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NASA NTRS1999

Entropy Splitting and Numerical Dissipation

A rigorous stability estimate for arbitrary order of accuracy of spatial central difference schemes for initial-boundary value problems of nonlinear symmetrizable systems of hyperbolic conservation laws was established recently by Olsson and Oliger (1994) and Olsson (1995) and was applied to the two-dimensional compressible Euler equations for a perfect gas by Gerritsen and Olsson (1996) and Gerritsen (1996). The basic building block in developing the stability estimate is a generalized energy approach based on a special splitting of the flux derivative via a convex entropy function and certain homogeneous properties. Due to some of the unique properties of the compressible Euler equations for a perfect gas, the splitting resulted in the sum of a conservative portion and a non-conservative portion of the flux derivative. hereafter referred to as the "Entropy Splitting." There are several potential desirable attributes and side benefits of the entropy splitting for the compressible Euler equations that were not fully explored in Gerritsen and Olsson. The paper has several objectives. The first is to investigate the choice of the arbitrary parameter that determines the amount of splitting and its dependence on the type of physics of current interest to computational fluid dynamics. The second is to investigate in what manner the splitting affects the nonlinear stability of the central schemes for long time integrations of unsteady flows such as in nonlinear aeroacoustics and turbulence dynamics. If numerical dissipation indeed is needed to stabilize the central scheme, can the splitting help minimize the numerical dissipation compared to its un-split cousin? Extensive numerical study on the vortex preservation capability of the splitting in conjunction with central schemes for long time integrations will be presented. The third is to study the effect of the non-conservative proportion of splitting in obtaining the correct shock location for high speed complex shock-turbulence interactions. The fourth is to determine if this method can be extended to other physical equations of state and other evolutionary equation sets. If numerical dissipation is needed, the Yee, Sandham, and Djomehri (1999) numerical dissipation is employed. The Yee et al. schemes fit in the Olsson and Oliger framework.

Yee, H. C.↗

NASA NTRS2015

An Enriched Shell Element for Delamination Simulation in Composite Laminates

A formulation is presented for an enriched shell finite element capable of delamination simulation in composite laminates. The element uses an adaptive splitting approach for damage characterization that allows for straightforward low-fidelity model creation and a numerically efficient solution. The Floating Node Method is used in conjunction with the Virtual Crack Closure Technique to predict delamination growth and represent it discretely at an arbitrary ply interface. The enriched element is verified for Mode I delamination simulation using numerical benchmark data. After determining important mesh configuration guidelines for the vicinity of the delamination front in the model, a good correlation was found between the enriched shell element model results and the benchmark data set.

McElroy, Mark↗

DOE OSTI2019

Rapid Development of Hybrid Perovskites and Novel Tandem Architectures

Multijunction solar cells based on epitaxially grown III-V materials hold the record for solar energy power conversion efficiency (PCE). However, due to the high cost of fabricating these devices, they are typically only used for concentrator cells and space applications. The overarching goal of this project was to develop low-cost printable hybrid perovskite (HP) materials appropriate and optimized for tandem solar cells with high power conversion efficiency under “1 Sun” illumination. Key results and findings over the course of the project we: Developed higher-performance high-bandgap (1.75 eV) perovskite materials and devices. In particular, we explored tens-of-thousands of compositions for high bandgap perovskites, achieving quasi-Fermi level splitting of 1.35 eV for a 1.75 eV bandgap material. We achieved World-record open circuit voltages from single junction p-i-n devices, 1.24 V from 1.75 eV bandgap material, which is what is preferable for tandems with a PCE of 14.3% using a guanidinium/formanadinium/ cesium alloyed lead iodobromide. We also developed a series of World-record efficiency devices at higher band-gaps based on 2D/3D perovskites using PEA. Developed higher-performance low-bandgap (1.35 eV) perovskite materials and devices. In particular, we developed a 1.35 eV bandgap perovskite of composition MAPb0.5Sn0.5(I0.8Br0.2)3 and showed its superiority to MAPb0.75Sn0.25I3. High efficiency solar cells were fabricated using PEDOT:PSS and doped-ICBA as HTL and ETL, respectively. Short circuit currents of 25.7 mA/cm2 and PCEs of 17.1% were obtained. Developed mechanically stacked 4-terminal CIGS-Perovskite tandems with PCE of 18.8% and monolithic 2-terminal CIGS-Perovskite tandems with PCE of 8.5%. The low efficiency of the monolithic device is a result of the high surface roughness of the solution processed CIGS bottom cells. This is not an intrinsic problem for CIGS-perovskite tandems, but does mean that smooth evaporated or sputtered CIGS films likely need to be used, unless a polishing step is employed. Developed monolithic 2-terminal Perovskite-Perovskite tandems with a stabilized PCE of 18.5%. This was the World-record perovskite-perovskite monolithic tandems for over a year in 2017-2018. Revealed that light is not an essential component of the so-called “light-induced” phase segregation. By using charge injection in the dark and electroluminescence, we showed that the presence of electrons in the conduction band and hole in the valence band is sufficient to drive the nearly ubiquitously observed phase segregation in high bandgap perovskites. Developed a new method to simultaneously measure absolute intensity photoluminescence and photoconductivity and use them to obtain simultaneous in-situ measurement of quasi-Fermi level splitting and diffusion length. This is important since it provides a proxy for device Voc and device Jsc. In addition, 67 papers were published with support from this award that detail many more advances in the field, including numerous publications in high impact journals such as Nature Photonics, Advanced Materials, ACS Energy Letters, and Energy and Environmental Science.

