Axisymmetric buckling of uniformly loaded spherical caps undergoing plastic deformation.
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Wilkinson, M. T.↗
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Models of spherical cap bubbles
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Collins, R.↗
Calorimetric Energies and Chemical Potentials of Metal Atoms in Catalytic Nanoparticles on Oxide and Carbon Supports: Improved Size Dependencies and Adhesion Energies
The chemical potential of metal atoms, μM, in supported metal nanoparticles is an important descriptor related to both the catalytic activity and the stability of the nanoparticles. Here, we derive an expression relating μM to the radius of the particle’s contact area with the support and the adhesion energy at the metal/support interface (E adh ) that assumes the particles have the shape of spherical caps but of arbitrary contact angle with the support (θ c ) and includes an empirical correction for the increase in metal surface energy and adhesion energy with decreasing radius of curvature. We then show that, at any assumed contact angle, we can simultaneously fit previously reported measurements of both calorimetric μ M (from heats of metal vapor adsorption during nanoparticle growth by vapor deposition) versus metal coverage data and the He + low-energy ion scattering (LEIS) intensities for the metal and/or support versus metal coverage (using our recently developed spherical cap model for quantitative LEIS intensities), to determine the particle size versus coverage and E adh . Only one choice of contact angle gives a pair of values for contact angle and E adh , which is consistent with the Young–Dupré equation for the equilibrium shape of a spherical particle. At this equilibrium shape, we then applied this spherical cap model (SCM) to reanalyze microcalorimetric metal chemical potentials and LEIS signals versus coverage data for nine metal/support combinations that were previously analyzed by assuming that the particles had the shape of hemispherical caps, i.e., with a contact angle of 90°. We show that this revised approach gives close agreement with the calorimetric and LEIS data; the best-fit contact angles vary from 64 to 84°, correcting the earlier assumption of 90°. Furthermore, these results provide significant accuracy improvements in particle size versus coverage, metal chemical potential versus size and coverage, metal/support adhesion energies and contact angles for Cu, Ag and Au on CeO 2 (111), Ni on MgO(100), Ag on Fe 3 O 4 (111) and TiO 2 (100), and Ag, Ni and Pd on Ni-supported graphene. This revised approach is much more broadly applicable than the earlier hemispherical cap model (HCM).
99 GENERAL AND MISCELLANEOUS↗
Preliminary Study of Iodine Gas Removal in Sodium Pools
Potential iodine gas release from failed fuel pins is a critical factor in the source term analysis of oxide fuel-loaded sodium fast reactors (SFRs). The accumulated iodine-containing gas mixtures inside pin plenums are expected to be ejected during pin failures and rise through sodium pool, with potential release of gaseous iodine to the cover gas region. Due to its potential radiological impacts, a proper assessment of iodine behavior is necessary for an accurate source term assessment. Throughout the bubble rise trajectory in the sodium pool, iodine gas is continuously removed or transformed at the bubble interface by diffusion, as the combining reaction between the iodine and sodium to form sodium iodide (NaI) is a chemically preferred process. As the final amount of iodine released from the facility is strongly influenced by the removal phenomenon inside the sodium pool, experiments were previously performed by PNC (Power Reactor and Nuclear Fuel Development Corporation) to provide insight into this phenomenon. To assess the accuracy of present methods for predicting iodine gas removal within sodium pools, several candidate approaches, available in source term analysis codes, have been summarized and evaluated in this study. Spherical cap bubbles and spherical bubbles are considered in accordance with the methods adopted in each approach, and different forms of correlations for major parameters have been implemented in accordance with the original adoptions. Based on the summarized results, important aspects to be considered have been derived.
Decontamination↗
Modifying Stokes' function to reduce the error of geoid undulation computations
Errors in computations of the geoid undulation, which determines the position of the geoid with respect to a reference ellipsoid, introduced by various modifications of the Stokes' function in the Stokes integral formula for the undulation are examined in light of currently available harmonic coefficients. The variants considered include the conventional Molodenskii truncation theory, in which integration is limited to a spherical cap, and the variations suggested by Molodenskii (1958) and Meissl (1971). In computations of the undulation from gravity anomalies in a spherical cap and terrestrial and satellite harmonic potential coefficients (GEM 9 and GEM 10B), it is shown that either of the modifications to the conventional Molodenskii theory results in substantial reductions in truncation errors, with the simpler modification of Meissl even providing superior results in certain circumstances.
