HEXAGONAL CELL STRUCTURES UNDER POST-BUCKLING AXIAL LOAD
Determining the approximate crushing stress of hexagonal cell structures subject to axial loading
PLASTIC DEFORMATION↗
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Probing topological relations between high-density and low-density regions of 2MASS with hexagon cells
We introduced a new two-dimensional (2D) hexagon technique for probing the topological structure of the universe in which we mapped regions of the sky with high and low galaxy densities onto a 2D lattice of hexagonal unit cells. We defined filled cells as corresponding to high-density regions and empty cells as corresponding to low-density regions. The numbers of filled cells and empty cells were kept the same by controlling the size of the cells. By analyzing the six sides of each hexagon, we could obtain and compare the statistical topological properties of high-density and low-density regions of the universe in order to have a better understanding of the evolution of the universe. We applied this hexagonal method to Two Micron All Sky Survey data and discovered significant topological differences between the high-density and low-density regions. Both regions had significant (>5σ) topological shifts from both the binomial distribution and the random distribution.
79 ASTRONOMY AND ASTROPHYSICS↗
Spectral radiation analyses of the GOES solar illuminated hexagonal cell scan mirror back
A ray tracing analytical tool has been developed for the simulation of spectral radiation exchange in complex systems. Algorithms are used to account for heat source spectral energy, surface directional radiation properties, and surface spectral absorptivity properties. This tool has been used to calculate the effective solar absorptivity of the geostationary operational environmental satellites (GOES) scan mirror in the calibration position. The development and design of Sounder and Imager instruments on board GOES is reviewed and the problem of calculating the effective solar absorptivity associated with the GOES hexagonal cell configuration is presented. The analytical methodology based on the Monte Carlo ray tracing technique is described and results are presented and verified by experimental measurements for selected solar incidence angles.
Fantano, Louis G.↗
MOOSE Framework Meshing Enhancements to Support Reactor Analysis
MOOSE-based physics codes require an input finite element mesh on which the physics solution is calculated, reported, and transferred to other physics codes. The use of difficult-touse, external licensed software is often required to generate high quality meshes for reactor geometries. High-fidelity geometry modeling also requires elaborate tracking of groups of elements for material property assignment and output reporting which can be considerably complex for the user to identify and maintain. Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, several meshingrelated enhancements have been developed for the MOOSE framework to address user challenges in creating finite element meshes for advanced reactor geometries. MOOSE mesh generators have been developed to mesh hexagonal geometries (pins, ducted assemblies, and cores) commonly found in liquid-metal cooled fast reactor concepts. The mesh generator used for hexagonal pin cells is generic for regular polygons and therefore may also be used for Cartesian pin cells. Hexagonal pin cells can be stitched into ducted assemblies, and assemblies can be stitched together into a core. The user may specify region ids, region names, and other preferences on the mesh. This control is useful for later material mapping in the MOOSE-based physics codes input. A capability was also developed for meshing rotating control drums including determination of material volume fractions in each mesh element as a function of time. Control drum meshes may be stitched to other hexagonal assemblies to create a core configuration. Additional mesh generators were developed that wrap around the hexagonal meshing capabilities and utilize “extra element integer” ID values on each element. In regular Cartesian or hexagonal assemblies or cores, the bookkeeping of element groups for both material assignment and output reporting can now be automated through assignment of pin, assembly, core, axial and depletion id values stored as extra element integers. The extra element tags on the mesh greatly speed the reactor analyst’s efforts to map materials to meshes, track depletion zones, and parse output such as axial pin power distributions. At the highest level, pin, assembly, and core mesh generators (with this reactor terminology) have also been developed to easily generate regular Cartesian and hexagonal cores, including axial extrusion. These reactor geometry builders call upon the previously mentioned capabilities to produce analysis-ready 3D meshes including material assignments. Open source mesh triangulation capabilities were also investigated for integration into the MOOSE framework to address the need for meshing the core periphery region which extends from the irregular outer assembly border to a cylindrical boundary. Options are limited due to licensing constraints, and the recommendation is pursue building a native MOOSE Delaunay triangulator routine with full functionality. Finally, a series of verification problems were performed with NEAMS physics tools. All developed capabilities will be available in the new open-source “Reactor” module of the MOOSE framework, which is accessible to any MOOSE-based NEAMS physics tool.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Demonstration of the feasibility of automated silicon solar cell fabrication
An analysis of estimated costs indicate that for an annual output of 4,747,000 hexagonal cells (38 mm. on a side) a total factory cost of $0.866 per cell could be achieved. For cells with 14% efficiency at AMO intensity (1353 watts per square meter), this annual production rate is equivalent to 3,373 kilowatts and a manufacturing cost of $1.22 per watt of electrical output. A laboratory model of such a facility was operated to produce a series of demonstration runs, producing hexagonal cells, 2 x 2 cm cells and 2 x 4 cm cells.