14 SOLAR ENERGY↗

NASA NTRS1992

A new Lagrangian method for real gases at supersonic speed

With the renewed interest in high speed flights, the real gas effect is of theoretical as well as practical importance. In the past decade, upwind splittings or Godunov-type Riemann solutions have received tremendous attention and as a result significant progress has been made both in the ideal and non-ideal gas. In this paper, we propose a new approach that is formulated using the Lagrangian description, for the calculation of supersonic/hypersonic real gas inviscid flows. This new formulation avoids the grid generation step which is automatically obtained as the solution procedure marches in the 'time-like' direction. As a result, no remapping is required and the accuracy is faithfully maintained in the Lagrangian level. In this paper, we give numerical results for a variety of real gas problems consisting of essential elements in high speed flows, such as shock waves, expansion waves, slip surfaces and their interactions. Finally, calculations for flows in a generic inlet and nozzle are presented.

Loh, C. Y.↗

NASA NTRS2003

Inertial sensor and method of use

The inertial sensor of the present invention utilizes a proof mass suspended from spring structures forming a nearly degenerate resonant structure into which a perturbation is introduced, causing a split in frequency of the two modes so that the mode shape become uniquely defined, and to the first order, remains orthogonal. The resonator is provided with a mass or inertia tensor with off-diagonal elements. These off-diagonal elements are large enough to change the mode shape of the two nearly degenerate modes from the original coordinate frame. The spring tensor is then provided with a compensating off-diagonal element, such that the mode shape is again defined in the original coordinate frame. The compensating off-diagonal element in the spring tensor is provided by a biasing voltage that softens certain elements in the spring tensor. Acceleration disturbs the compensation and the mode shape again changes from the original coordinate frame. By measuring the change in the mode shape, the acceleration is measured.

Gutierrez, Roman C.↗

DOE OSTI2019

Measuring Magnetic Fields in Collisionless Experiments

Magnetic field and electron density diagnostics are critical tools in the characterization of high energy density laboratory plasmas. These plasma environments are complex and the magnetic fields and electron densities often exhibit significant spatial and temporal variation leading to significant challenges in these measurements. Even the most promising technique, Zeeman splitting, faces challenges under plasma conditions where broadening due to high density and temperature is greater than the Zeeman splitting. Here we propose and describe a diagnostic based on Zeeman broadening. The Zeeman broadening diagnostic relies on measuring the widths of multiplet components simultaneously. The method does not depend on resolved lines, but rather on measuring the difference in the widths of multiplet lines. Experiments were performed at the University of Nevada, Reno, Nevada Terawatt Facility (NTF). The Zeeman broadening diagnostic gathered visible broadened multiplet spectra from laser produced plasmas, and plasmas generated from wire-arrays driven by the Zebra z-pinch pulsed power apparatus. The laser produced plasma, created by the Leopard pulsed laser (I>1014 W/cm 2 ), evolved in an external magnetic field (B<40T) generated by current driven through a solid electrode by the Zebra current pulse. For laser produced plasmas, observation of the magnetic field radial profile showed that the external field completely diffuses into the plasma after approximately 100 ns. Further, as the plasma continues to evolve, the field profiles within the plasma develop modulations that do not map the external field profile. For the wire array experiments, radial electron density, and magnetic field, profiles were measured. Here the Zeeman splitting was not resolved and the magnetic fields were determined from the difference between the widths of the multiplet line profiles. Thus, it has been demonstrated that Zeeman broadening may be used as a magnetic field diagnostic.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Response of Graphite to Dynamic Loading and Hypervelocity Jet Impacts