Jekeli, C.↗
BUCKLING OF A SPHERE OF EXTREMELY HIGH RADIUS-THICKNESS RATIO
Proposed passive communications satellites are ultrathin-walled spherical shells which may experience buckling from external pressure due to solar radiation or atmospheric drag. Large buckling deformations of such a satellite are undesirable because they seriously reduce the satellite’s performance as a reflector. At present, shell buckling technology is lacking in several respects with regard to design of spherical shells subjected to external pressure. Large discrepancies exist between theoretical and experimental buckling pressure; therefore, the designer must be guided primarily by experimental data. However, very little experimental data on complete spheres are available; the primary research effort has been concerned with shallow spherical caps. All available experimental data are for radius-thickness ratios several orders of magnitude smaller than that for the proposed satellites. In order to provide a basis for estimating the buckling strength of these satellites, therefore, buckling experiments were conducted on a complete spherical shell having a radius-thickness ratio of about 85,000. This value is much higher than that of any spherical cap or complete sphere used in previously reported experiments.
SHELL STABILITY↗
Comparison of undulation difference accuracies using gravity anomalies and gravity disturbances
Errors in the outer zone contribution to oceanic undulation differences computed from a finite set of potential coefficients based on satellite measurements of gravity anomalies and gravity disturbances are analyzed. Equations are derived for the truncation errors resulting from the lack of high-degree coefficients and the commission errors arising from errors in the available lower-degree coefficients, and it is assumed that the inner zone (spherical cap) is sufficiently covered by surface gravity measurements in conjunction with altimetry or by gravity anomaly data. Numerical computations of error for various observational conditions reveal undulation difference errors ranging from 13 to 15 cm and from 6 to 36 cm in the cases of gravity anomaly and gravity disturbance data, respectively for a cap radius of 10 deg and mean anomalies accurate to 10 mgal, with a reduction of errors in both cases to less than 10 cm as mean anomaly accuracy is increased to 1 mgal. In the absence of a spherical cap, both cases yield error estimates of 68 cm for an accuracy of 1 mgal and between 93 and 160 cm for the lesser accuracy, which can be reduced to about 110 cm by the introduction of a perfect 30-deg reference field.
Jekeli, C.↗
Effect of probe configuration on radiative heating during Jovian entry
The radiative heating to the probe's surface and the effects of the recession of the heat shield caused by this heating are analyzed for five initial probe configurations for a Jovian entry. The initial configurations are spherically capped, conical bodies and hyperboloids. The results show that severe blunting of the nose region occurs for all configurations due to ablation of the heat shield caused by the large radiative heating rates. Recession at the nose region can possibly cause a concavity at the stagnation point. Furthermore, the recession of the heat shield, especially for the spherically capped, conical bodies, will be underpredicted if the change in the probe's shape during the entry is neglected in an analysis.
Sutton, K.↗
Seeing the entanglement wedge
We study the problem of revealing the entanglement wedge using simple operations. We ask what operation a semiclassical observer can do to bring the entanglement wedge into causal contact with the boundary, via backreaction. In a generic perturbative class of states, we propose a unitary operation in the causal wedge whose backreaction brings all of the previously causally inaccessible ‘peninsula’ into causal contact with the boundary. This class of cases includes entanglement wedges associated to boundary sub-regions that are unions of disjoint spherical caps, and the protocol works to first order in the size of the peninsula. The unitary is closely related to the so-called Connes Cocycle flow, which is a unitary that is both well-defined in QFT and localised to a sub-region. Our construction requires a generalization of the work by Ceyhan & Faulkner to regions which are unions of disconnected spherical caps. We discuss this generalization in the appendix. We argue that this cocycle should be thought of as naturally generalizing the non-local coupling introduced in the work of Gao, Jafferis & Wall.
