institute (LPI) and the JEOL JXA-8530F electron probe microanalyzer (EPMA) at Johnson Space Center (JSC)-NASA. Additionally, energy dispersive X-ray spectrometry (EDS) elemental maps of select areas for these samples were collected using a 15.0kV beam energy and a 40µA emission current. Using the EPMA, wavelength-dispersive X-ray spectroscopy (WDS) quantitative data were collected. In-situ trace element measurements for both CAIs were determined at JSC-NASA using a Photon Machines 193nm laser ablation system and a Thermo-Scientific Element-XR inductively coupled plasma mass spectrometer (ICP-MS). Analyses consisted of 30s ablations at 10Hz, spot sizes of 20-25µm, and a fluence of 6.0 J/cm2 for anorthite and melilite, and a 3.5 J/cm2 fluence for all other phases. NIST612 was used to correct for instrument drift, while BHVO-2g was used as a primary calibration standard. BCR-2g and in-house mineral standards were regularly measured as unknowns to ensure accuracy. Results: Saguaro is a coarse-grained CAI, ~11 x 6 mm in dimensions. Saguaro contains spinel, Al-rich pyroxene, anorthite, Mg-rich melilite, and minor perovskite in its interior and is therefore classified as a Type B CAI. Individual melilite grains shows normal compositional zoning with an Ak content ranging from ~24 to 54 with no apparent trend from the core to the edge of the CAI. The spinel appears euhedral and occurs both as clusters and as spinel palisades [8]. Two rim sequences surround most of the sample: the inner rim being a Wark-Lovering (WL) rim (~10-35 µm) containing pyroxene, spinel, and melilite (or anorthite), and the outer rim is a finer-grained, thicker (~100 µm), accretionary rim (Fig. 1). The mineral phases in Saguaro record an overall flat REE pattern with an average negative Eu anomaly in pyroxene, and an average positive Eu anomaly in anorthite and melilite respectively. Anorthite, melilite, and pyroxene have a minor depletion in Tm (Fig. 2). The Hoopoe CAI is a compact, coarse-grained ~6 × 4 mm in size. The major mineralogy includes hibonite, spinel, melilite, anorthite, and perovskite. Therefore, it is classified as a compact transitional type A and B. (?)zoning was observed in some hibonites. Individual melilite grains show both reverse and normal zoning, where the Ak content ranges from ~6- to 28. Melilite shows two distinct textures. One texture consisted of smooth melilite that appeared homogenous, while the second appeared to consist of many fine fractures. The spinel also often appears clustered. The WL-rim sequence surrounding Hoopoe is ~25 µm thick and composed of spinel, perovskite, hibonite, and melilite/anorthite. It is then partially surrounded by an outer accretionary rim (~75µm). Like before, refractory metal nuggets appeared concentrated near the WL rims. Other metal assemblages rich in Fe and Ni were also observed. All major mineral phases in Hoopoe display relatively flat REE patterns, except for varying Eu and Tm between phases (Fig. 2). There is a prominent negative Eu anomaly in perovskite and an average positive Eu anomaly in spinel, anorthite, and hibonite respectively (Fig. 2, 3). The mixed phases along the rim of the CAI also display a negative Eu anomaly, and all phases the CAI were depleted in Pb. Discussion: The CV3 CAIs analyzed in this study were classified based on their mineralogy and textures into Type A versus Type B CAIs [10]. Hibonite appears to be pseudomorphically replacing the spinel, (i.e., is hibonite in composition, but appears in the shape of spinel). Spinel palisades. The presence of spinel palisades present in Saguaro are consistent with the melting and recrystallization experienced by this CAI. Trace elemental analyses. Saguaro and Hoopoe display similar trace element patterns to each other, with both appearing generally flat, with anomalies in Eu, and Tm. Melilite and anorthite display positive Eu anomalies in both CAIs, in addition to the hibonite in Hoopoe (Fig. 2). The phases that are depleted in Eu are pyroxene and perovskite in both Saguaro and Hoopoe, respectively (Fig. 3). Given that Eu is volatile in reducing environments [11], this could possibly indicate reducing conditions at the time anorthite and melilite crystallized, with the gas they formed from containing Eu. As these CAIs continued to form, this gas as a result would become depleted in Eu. This also could be supported by the propensity of anorthite and melilite to take up Eu from its surroundings and incorporate it into their structure [12]. In addition, analyzing the assemblage of the phases in the Saguaro, melilite and anorthite (Eu enriched) often surround the pyroxene (Eu depleted) as they are crystallized. This intergrowth of phases and the proximity of the phases would support that the Eu is being incorporated into some phases, preventing it from incorporating into other. Trace elemental analyses of the CAI rims will be evaluated in more detail, as they are complicated by the transient signal being composed of a mixture of mineral phases. Broadly, however, the patterns in the rims of both CAIs are comparable to each other, and for Hoopoe, to the mixed phase patterns in the core (Fig. 3). Other studies have found that CAI rims can be depleted in Ce and Yb [13], however we did not observe these anomalies in the two CAIs discussed here. Given their similarity, the trace elemental analyses of the mixed interior (i.e. core) and rim phases could be interpreted as forming from similar, if not the same, reservoirs. The REE abundance between the rim and core of Hoopoe are also similar, indicating they may have formed from a gas of the same or similar composition. Acknowledgments: We thank the ASU Center for Meteorite Studies for loaning the samples used in this work and Tabb Prissel for his assistance with the analysis. Mouti Al-Hashimi thanks Sam Crossley and Cyrena Goodrich for their help with the LPI SEM training. This work was supported by the LPI Summer Intern Program in Planetary Science and the LPI Cooperative Agreement. References: [1] Connelly J.N. (2012) Science, 338, 651-655. [2] MacPherson G. J. (2014) Treatise on Geochem., 2, 139-179. [3] Grossman L. (1972) GCA, 36, 597-619. [4] Ebel, D.S. (2006) Meteorites and the Early Solar System II (D. S. Lauretta & H. Y. McSween, Eds.) 253-277. [5] MacPherson G. J. (2012) Earth Planet. Sci. Lett., 331-332, 43-54. [6] MacPherson G.J. (2017) GCA, 201, 65-82. [7] Krot A.N. (1995) Meteoritics & Planet. Sci., 30, 748-775. [8] Wark and Lovering (1982) GCA, 46, 2595-2607. [9] Palme H. and Jones A. (2003) Treatise on Geochemistry (H. D. Holland and K. K. Turekian Eds.), 1, 41-61. [10] Grossman L. (1980) Ann. Rev. Earth Planet. Sci., 8, 559-608. [11] Floss C. et al. (1996) GCA, 60, 1975-1997. [12] Mason B. and Martin P. M. (1974) Earth Planet. Sci. Lett., 22, 141-144. [13] Wark B. and Boynton W. V. (2001) Meteoritics & Planet. Sci., 36, 1135-1166.