The compressive strengths of three varieties of high purity graphite, PCEA, NBG-18, and NBG-25, as well as the depth of penetration of small-scale charges into these materials was experimentally determined. These grades are similar in density, ranging from 1.80 – 1.85 g/cc, and nominal apparent porosity, ranging from 18% to 20%, but provide a wide range in maximum grain or particle size from 10s to 1000s of µm. Two very different manufacturing methods are also represented; PCEA is extruded while NBG-18 and NBG-25 are iso-molded. The quasistatic and dynamic strengths of each grade were determined on a load frame and split-Hopkinson pressure bar, respectively. The depth of penetration (DOP) of two small-scale shaped charges, the Teledyne RP-1 and RP-4, was determined against graphite. The global response of the RP-4 impacts was markedly different as the PCEA samples remained intact while all the NBG-25 samples split into 2 or 3 pieces after the jet penetration had completed. However, for all tests, the trusted DOPs fell within 2 cm. Preliminary hydrocode modeling of the penetration events used existing models that were not designed for graphite. The results can be tuned to reasonably reproduce the DOP, but the wound channel geometry is not reproduced well. A model designed for graphite would need to represent graphite’s non-linear and energy dissipation characteristics.

36 MATERIALS SCIENCE↗

NASA NTRS2014

Solar Metal Sulfate-Ammonia Based Thermochemical Water Splitting Cycle for Hydrogen Production

Two classes of hybrid/thermochemical water splitting processes for the production of hydrogen and oxygen have been proposed based on (1) metal sulfate-ammonia cycles (2) metal pyrosulfate-ammonia cycles. Methods and systems for a metal sulfate MSO.sub.4--NH3 cycle for producing H2 and O2 from a closed system including feeding an aqueous (NH3)(4)SO3 solution into a photoctalytic reactor to oxidize the aqueous (NH3)(4)SO3 into aqueous (NH3)(2)SO4 and reduce water to hydrogen, mixing the resulting aqueous (NH3)(2)SO4 with metal oxide (e.g. ZnO) to form a slurry, heating the slurry of aqueous (NH4)(2)SO4 and ZnO(s) in the low temperature reactor to produce a gaseous mixture of NH3 and H2O and solid ZnSO4(s), heating solid ZnSO4 at a high temperature reactor to produce a gaseous mixture of SO2 and O2 and solid product ZnO, mixing the gaseous mixture of SO2 and O2 with an NH3 and H2O stream in an absorber to form aqueous (NH4)(2)SO3 solution and separate O2 for aqueous solution, recycling the resultant solution back to the photoreactor and sending ZnO to mix with aqueous (NH4)(2)SO4 solution to close the water splitting cycle wherein gaseous H2 and O2 are the only products output from the closed ZnSO4--NH3 cycle.

Huang, Cunping↗

DOE OSTI2024

A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation

In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in Chacón et al. (2014) [18] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ $\ggg$ 1 (with $\mathcal{X}$∥, $ \mathcal{X}$⟂ the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. Further, the implicit algorithm is second-order accurate temporally and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the finite-dimensional linear operator compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as ~ (NΔt) 1/4 (with N the total mesh size and Δt the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios $\mathcal{X}$∥ /$ \mathcal{X}$⟂ = 10 10 ) .