2D gravity↗
The stability of shallow spherical shells under concentrated load
Effect of load area on deformation of clamped spherical cap and behavior of transition from axisymmetric to asymmetric deflection shapes
SPHERICAL CAP↗
Investigation of the Crust of the Pannonian Basin, Hungary Using Low-Altitude CHAMP Horizontal Gradient Magnetic Anomalies
The Pannonian Basin is a deep intra-continental basin that formed as part of the Alpine orogeny. It is some 600 by 500 km in area and centered on Hungary. This area was chosen since it has one of the thinnest continental crusts in Europe and is the region of complex tectonic structures. In order to study the nature of the crustal basement we used the long-wavelength magnetic anomalies acquired by the CHAMP satellite. The SWARM constellation, scheduled to be launched next year, will have two lower altitude satellites flying abreast, with a separation of between ca. 150 to 200 km. to record the horizontal magnetic gradient. Since the CHAMP satellite has been in orbit for eight years and has obtained an extensive range of data, both vertically and horizontally there is a large enough data base to compute the horizontal magnetic gradients over the Pannonian Basin region using these many CHAMP orbits. We recomputed a satellite magnetic anomaly map, using the spherical-cap method of Haines (1985), the technique of Alsdorf et al. (1994) and from spherical harmonic coefficients of MF6 (Maus et aI., 2008) employing the latest and lowest altitude CHAMP data. We then computed the horizontal magnetic anomaly gradients (Kis and Puszta, 2006) in order to determine how these component data will improve our interpretation and to preview what the SW ARM mission will reveal with reference to the horizontal gradient anomalies. The gradient amplitude of an 1000 km northeast-southwest profile through our horizontal component anomaly map varied from 0 to 0.025 nT/km with twin positive anomalies (0.025 and 0.023 nT/km) separated by a sharp anomaly negative at o nT/km. Horizontal gradient indicate major magnetization boundaries in the crust (Dole and Jordan, 1978 and Cordell and Grauch, 1985). Our gradient anomaly was modeled with a twodimensional body and the anomaly, of some 200 km, correlates with a 200 km area of crustal thinning in the southwestern Pannonian Basin.
Taylor, Patrick T.↗
Implementation of a High-Fidelity Interface Resolving Method in Nek5000
The development and utilization of computational fluid dynamics (CFD) models for large, high-temperature electric melters in the Waste Treatment and Immobilization Plant (WTP) in eastern Washington State have proven to be valuable for various purposes. These models allow for a better understanding of the physio-chemical processes occurring within the melter vessels and can contribute to improving operational efficiency, throughput, and addressing operational issues related to vitrification. The CFD models employed for these melter vessels incorporate multiphase fluid flow and heat transfer simulations in different regions, including the plenum, cold cap, and molten glass regions. As the tank waste and glass formers are introduced into the melter, a reacting batch layer known as the cold cap forms on top of the molten glass. To enhance the melt rate, forced convection bubblers located at the bottom of the melters generate convection currents that help homogenize the molten glass and provide heat to the cold cap. As the bubbles rise through the highly viscous glass, they adopt a spherical-cap shape [1]. Meanwhile, the conversion of the batch to glass generates significant amounts of gases (such as water vapor, carbon dioxide, sulfur dioxide, and NOx) due to thermal decomposition [2]. These gases become trapped between the cold cap and molten glass, forming a foam layer [3]. For modeling multiphase flow in CFD and heat transfer simulations of waste glass melters at different scales, efforts are underway to augment the capabilities of the Nek5000 [4] and NekRS [5] open-source codes [6]. Nek5000/NekRS is a scalable and efficient spectral element code that has been successfully applied to a wide range of fluid dynamics problems. By leveraging the Nek5000/NekRS software, it becomes possible to model the melter systems more affordably and with lower computational requirements compared to currently utilized commercial CFD software. The specific objectives of this ongoing effort include: 1. Implementation of a level set method in Nek5000/NekRS: The level set method is a numerical technique commonly employed in CFD simulations to track and represent the interface between different phases or materials accurately. By incorporating this method into Nek5000/NekRS, the ability to simulate multiphase flows in waste glass melters at a high level of fidelity can be achieved. 