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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Survey of the status of finite element methods for partial differential equations

The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

Temam, Roger↗
NASA NTRS1989

Control of flexible beams using a free-free active truss

An analytical and experimental study involving controlling flexible beams using a free-free active truss is presented. This work extends previous work in controlling flexible continua with active trusses which were configured with fixed-free boundary conditions. The following describes the Lagrangian approach used to derive the equations of motion for the active truss and the beams attached to it. A partial-state feedback control law is derived for this system based on a full-state feedback Linear Quadratic Regulator method. The analytical model is examined via numerical simulations and the results are compared to a similar experimental apparatus described herein. The results show that control of a flexible continua is possible with a free-free active truss.

Clark, W. W.↗
NASA NTRS1992

Nonlinear development and secondary instability of large-amplitude Goertler vortices in hypersonic boundary layers

The weakly nonlinear development of large-amplitude Goertler vortices in a small neighborhood of the neutral stability position given by the linear theory is considered. It is shown that if the basic state and the wall curvature satisfy a certain condition, the Goertler vortices will grow until they become so large as to drive a mean flow correction as large as the basic state. Attention is then given to the further downstream evolution of these large-amplitude vortices, and it is shown that the vortices have a triple layer structure which consists of a region of vortex activity bounded by two transition layers over which the amplitude of the harmonic part of the vortex decays to zero exponentially. The positions of the two transition layers are found to be governed by a free boundary problem, which is solved for a number of curvature distribution cases. The secondary instability of the two transition layers is investigated with respect to traveling waves which are pi/2 out of phase in the spanwise direction with the steady Goertler vortices.

Fu, Y.↗
NASA NTRS1975

Cosmic ray propagation in interplanetary space

The validity of the test-particle picture, the approximation of static fields, and the spatial-diffusion approximation are discussed in a general way before specific technical assumptions are introduced. It is argued that the spatial-diffusion equation for the intensity per unit energy has a much wider range of applicability than the kinetic (Fokker-Planck) equation it is derived from. This gives strong weight to the phenomenological propagation theory. The general success (and possible failure at small energies) of the phenomenological theory for the modulation of galactic cosmic rays and solar events is described. Apparent effects such as the 'free boundary' are given disproportionate weight since they establish the connection with the detailed plasma physics of the solar wind. Greatest attention is paid to the pitch-angle diffusion theory. A general theory is presented which removes the well-known secularities of the quasi-linear approximation. The possible breakdown of any pitch-angle diffusion theory at very small energies is perhaps connected with the observed 'turn up' of the spectrum at low energies. A first attempt to derive the spatial dependence of the diffusion coefficient in the solar cavity, using such a divergence free scattering theory, is described and compared with recent observations out to 5 AU.

Voelk, H. J.↗
NASA NTRS1982

Fast generation of three-dimensional computational boundary-conforming periodic grids of C-type

A fast computer program, GRID3C, was developed to generate multilevel three dimensional, C type, periodic, boundary conforming grids for the calculation of realistic turbomachinery and propeller flow fields. The technique is based on two analytic functions that conformally map a cascade of semi-infinite slits to a cascade of doubly infinite strips on different Riemann sheets. Up to four consecutively refined three dimensional grids are automatically generated and permanently stored on four different computer tapes. Grid nonorthogonality is introduced by a separate coordinate shearing and stretching performed in each of three coordinate directions. The grids are easily clustered closer to the blade surface, the trailing and leading edges and the hub or shroud regions by changing appropriate input parameters. Hub and duct (or outer free boundary) have different axisymmetric shapes. A vortex sheet of arbitrary thickness emanating smoothly from the blade trailing edge is generated automatically by GRID3C. Blade cross sectional shape, chord length, twist angle, sweep angle, and dihedral angle can vary in an arbitrary smooth fashion in the spanwise direction.