Thornhill, J. W.↗
On the Effect of Feedback Control on Benard Convection in a Boussinesq Fluid
The effect of nonlinear feedback control strategies on the platform of convection in a Boussinesq fluid heated from below is investigated. In the absence of the control, given that non-Boussinesq effects may be neglected, it is well known that convection begins in the form of a supercritical bifurcation to rolls. Non-Boussinesq behaviour destroys the symmetry of the basic state, and through a subcritical bifurcation leads to the formation of hexagonal cells. Here we discuss the influence of regulation of the lower surface temperature by means of a control mechanism, made up of a combination of a proportional linear and nonlinear controller, on the stability of the hexagonal cell pattern.
Shortis, Trudi A.↗
Effect of surface tension anisotropy on cellular morphologies
A three-dimensional weakly nonlinear analysis for conditions near the onset of instability at the crystal-melt interface was carried out to second order, taking into account the effects of latent heat generation and surface-tension anisotropy of the crystal-melt interface; particular consideration was given to the growth of a cubic crystal in the 001-, 011-, and 111-line directions. Numerical calculations by McFadden et al. (1987), performed for an aluminum-chromium alloy with the assumption of a linear temperature field and an isotropic surface tension, showed that only hexagonal nodes (and not hexagonal cells) occurred near the onset of instability. The results of the present analysis indicate that the nonlinear temperature field (which occurs when thermal conductivities of the crystal and the melt are different and/or the latent heat effects are not negligible) can modify this result and, for certain alloys and processing conditions, can cause the occurrence of hexagonal cells near the onset of instability.
Mcfadden, G. B.↗
Evaluation of Voronoi Meshes for Large Eddy Simulations of High Lift Aerodynamics
Numerical sensitivity to 3 different Voronoi seeding methods is investigated for Large Eddy Simulations (LES). A second order accurate, non-dissipative finite volume discretization is used to systematically investigate the effects of different polyhedral Voronoi mesh types using a sequence of three canonical problems with increasing complexity. First, inviscid isentropic vortex propagation is studied to demonstrate the substantial reduction of errors for rhombic dodecahedron and truncated octahedral cell types over Cartesian hexagonal cells of identical spacing. Furthermore, the reduction of errors induced at cell-size transitions (grid-coarsening interfaces) due to Lloyd smoothing iterations is quantified. It is shown that by utilizing an appropriate viscous flux discretization, a constant coefficient subgrid scale model is sufficient for non-linear stability at the 2:1 cell-size transitions on polyhedral grids, although some further error reduction does occur when smoothing is utilized. Next, forced homogeneous isotropic turbulence at an asymptotically large Reynolds number is studied to demonstrate the non-dissipative character of the inviscid flux discretization, and the non-linear robustness and accuracy offered by the viscous flux discretization using a subgrid scale model for all three Voronoi grid types. Finally,Wall-Modeled Large Eddy Simulations (WMLES) are performed to study the high-lift aerodynamics on the McDonnell Douglas 30P30N multi-element airfoil at two distinct grid levels and for two distinct Voronoi cell types. The formulation is shown to predict the aerodynamic loading with high accuracy at all angles of attack when sufficient resolution is reached, and the hexagonal prism grid topology, while computationally more expensive, has higher effective resolution compared to the Cartesian grid topology with the same spacing.
TTT↗
Evaluation of Voronoi Meshes for Large Eddy Simulations of High Lift Aerodynamics
Numerical sensitivity to 3 different Voronoi seeding methods is investigated for Large Eddy Simulations (LES). A second order accurate, non-dissipative finite volume discretization is used to systematically investigate the effects of different polyhedral Voronoi mesh types using a sequence of three canonical problems with increasing complexity. First, inviscid isentropic vortex propagation is studied to demonstrate the substantial reduction of errors for rhombic dodecahedron and truncated octahedral cell types over Cartesian hexagonal cells of identical spacing. Furthermore, the reduction of errors induced at cell-size transitions (grid-coarsening interfaces) due to Lloyd smoothing iterations is quantified. It is shown that by utilizing an appropriate viscous flux discretization, a constant coefficient subgrid scale model is sufficient for non-linear stability at the 2:1 cell-size transitions on polyhedral grids, although some further error reduction does occur when smoothing is utilized. Next, forced homogeneous isotropic turbulence at an asymptotically large Reynolds number is studied to demonstrate the non-dissipative character of the inviscid flux discretization, and the non-linear robustness and accuracy offered by the viscous flux discretization using a subgrid scale model for all three Voronoi grid types. Finally, Wall-Modeled Large Eddy Simulations (WMLES) are performed to study the high-lift aerodynamics on the McDonnell Douglas 30P30N multi-element airfoil at two distinct grid levels and for two distinct Voronoi cell types. The formulation is shown to predict the aerodynamic loading with high accuracy at all angles of attack when sufficient resolution is reached, and the hexagonal prism grid topology, while computationally more expensive, has higher effective resolution compared to the Cartesian grid topology with the same spacing.