2. Demonstration of capability for air bubbling through molten glass: As part of the development process, a specific case of air bubbling through molten glass will be simulated using the augmented Nek5000/NekRS code. This demonstration aims to showcase the ability of the software to accurately capture and analyze the complex phenomena involved in the multiphase flow within waste glass melters. By achieving these objectives, the improved Nek5000/NekRS code will offer a powerful computational tool for simulating and analyzing waste glass melter systems, enabling better understanding, optimization, and troubleshooting of these vitrification processes. The ability to accurately model and simulate multiphase flows has broad relevance across many industries and scientific domains, and the improved functionality can contribute to advancements in various fields beyond waste glass melter simulations.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Comprehensive Synthesis and Structural Trends in Tetramethyl Diglycolamide (TMDGA) Nitrate Complexes with Lanthanides and Americium
Complexes of N,N,N',N'-tetramethyl diglycolamide (TMDGA), a hydrophilic diglycolamide (DGA) proposed as an aqueous phase holdback reagent, have been crystallized for the majority of the lanthanide series (excluding promethium), yttrium, and americium to deepen our structural understanding of trivalent metal ion (M 3+ ) DGA coordination compounds in the presence of nitrate counter-anions. The presented collection of 16 complexes with accompanying single-crystal structures, taking formulas [M(TMDGA) 3 ][M(NO 3 ) 6 ] (M = La, Ce, Pr, Nd, Sm, Am), [M(TMDGA) 3 ][M(NO 3 ) 5 (H 2 O)] 1–x [M(NO 3 ) 4 (H 2 O) 2 ] x (NO 3 ) 1+x (M = Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb), [M(TMDGA) 3 ] 2 [M(NO 3 ) 4 (H 2 O) 2 ] 0.75 [M(NO 3 ) 5 (H 2 O)] 1.25 (NO 3 ) 2.75 ·H 2 O (M = Lu), and [M(TMDGA) 3 ][M(NO 3 ) 5 (H 2 O)](NO 3 )·CH 3 OH (M = Y) were all synthesized via solvent diffusion of reaction mixtures containing the metal nitrate M(NO 3 ) 3 ·nH 2 O and TMDGA. Single-crystal X-ray diffraction analyses of these new structures show that each TMDGA complex comprises of three TMDGA ligands coordinating the metal ion via carbonyl and etheric oxygen atoms forming [M(TMDGA) 3 ] 3+ cations. Spectroscopy measurements under high pressure displayed notable differences in the f → f transition shifting between that of Nd(III) and Am(III). Shifting of transitions by 2.0 nm were observed in Nd up to 8.50 ± 0.09 GPa, while Am saw shifting between 11.0 to 13.5 nm at pressures up to 20.06 ± 1.90 GPa. The local geometry in these complexes is a distorted spherical capped square antiprism (CSAPR-9) except for of the yttrium complex, which exhibits a distorted spherical tricapped trigonal prismatic (TCTPR-9) geometry. Further, the anions that form concomitantly with the TMDGA complexes are composed of hexanitrato species for the early lanthanide ions (lanthanum to samarium); whereas the remaining smaller lanthanides did not possess sufficiently large ionic radii to coordinate six bidentate nitrate anions, instead, one or two nitrate anions are situated in the outer sphere. The systematic progression of changes in the anionic environments of these complexes outlines the changing coordination habits afforded by the lanthanide contraction.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Three-dimensional computer model for the atmospheric general circulation experiment
An efficient, flexible, three-dimensional, hydrodynamic, computer code has been developed for a spherical cap geometry. The code will be used to simulate NASA's Atmospheric General Circulation Experiment (AGCE). The AGCE is a spherical, baroclinic experiment which will model the large-scale dynamics of our atmosphere; it has been proposed to NASA for future Spacelab flights. In the AGCE a radial dielectric body force will simulate gravity, with hot fluid tending to move outwards. In order that this force be dominant, the AGCE must be operated in a low gravity environment such as Spacelab. The full potential of the AGCE will only be realized by working in conjunction with an accurate computer model. Proposed experimental parameter settings will be checked first using model runs. Then actual experimental results will be compared with the model predictions. This interaction between experiment and theory will be very valuable in determining the nature of the AGCE flows and hence their relationship to analytical theories and actual atmospheric dynamics.