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Local element operations for curved simplex meshes

Summary Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post‐processing step in mesh generation procedures and in applications such as fluid simulations with severely deforming domains. In order to perform high‐order mesh optimization, these ingredients must also be extended to high‐order (curved) meshes. In this work, we present a method to perform local element operations on curved meshes. The mesh operations discussed in this work are edge/face swaps, edge collapses, and edge splitting (more generally refinement) for triangular and tetrahedral meshes. These local operations are performed by first identifying the patch of elements which contain the edge/face being acted on, performing the operation as a “straight‐sided one" by placing the high‐order nodes via an isoparametric mapping from the master element, and smoothing the high‐order nodes on the elements in the patch by minimizing a Jacobian‐based high‐order mesh distortion measure. Since the initial “straight‐sided guess” from the placement of the nodes via the isoparametric mapping frequently results in invalid elements, the distortion measure must be regularized which allows for mesh untangling for the optimization to succeed. We present several examples in 2D and 3D to demonstrate these local operations and how they can be combined with a high‐order node smoothing procedure to maintain mesh quality when faced with severe deformations.

Shi, A.↗

DOE OSTI2022

A new generation of effective core potentials from correlated and spin–orbit calculations: Selected heavy elements

We introduce new correlation consistent effective core potentials (ccECPs) for the elements I, Te, Bi, Ag, Au, Pd, Ir, Mo, and W with 4d, 5d, 6s, and 6p valence spaces. These ccECPs are given as a sum of spin-orbit averaged relativistic effective potential (AREP) and effective spin–orbit (SO) terms. The construction involves several steps with increasing refinements from more simple to fully correlated methods. The optimizations are carried out with objective functions that include weighted many-body atomic spectra, norm-conservation criteria, and SO splittings. Transferability tests involve molecular binding curves of corresponding hydride and oxide dimers. The constructed ccECPs are systematically better and in a few cases on par with previous effective core potential (ECP) tables on all tested criteria and provide a significant increase in accuracy for valence-only calculations with these elements. Our study confirms the importance of the AREP part in determining the overall quality of the ECP even in the presence of sizable spin–orbit effects. The subsequent quantum Monte Carlo calculations point out the importance of accurate trial wave functions that, in some cases (mid-series transition elements), require treatment well beyond a single-reference.

Wang, Guangming (ORCID:0000000231327925)↗

DOE OSTI2025

Hydrogen and deuterium tunneling in niobium

We use density functional methods to identify the atomic configurations of H and D atoms trapped by O impurities embedded in bulk Nb. The O atoms are located at the octahedral position in the Nb body-centered cubic (BCC) lattice, and H (D) atoms tunnel between two degenerate tetrahedral sites separated by a mirror plane. Using nudged elastic band (NEB) methods, we calculate the double-well potential for O-H and O-D impurities and the wave functions and tunnel splittings for H and D atoms. Our results agree with those obtained from analysis of heat capacity and neutron scattering measurements on Nb with low concentrations of O-H and O-D.

density functional theory↗

DOE OSTI2025

Advanced Brine Processing to Enable U.S. Lithium Independence (CRADA Report)

Current production of LiOH, which is needed to make Li-ion battery cathode active materials, utilizes a multistep process including solar evaporation, precipitation with Na 2 CO 3 and then conversion to LiOH using Ca(OH) 2 . This process requires a large amount of land area for solar evaporation, the right weather conditions, and chemicals for the conversion process that result in NaCl and CaCO 3 waste products. The production of Ca(OH) 2 is very energy intensive and evolves significant quantities of CO 2 . An alternative process flow utilizing direct lithium extraction techniques, followed by a chemical free conversion process can have benefits in reducing the needed land requirements and chemicals for traditional brine processing. There are many potential direct lithium extraction technologies that are currently being developed. The direct lithium extraction process from typical brine sources will produce a LiCl solution with some impurities including typically high concentrations of Na. This brine then needs to be converted to LiOH for use in battery cathode production. Ideally this conversion could occur without the use of additional chemicals. Electrochemistry can do this conversion either via electrolysis or bipolar membrane electrodialysis (BPED) to produce LiOH and HCl in solution. BPED utilized bipolar membranes to split water, which has a reduced potential as compared to splitting water at electrodes into hydrogen and oxygen gas. This reduced potential required results in a significant energy savings for BPED over electrolysis methods. This CRADA project aimed to develop such an integrated process using direct lithium extraction followed by BPED to produce a LiOH solution. That solution can then be crystallized into battery grade LiOH. In particular, Albemarle utilized a direct lithium extraction process to produce a concentrated LiCl solution that could be used for the BPED process. The BPED process was first tested using various LiCl solutions with impurity ions added at bench scale to understand the effects of impurities and determine processing parameters. Then testing was performed using the direct lithium extracted brine at the bench scale before scaling the process up. After the process was scaled up a long duration test was carried out to estimate the lifetime of the membranes, which is key to the economics of the BPED process.