TTT↗
Ensuring reliable connectivity to cellular-connected UAVs with up-tilted antennas and interference coordination
To integrate unmanned aerial vehicles (UAVs) in future large-scale deployments, a new wireless communication paradigm, namely, the cellular-connected UAV has recently attracted interest. However, the line-of-sight dominant air-to-ground channels along with the antenna pattern of the cellular ground base stations (GBSs) introduce critical interference issues in cellular-connected UAV communications. In particular, the complex antenna pattern and the ground reflection (GR) from the down-tilted antennas create both coverage holes and patchy coverage for the UAVs in the sky, which leads to unreliable connectivity from the underlying cellular network. To overcome these challenges, in this paper, we propose a new cellular architecture that employs an extra set of co-channel antennas oriented towards the sky to support UAVs on top of the existing down-tilted antennas for ground user equipment (GUE). To model the GR stemming from the down-tilted antennas, we propose a path-loss model, which takes both antenna radiation pattern and configuration into account. Next, we formulate an optimization problem to maximize the minimum signal-to-interference ratio (SIR) of the UAVs by tuning the up-tilt (UT) angles of the up-tilted antennas. Since this is an NP-hard problem, we propose a genetic algorithm (GA) based heuristic method to optimize the UT angles of these antennas. After obtaining the optimal UT angles, we integrate the 3GPP Release-10 specified enhanced inter-cell interference coordination (eICIC) to reduce the interference stemming from the down-tilted antennas. Our simulation results based on the hexagonal cell layout show that the proposed interference mitigation method can ensure higher minimum SIRs for the UAVs over baseline methods while creating minimal impact on the SIR of GUEs.
3GPP↗
Single-crystal equations of state of magnesiowüstite at high pressures
Solid solutions of (Mg,Fe)O with high iron enrichment may be an important component of ultralow-velocity zones at Earth’s core-mantle boundary. However, to date there have been few high-precision studies on the elastic properties of these materials. In this study we present results on the compression of (Mg 0.22 Fe 0.78 )O magnesiowüstite in both neon and helium pressure media using single-crystal diffraction to ~55 GPa. In addition, our sample was characterized by time-domain synchrotron Mössbauer spectroscopy at ambient pressure using an extended time range that resulted in vastly improved energy resolution. The combination of these high-resolution techniques tightly constrains the presence of a defect-structure component at room pressure due to 4.7 mol% tetrahedrally-coordinated ferric iron, resulting in a renormalized composition of (Mg 0.215 Fe 0.762 ⟂ 0.023 )O. Both high-pressure diffraction datasets are well described by a 3rd-order Birch-Murnaghan equation of state. The best fit-parameters for a crystal with cubic structure in helium are K 0T = 148(3) GPa, K' 0T = 4.09(12), and V 0 = 78.87(6) Å 3 . Increasing differential stress in the neon-containing sample chamber was correlated with increasing apparent distortion of the initially cubic unit cell, requiring a lower-symmetry hexagonal cell to fit the data above ~20 GPa. For fit equations of state, we determine the pressure-dependent correlation ellipses for the equation of state parameters and compare with previously published single-crystal diffraction data from (Mg,Fe)O crystals in a helium medium. We make two main observations from the datasets using a helium pressure medium: K 0T decreases as a function of increasing iron content from periclase to wüstite and K' 0T is consistent with an approximately constant value of 4.0 that is independent of iron content, at least up to (Mg,Fe)O containing ~78 mol% FeO. Finally, in combination with previously reported thermal parameters, we compute the density of Mw78 at core-mantle boundary conditions and discuss the implications.
58 GEOSCIENCES↗
Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Aftosmis, Michael J.↗
A selection principle in Benard-type convection
In a Benard-type convection problem, the stationary flows of an infinite layer of fluid lying between two rigid horizontal walls and heated uniformly from below are determined. As the temperature difference across the layer increases beyond a certain value, other convective motions appear. These motions areoften cellular in character in that their streamlines are confined to certain well-defined cells having, for example, the shape of rolls or hexagons. A selection principle that explains why hexagonal cells seem to be preferred for certain ranges of the parameters is formulated. An operator-theoretical formulation of one generalized Bernard problem is given. The infinite dimensional problem is reduced to one of solving a finite dimensional system of equations, namely, the selection equations. These equations are solved and a linearized stability analysis of the resultant stationary flows is presented.