Roberts, G. O.↗
Local Lunar Gravity Field Analysis over the South Pole-aitken Basin from SELENE Farside Tracking Data
We present a method with which we determined the local lunar gravity field model over the South Pole-Aitken (SPA) basin on the farside of the Moon by estimating adjustments to a global lunar gravity field model using SELENE tracking data. Our adjustments are expressed in localized functions concentrated over the SPA region in a spherical cap with a radius of 45deg centered at (191.1 deg E, 53.2 deg S), and the resolution is equivalent to a 150th degree and order spherical harmonics expansion. The new solution over SPA was used in several applications of geophysical analysis. It shows an increased correlation with high-resolution lunar topography in the frequency band l = 40-70, and admittance values are slightly different and more leveled when compared to other, global gravity field models using the same data. The adjustments expressed in free-air anomalies and differences in Bouguer anomalies between the local solution and the a priori global solution correlate with topographic surface features. The Moho structure beneath the SPA basin is slightly modified in our solution, most notably at the southern rim of the Apollo basin and around the Zeeman crater
Lunar Gravity↗
Simplified Formulas for External Pressure Design
Design of vessels for external pressure currently requires a chart-based solution or analytical approaches which are not necessarily intuitive. In this paper, we propose simple formulas for the external pressure evaluation of pipes and other cylindrical pressure vessels. We present a conceptual comparison between the elastic and elastic-plastic stability of structural columns and that of cylindrical vessels of long, intermediate, and short length. Their common features allow an accurate and straightforward approach for external pressure design. The approach is also extended to spherical caps, conical vessels, and formed heads.We compare the method presented to the current acceptance criteria from various design codes, including the ASME Boiler and Pressure Vessel Code Section VIII, Code Case 2286, and EN 13445-3, as well as codes for steel and aluminum structures. In further discussion, the simplified method is compared against the results of more than 500 experiments on the buckling of cylindrical and spherical vessels published over the past two centuries.This simple but accurate approximation is conceptually intuitive, analytically straightforward, and shows potential utility in pressure vessel design codes, as well as piping design codes such as B31 that currently reference ASME VIII for external pressure design.
Kirkland, Will↗
Evaporation from thin porous Coatings: Pore size effects and predictive equation for homogeneous coatings
Evaporation of small water droplets on solids is hindered because surface tension pulls the droplet into a spherical cap that has a small perimeter. Our solution is to coat a solid with a very thin, porous layer into which the droplet flows to create a large-area disk with concomitant high rate of evaporation. We investigate evaporation by varying factors that have not been previously considered: pore size and distribution, contact angle, temperature, and relative humidity (RH). A larger pore size resulted in faster evaporation, which we explain through faster transport within the coating. Even faster evaporation occurred for a bilayer structure with small particles on the air side and larger particles on the solid side. Further, the water advancing contact angle had an insignificant effect in the range from < 10° through to 60°. Our results for different pore sizes, temperature, humidity, and contact angle all collapse onto a single curve when appropriately normalized. This validates an equation that can be used for the evaporation from a homogeneous coating that depends only one empirical factor and the droplet volume. Since the volume is often user-controlled, we envisage that this equation can be used to predict evaporation and guide design of fast-drying coatings.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Energetics of Cu Adsorption on and Adhesion to Rutile-TiO 2 (100) Studied by Cu Vapor Adsorption Calorimetry
The heat of adsorption of Cu vapor versus coverage was measured on rutile-TiO 2 (100) at 300 and 100 K using single-crystal adsorption calorimetry. At these conditions, Cu nanoparticles nucleate and then grow larger. The average Cu particle size versus Cu coverage was measured using He + low-energy ion scattering spectroscopy. These data were analyzed with the recently introduced spherical cap model (SCM) to provide the heat of Cu adsorption and Cu chemical potential versus Cu particle size, as well as the contact angle (67°) and adhesion energy (2.50 J/m 2 ) at the Cu particle/rutile-TiO 2 (100) interface. The hemispherical cap model (HCM) was used to model the data first, and then those HCM results were converted to the more accurate SCM results using a recently published mathematical approximation whose high accuracy was validated here. Furthermore, the adhesion energy of Cu on rutile-TiO 2 (100) measured here is compared to prior values for Ag and Au on rutile-TiO 2 (100), showing a nearly proportional increase in adhesion energy with metal oxophilicity (per unit area).
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