X Mouti↗

Bulk Major and Trace Elemental Composition of an Aggregate Sample From Asteroid Bennu

On September 24, 2023, NASA’s OSIRIS-REx mission returned a capsule to Earth carrying material from asteroid Bennu. This event was the first time a U.S. mission delivered pristine samples from an asteroid and is the largest asteroid sample return to date. As these samples represent some of the oldest, most primitive, and pristine materials available to us, and which originate from a known and well-studied asteroid, they allow us a rare opportunity to gain a better understanding of the formation and evolution of our solar system. Key to understanding the material returned from asteroid Bennu is establishing its bulk chemical composition. Previous studies have shown that each chondrite group has a distinct elemental composition. For the carbonaceous chondrites specifically, each group exhibits a distinct pattern of moderately and highly volatile elemental depletions, relative to CI chondrites. CI chondrites are considered the most primitive chondrite group and broadly represent the solar photosphere composition. The two most striking features of these depletion patterns is that the moderately volatile element depletions increase with decreasing 50% condensation temperature and then plateau out at abundances that roughly correlate with matrix abundance. Due to these distinctive patterns, bulk elemental composition has become an important classification tool for establishing the different chondrite groups and the connections between them. As such, determining the bulk chemical composition of the Bennu aggregates will help to test two mission hypothesis: “Bennu’s bulk elemental composition reflects that of its main parent asteroid and is similar to the composition of the Sun, with depletions in moderately to highly volatile elements” and “Bennu’s dominant lithologies are comparable in bulk mineralogy, petrology, and composition to the most aqueously altered carbonaceous chondrites” . Furthermore as the carbonaceous and non-carbonaceous chondrites are thought to have likely formed in the inner and outer protoplanetary disk, respectively (e.g., [8]), determining the bulk chemical compositions of the Bennu aggregates will also help test the major mission hypothesis that “Bennu's parent body formed beyond the snow line by accretion of material in the pro-toplanetary disk” . Regarding chondrite formation, observed elemental patterns have been successfully used to model how the mixing of volatile-rich and volatile-poor chondritic components can produce the observed carbonaceous chondrites groups. They have also been significant in investigating how volatilization processes influenced chondrite formation. As such, establishing bulk chemical compositions of the pristine Bennu samples is vital for understanding the asteroid, and solar system formation. To begin this processes, we analyzed the bulk major and trace elemental compositions of Bennu aggregates.