Dulikravich, D. S.↗
DOE OSTI2021

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1982

Design of supercritical swept wings

Computational fluid dynamics are used to discuss problems inherent to transonic three-dimensional flow past supercritical swept wings. The formulation for a boundary value problem for the flow past the wing is provided, including consideration of weak shock waves and the use of parabolic coordinates. A swept wing code is developed which requires a mesh of 152 x 10 x 12 points and 200 time cycles. A formula for wave drag is calculated, based on the idea that the conservation form of the momentum equation becomes an entropy inequality measuring the drag, expressible in terms of a small-disturbance equation for a potential function in two dimensions. The entropy inequality has been incorporated in a two-dimensional code for the analysis of transonic flow over airfoils. A method of artificial viscosity is explored for optimum pressure distributions with design, and involves a free boundary problem considering speed over only a portion of the wing.

Garabedian, P.↗
DOE OSTI2022

A model of thermal creep and annealing in finite domains based on coupled dislocation climb and vacancy diffusion

Here, we develop a framework to investigate thermal creep and annealing in finite domains, where the climb motion of discrete dislocations is coupled to the diffusion of a continuum vacancy field. The model is first formulated in a continuum finite-deformation setting. All governing equations and boundary conditions are obtained from a unified irreversible thermodynamics principle. The resulting model couples a mechanical boundary value problem (BVP), a vacancy diffusion BVP, and the climb and glide motion of the discrete dislocation network within the crystal. The framework is then linearized for implementation in three-dimensional (3D) discrete dislocation dynamics (DDD) simulations for arbitrary anisotropic crystals. A solution scheme is developed based on the superposition principle, which is imposed weakly on the dislocation network to obtain a Galerkin solution for the nodal climb velocities. The framework includes diffusional (Nabarro–Herring) creep deformation as well as dislocation creep by climb-assisted-glide. The method is applied to simulate the annealing of vacancy loops in Al, with good agreement to experimental measurements by Silcox and Hirsch. We further consider the effects of annealing under stress, and of the proximity of the vacancy loops to loaded and free boundaries Simulations in polycrystalline materials are carried out to highlight the effects of the grain size on dislocation climb and vacancy loop annealing. The method is also applied to estimate the creep rate due to climb-assisted glide of jogged-screw dislocations in γ-TiAl, and results are compared to experiments by Viswanathan et al. Finally, we discuss the effects of uniaxial and hydrostatic stresses on the two diffusive deformation pathways of the material, namely Nabarro–Herring creep and dislocation climb.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Uncovering the Network Modifier for Highly Disordered Amorphous Li‐Garnet Glass‐Ceramics

Abstract Highly disordered amorphous Li 7 La 3 Zr 2 O 12 (aLLZO) is a promising class of electrolyte separators and protective layers for hybrid or all‐solid‐state batteries due to its grain‐boundary‐free nature and wide electrochemical stability window. Unlike low‐entropy ionic glasses such as Li x PO y N z (LiPON), these medium‐entropy non‐Zachariasen aLLZO phases offer a higher number of stable structure arrangements over a wide range of tunable synthesis temperatures, providing the potential to tune the LBU‐Li + transport relation. It is revealed that lanthanum is the active “network modifier” for this new class of highly disordered Li + conductors, whereas zirconium and lithium serve as “network formers”. Specifically, within the solubility limit of La in aLLZO, increasing the La concentration can result in longer bond distances between the first nearest neighbors of Zr─O and La─O within the same local building unit (LBU) and the second nearest neighbors of Zr─La across two adjacent network‐former and network‐modifier LBUs, suggesting a more disordered medium‐ and long‐range order structure in LLZO. These findings open new avenues for future designs of amorphous Li + electrolytes and the selection of network‐modifier dopants. Moreover, the wide yet relatively low synthesis temperatures of these glass‐ceramics make them attractive candidates for low‐cost and more sustainable hybrid‐ or all‐solid‐state batteries for energy storage.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Real-time estimation and control of divertor surface heat flux on the DⅢ-D tokamak

We report Future tokamaks will require robust technologies for the mitigation of heat exhaust onto the plasma-facing components. As a first step towards this development, a system has been developed at DIII-D that estimates and controls in real-time the heat flux to the PFCs. Real-time estimation of the peak power flux from this model-based approach is validated with off-line infra-red measurements for various DIII-D plasma discharges. A nonlinear free-boundary simulation code (GSevolve) is used for simulating the closed loop response and for the off-line determination of the control parameters. The implementation and first experimental results of the application during the DIII-D plasma campaign are reported.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Validation of NSFsim as a Grad-Shafranov equilibrium solver at DIII-D