Knightly, G. H.↗
A selection principle for Benard-type convection
In a Benard-type convection problem, the stationary flows of an infinite layer of fluid lying between two rigid horizontal walls and heated uniformly from below are determined. As the temperature difference across the layer increases beyond a certain value, other convective motions appear. These motions are often cellular in character in that their streamlines are confined to certain well-defined cells having, for example, the shape of rolls or hexagons. A selection principle that explains why hexagonal cells seem to be preferred for certain ranges of the parameters is formulated. An operator-theoretical formulation of one generalized Bernard problem is given. The infinite dimensional problem is reduced to one of solving a finite dimensional system of equations, namely, the selection equations. These equations are solved and a linearized stability analysis of the resultant stationary flows is presented.
Knightly, G. H.↗
The development of hexagonal and nonhexagonal cell phenolic honeycomb as an energy- dissipating material.
Hexagonal and nonhexagonal cell phenolic honeycomb design as energy dissipating material noting processing, composite constituents, cell configuration and usage environment
Knoell, A. C.↗
Demonstration of the feasibility of automated silicon solar cell fabrication
A study effort was undertaken to determine the process, steps and design requirements of an automated silicon solar cell production facility. Identification of the key process steps was made and a laboratory model was conceptually designed to demonstrate the feasibility of automating the silicon solar cell fabrication process. A detailed laboratory model was designed to demonstrate those functions most critical to the question of solar cell fabrication process automating feasibility. The study and conceptual design have established the technical feasibility of automating the solar cell manufacturing process to produce low cost solar cells with improved performance. Estimates predict an automated process throughput of 21,973 kilograms of silicon a year on a three shift 49-week basis, producing 4,747,000 hexagonal cells (38mm/side), a total of 3,373 kilowatts at an estimated manufacturing cost of $0.866 per cell or $1.22 per watt.
Taylor, W. E.↗
Novel mixed hydroxy-carbonate precursor assisted synthetic technique for LiNi{sub 1/3}Mn{sub 1/3}Co{sub 1/3}O{sub 2} cathode materials
Highlights: • MHC method used to overcome drawbacks of solid state synthesized materials. • Least cation mixing, phase purity, good reversibility and rate capability achieved. • XRD I {sub 0} {sub 0} {sub 3}/I{sub 1} {sub 0} {sub 4} factor, indicating electrochemical reactivity is maximum at 1.6984. • Li/LiNi{sub 1/3}Mn{sub 1/3}Co{sub 1/3}O{sub 2} cell delivered an initial discharge capacity of 175 mAh g{sup −1}. - Abstract: Novel mixed hydroxy-carbonate (MHC) precursors were used to synthesis technique of LiNi{sub 1/3}Mn{sub 1/3}Co{sub 1/3}O{sub 2} cathode material. The powder X-ray diffraction (XRD) pattern of the synthesized LiNi{sub 1/3}Mn{sub 1/3}Co{sub 1/3}O{sub 2} cathode materials exhibited a hexagonal cell with a = 2.8535 Å and c = 14.2040 Å. Fourier transform infrared spectroscopy (FT-IR) spectrum of MHC and LiNi{sub 1/3}Mn{sub 1/3}Co{sub 1/3}O{sub 2} consistent with vibration modes of functional group. Presence of sub-micrometer particle size (200 nm) and highly crystalline morphology confirmed using scanning electron microscopy (SEM). X-ray photoelectron spectroscopy (XPS) suggested that oxidation state of the transition metals; Ni in +2, Mn in +4 and Co in +3 states, respectively in LiNi{sub 1/3}Mn{sub 1/3}Co{sub 1/3}O{sub 2} cathode materials. Cyclic voltammograms (CV) revealed only one major redox couple at 4 V and suggested the absence of structural transitions from hexagonal to monoclinic structure. The Li vs. LiNi{sub 1/3}Mn{sub 1/3}Co{sub 1/3}O{sub 2} cell delivered an initial discharge capacity of 175 mAh g{sup −1} in the voltage range 2.5–4.6 V @ 0.1 C.
36 MATERIALS SCIENCE↗
Investigation of surface tension driven convection as a feasibility study for a micro-gravity experiment
The work performed for the feasibility study of a microgravity surface tension driven convection experiment was reviewed. An experimental investigation of the onset of convection in shallow fluid layers heated uniformly from below and cooled from above by an air layer was made. Results are discussed in relation to the formation of Benard cells. The onset of Rayleigh-Benard convection in thin fluid layers heated uniformly from below were studied experimentally. It was found that in thin fluid layers the onset of Rayleigh-Benard convection is preceded by subcritical convective motions. Secondly, it was found that the onset of Rayleigh-Benard convection in non-Boussinesq fluid layers takes place in the form of hexagonal cells at Rayleigh numbers larger than the critical Rayleigh number R sub C = 1708 which determines the onset of convection in Boussinesq fluid layers.
Koschmieder, E. L.↗