P Koefoed↗

Removal of Bond Sodium from Full-Length Unirradiated Fermi-1 Blanket Elements and Assembly via Melt-Drain-Evaporate Process

Equipment was designed, fabricated, tested, and operated in an inert atmosphere radiological glovebox at Idaho National Laboratory to demonstrate the removal of bond sodium from full-length unirradiated Fermi-1 radial blanket elements and an entire radial blanket assembly using a Melt-Drain-Evaporate process. A series of three runs was performed with individual and multiple radial Fermi-1 blanket elements, and a fourth run was conducted with an entire Fermi-1 radial blanket assembly. After each run, the depleted uranium alloy slugs in every element slid out of its cladding, mechanically exhibiting the effectual absence of bond sodium. Quantitative and further qualitative analyses of the treated Fermi-1 material revealed the substantive, if not complete, absence of sodium metal in blanket element components. Indeed, entire columns of depleted uranium alloy slugs and associated cladding from select treated elements were separately contacted with water to react with residual sodium metal on the element surfaces, forming hydrogen gas. Samples of the resultant gas were analyzed to quantify the hydrogen concentration, which correlated to a residual sodium metal content for the treated element. Accordingly, no detectable sodium metal (<7 µg) was found on the surfaces of multiple depleted uranium alloy slugs after removal from its cladding. Detectable sodium metal, ranging from 14 to 30 µg, was found on the surfaces of one separated column of slugs and two separated full-length cladding segments. Each element originally contained ~25 g of bond sodium, resulting in quantitative sodium metal removal efficiencies of =99.9998%. The remaining separated uranium alloy slugs and cladding segments from the four runs were piece-wise immersed in alcohol while videorecording possible gas bubble formation as an additional qualitative analysis for residual sodium metal on treated surfaces, which identified the predominant absence of sodium reactivity on the balance of treated Fermi-1 blanket material. The results of this demonstration substantiate a path forward for treatment and disposal of 34 metric tons heavy metal of irradiated sodium-bonded Fermi-1 blanket material currently stored at Idaho National Laboratory.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

THE HEAVY-ELEMENT MASSES OF EXTRASOLAR GIANT PLANETS, REVEALED

We investigate a population of transiting planets that receive relatively modest stellar insolation, indicating equilibrium temperatures <1000 K, and for which the heating mechanism that inflates hot Jupiters does not appear to be significantly active. We use structural evolution models to infer the amount of heavy elements within each of these planets. There is a correlation between the stellar metallicity and the mass of heavy elements in its transiting planet(s). It appears that all giant planets possess a minimum of {approx}10-15 Earth masses of heavy elements, with planets around metal-rich stars having larger heavy-element masses. There is also an inverse relationship between the mass of the planet and the metal enrichment (Z{sub pl}/Z{sub star}), which appears to have little dependency on the metallicity of the star. Saturn- and Jupiter-like enrichments above solar composition are a hallmark of all the gas giants in the sample, even planets of several Jupiter masses. These relationships provide an important constraint on planet formation and suggest large amounts of heavy elements within planetary H/He envelopes. We suggest that the observed correlation can soon also be applied to inflated planets, such that the interior heavy-element abundance of these planets could be estimated, yielding better constraints on their interior energy sources. We point to future directions for planetary population synthesis models and suggest future correlations. This appears to be the first evidence that extrasolar giant planets, as a class, are enhanced in heavy elements.