Plasma shape is a significant factor that must be considered for any Fusion Pilot Plant (FPP) as it has significant consequences for plasma stability and core confinement. A new simulator, NSFsim, has been developed based on a historically successful code, DINA [1], offering tools to simulate both transport and plasma shape. Specifically, NSFsim is a free boundary equilibrium and transport solver and has been configured to match the properties of the DIII-D tokamak. This paper is focused on validating the Grad-Shafranov (GS) solver of NSFsim by analyzing its ability to recreate the plasma shape, the poloidal flux distribution, and the measurements of the simulated diagnostic signals originating from flux loops and magnetic probes in DIII-D. Five different plasma shapes are simulated to show the robustness of NSFsim to different plasma conditions; these shapes are Lower Single Null (LSN), Upper Single Null (USN), Double Null (DN), Inner Wall Limited (IWL), and Negative Triangularity (NT). The NSFsim results are compared against real measured signals, magnetic profile fits from EFIT [2], and another plasma equilibrium simulator, GSevolve [3]. EFIT reconstructions of shots are readily available at DIII-D, but GSevolve was manually ran by us to provide simulation data to compare against.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Highly disordered amorphous Li-battery electrolytes

"Medium-entropy" highly disordered amorphous Li garnets, with ≥4 unique local bonding units (LBUs), hold promise for use as solid-state electrolytes in hybrid or all-solid-state batteries owing to their grain-boundary-free nature and low-temperature synthesis requirement. Through this work, we resolved the local structure of amorphous Li garnet and understood their implication for Li dynamics. These medium-entropy amorphous structures possess unique characteristics with edge- and face-sharing LBUs, not conforming to the classic Zachariasen glass formation rules, and can be synthesized in a wide but processing-friendly temperature range (<680°C). Within these amorphous structures, Li and Zr are identified as the network formers and La as network modifier, with maxima in Li dynamics observed for smaller Li-O and Zr-O coordination; this structure understanding serves as a baseline for identifying additional network formers to further modulate Li transport. In conclusion, our insight provides fundamental guidelines for the structure and phase design for amorphous Li garnets and paves the way for their integration in next-generation batteries.

25 ENERGY STORAGE↗
DOE OSTI2022

First snowflake divertor experiments in MAST-U tokamak

First snowflake (SF) divertor experiments in the MAST-U tokamak demonstrated steady-state snowflake-plus divertor configurations in 450 kA ohmic L-mode plasmas. The SF divertor configuration features a second poloidal field (PF) null in the divertor region close by or overlapping with the main X-point. The resulting low PF region and two additional divertor legs (strike points) may lead to additional power and particle flux sharing via a hypothesized convective cell, and increased plasma-wetted area and radiation. The free-boundary Grad–Shafranov equilibrium code FIESTA was used to design SF configurations with several inter-null distances and orientations. In the experiment, the SF configurations with inter-null distances 0.13–0.20 m and lasting 0.2–0.3 s were obtained. Parallel connection lengths between the midplane and the outer strike point in the SF configurations (evaluated at field lines 1–2 mm from the separatrix in the midplane) were 25–30 m, higher than in the standard divertor (20–25 m) or the Super-X divertor (25 m). Diagnostic measurements highlighted salient SF features. The infra-red video bolometer diagnostic showed that the radiated power peaking in the PF null region was not as pronounces as in the standard divertor. Divertor ion fluxes measured by target Langmuir probes showed increased ion flux in the plate region where a secondary SF strike point landed, concomitantly with the SF formation. These measurements may suggest that some particle and heat redistribution was taking place in the convective SF zone. The first SF experiments provide a basis for future SF studies in MAST-U tokamak with higher input power, improved plasma control and diagnostic measurements, to be compared with the modeling predictions of plasma convective SF mixing and lower density strike point detachment threshold.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Understanding the Performance Gap between Polycrystalline and Single-Crystal Nickel-Rich Layered Oxide Cathodes