25 ENERGY STORAGE↗

NASA NTRS1989

SAGE: A 2-D self-adaptive grid evolution code and its application in computational fluid dynamics

SAGE is a user-friendly, highly efficient, two-dimensional self-adaptive grid code based on Nakahashi and Deiwert's variational principles method. Grid points are redistributed into regions of high flowfield gradients while maintaining smoothness and orthogonality of the grid. Efficiency is obtained by splitting the adaption into 2 directions and applying one-sided torsion control, thus producing a 1-D elliptic system that can be solved as a set of tridiagonal equations.

Davies, Carol B.↗

NASA NTRS1989

A highly parallel multigrid-like method for the solution of the Euler equations

We consider a highly parallel multigrid-like method for the solution of the two dimensional steady Euler equations. The new method, introduced as filtering multigrid, is similar to a standard multigrid scheme in that convergence on the finest grid is accelerated by iterations on coarser grids. In the filtering method, however, additional fine grid subproblems are processed concurrently with coarse grid computations to further accelerate convergence. These additional problems are obtained by splitting the residual into a smooth and an oscillatory component. The smooth component is then used to form a coarse grid problem (similar to standard multigrid) while the oscillatory component is used for a fine grid subproblem. The primary advantage in the filtering approach is that fewer iterations are required and that most of the additional work per iteration can be performed in parallel with the standard coarse grid computations. We generalize the filtering algorithm to a version suitable for nonlinear problems. We emphasize that this generalization is conceptually straight-forward and relatively easy to implement. In particular, no explicit linearization (e.g., formation of Jacobians) needs to be performed (similar to the FAS multigrid approach). We illustrate the nonlinear version by applying it to the Euler equations, and presenting numerical results. Finally, a performance evaluation is made based on execution time models and convergence information obtained from numerical experiments.

Tuminaro, Ray S.↗

NASA NTRS1993

Simulation of tail buffet using delta wing-vertical tail configuration

Computational simulation of the vertical tail buffet problem is accomplished using a delta wing-vertical tail configuration. Flow conditions are selected such that the wing primary-vortex cores experience vortex breakdown and the resulting flow interacts with the vertical tail. This multidisciplinary problem is solved successively using three sets of equations for the fluid flow, aeroelastic deflections and grid displacements. For the fluid dynamics part, the unsteady, compressible, full Navier-Stokes equations are solved accurately in time using an implicit, upwind, flux-difference splitting, finite-volume scheme. For the aeroelastic part, the aeroelastic equation for bending vibrations is solved accurately in time using the Galerkin method and the four-stage Runge-Kutta scheme. The grid for the fluid dynamics computations is updated every few time steps using a third set of interpolation equations. The computational application includes a delta wing of aspect ratio 1 and a rectangular vertical tail of aspect ratio 2, which is placed at 0.5 root-chord length downstream of the wing trailing edge. The wing angle of attack is 35 deg and the flow Mach number and Reynolds number are 0.4 and 10,000, respectively.

Kandil, Osama A.↗

NASA NTRS1995

Vibration Analysis of a Split Path Gearbox

Split path gearboxes can be attractive alternatives to the common planetary designs for rotorcraft, but because they have seen little use, they are relatively high risk designs. To help reduce the risk of fielding a rotorcraft with a split path gearbox, the vibration and dynamic characteristics of such a gearbox were studied. A mathematical model was developed by using the Lagrangian method, and it was applied to study the effect of three design variables on the natural frequencies and vibration energy of the gearbox. The first design variable, shaft angle, had little influence on the natural frequencies. The second variable, mesh phasing, had a strong effect on the levels of vibration energy, with phase angles of 0 deg and 180 deg producing low vibration levels. The third design variable, the stiffness of the shafts connecting the spur gears to the helical pinions, strongly influenced the natural frequencies of some of the vibration modes, including two of the dominant modes. We found that, to achieve the lowest level of vibration energy, the natural frequencies of these two dominant modes should be less than those of the main excitation sources.

Krantz, Timothy L.↗

NASA NTRS1997

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.

Barth, Timothy↗