79 ASTRONOMY AND ASTROPHYSICS↗

Magnetic Nanofluid Rare Earth Element Extraction Process Report, Techno Economic Analysis, and Results for Geothermal Fluids

This GDR submission is an interim technical report and raw data files from the first year of testing on functionalized nanoparticles for rare earth element extraction from geothermal fluids. The report contains Rare Earth Element uptake results (percent removal, mg Rare Earth Element/gram of sorbent, distribution coefficient) for the elements of Neodymium, Europium, Yttrium, Dysprosium, and Cesium. A detailed techno economic analysis is also presented in the report for a scaled up geothermal rare earth element extraction process. All rare earth element uptake testing was done on simulated geothermal brines with one rare earth element in each brine. The rare earth element uptake testing was conducted at room temperature.

15 GEOTHERMAL ENERGY↗

Variational multiscale element-free Galerkin method combined with the moving Kriging interpolation for solving some partial differential equations with discontinuous solutions

Solving partial differential equations with discontinuous solutions is an important challenging problem in numerical analysis. To this end, there are some methods such as finite volume method, discontinuous Galerkin approach and particle technique that are able to solve these problems. In the current paper, the moving Kriging element-free Galerkin method has been combined with the variational multiscale algorithm to obtain acceptable and high-resolution solutions. For testing this technique, we select some PDEs with discontinuous solution such as Burgers’, Sod’s shock tube, advection–reaction–diffusion, Kuramoto–Sivashinsky, Boussinesq and shallow water equations. First, we obtain a time-discrete scheme by approximating time derivative via finite difference technique. Then we introduce the moving Kriging interpolation and also obtain their shape functions. We use the element-free Galerkin method for approximating the spatial derivatives. This method uses a weak form of the considered equation that is similar to the finite element method with the difference that in the classical element-free Galerkin method test and trial functions are moving least squares approximation (MLS) shape functions. Since the shape functions of moving least squares (MLS) approximation do not have Kronecker delta property, we cannot implement the essential boundary condition, directly. Thus, we employ the shape functions of moving Kriging interpolation and radial point interpolation technique which have the mentioned property. Also, in the element-free Galekin method, we do not use any triangular, quadrangular or other type of meshes. The element-free Galerkin method is a global method while finite element method is a local one. This technique employs a background mesh for integration which makes it different from the truly mesh procedures. Several test problems are solved and numerical simulations are reported which confirm the efficiency of the proposed schemes.

97 MATHEMATICS AND COMPUTING↗

First-principles search for alloying elements that increase corrosion resistance of Mg with second-phase particles of transition metal impurities

A significant challenge for applications of Mg alloys is their poor corrosion resistance and hence Mg alloys designs with built-in corrosion resistance are of significant interest. Corrosion can result from the coupling of anodic dissolution of Mg and cathodic reduction of water on impurities such as Iron (Fe)-rich second-phase particles. Experiments have shown that small quantities of Arsenic (As) or Germanium (Ge) can inhibit Mg corrosion, possibly slowing the hydrogen evolution reaction (HER) as the cathodic reaction on Fe surfaces. Since a broader experimental search across the periodic table for other Mg corrosion inhibiting elements is unavailable, we designed thermodynamic and HER criteria, and used high-throughput computations to search a pool of 68 elements including As and Ge that can segregate from bulk Mg to surfaces of Fe particles and impede the HER there. Our computational procedure predicts that six p-block elements meet these criteria, and they rank according to their ability to reduce H adsorption energies and the HER rate as follows: As > Ge > Si > Ga > P ≈ Al. Results for As, the most effective corrosion-inhibiting element, and Ge are in qualitative accord with recent experiments. Further, while none of the 68 elements was found to enhance H adsorption, the six p-block elements reduce H adsorption via strong orbital overlap (Pauli repulsion) between their outer-shell orbitals and the s orbitals of H adsorbates. These p-block elements are also found to have the potential to reduce HER on surfaces of Ni second-phase particles in Mg according to the same criteria, but not on surfaces of Cu second-phase particles.

36 MATERIALS SCIENCE↗