Singe-crystal (SC) nickel-rich layered oxide cathodes, composed of boundary-free particles with high tap density, offer significant advantages in volumetric energy density and mechanical strength compared with polycrystalline (PC) cathode materials. However, as the nickel content increases (≥80%), SC Ni-rich cathodes often suffer from faster performance degradation than PC cathodes of the same composition, and the underlying causes of this discrepancy remain poorly understood. Herein, we reveal the distinct Ni redox behaviors that govern the electrochemical performance of SC and PC Ni-rich cathodes using multiscale and operando characterization techniques. Our results indicate that the increasingly heterogeneous Ni oxidation process in SC cathodes leads to the additional irreversible oxygen redox activity that deteriorates both the mechanical and chemical structures. In contrast, PC cathodes, despite with more pronounced surface reconstruction, exhibit greater chemomechanical stability due to homogeneous redox reactions during charging. Consequently, we find that bulk degradation, more than surface reactions, ultimately leads to fast capacity decay of SC Ni-rich cathodes during cycling. In conclusion, this work offers a comprehensive view on the impact of Ni redox evolutions on the chemomechanical stability in Ni-rich layered oxide cathodes, providing new insights into the longstanding performance gap between SC and PC cathodes, and guiding the rational design of Ni-rich cathode architectures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Nanoscopic strain evolution in single-crystal battery positive electrodes

Single-crystal Ni-rich layered oxides (SC-NMC) with a grain-boundary-free configuration have effectively addressed the long-standing cracking issue of conventional polycrystalline Ni-rich materials (PC-NMC) in lithium-ion batteries, prompting a shift in optimization strategies. However, continued reliance on anisotropic lattice volume change—a well-established failure indicator in PC-NMC—as a metric for understanding strain and guiding compositional design for SC-NMC becomes controversial. Here, in this study, by leveraging multiscale diagnostic techniques, we unravelled the distinct nanoscopic strain evolution in SC-NMC during battery operation, challenging the conventional composition-driven strategies and mechanical degradation indicators used for PC-NMC. Through particle-level chemomechanical analysis, we reveal a decoupling between mechanical stability and lattice volume change in SC-NMC, identifying that structural instability in SC materials is primarily driven by multidimensional lattice distortions induced by kinetics-driven reaction heterogeneity and progressively deactivating chemical phases. Using this mechanical failure mode, we redefine the roles of cobalt and manganese in maintaining mechanical stability. Unlike cobalt’s detrimental role in PC-NMC, we find cobalt to be critical in enhancing the longevity of SC-NMC by mitigating localized strain along the extended diffusion pathway, whereas manganese exacerbates mechanical degradation.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Plasma flux expansion control on the DIII-D tokamak

A new controller has been developed with help of the flexible divertor poloidal-field coil set of the DIII-D tokamak, to aid in the precise control of the flux expansion in the scrape-off layer (SOL). Here, the single-input multiple-output (SIMO) architecture ensures flexibility through a complementary set of orthogonal actuator direction to guarantee minimum effect on existing controlled variables, e.g. radial and vertical position control of the X-point. A non-linear free-boundary simulation code (GSevolve) is used for simulating the closed-loop response and for verifying the implementation of the control algorithm on the DIII-D plasma control system (PCS). First results of the experimental commissioning of the new controller during 2020 DIII-D campaign are also presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Neural net modeling of equilibria in NSTX-U

Neural networks (NNs) offer a path towards synthesizing and interpreting data on faster timescales than traditional physics-informed computational models. In this work we develop two NNs relevant to equilibrium and shape control modeling, which are part of a suite of tools being developed for the National Spherical Torus Experiment-Upgrade for fast prediction, optimization, and visualization of plasma scenarios. The networks include Eqnet, a free-boundary equilibrium solver trained on the EFIT01 (Equilibrium FITtting 01) reconstruction algorithm, and Pertnet, which is trained on the Gspert code and predicts the non-rigid plasma response, a nonlinear term that arises in shape control modeling. The NNs are trained with different combinations of inputs and outputs in order to offer flexibility in use cases. In particular, Eqnet can use magnetic diagnostics as inputs and act as an EFIT-like reconstruction algorithm, or, by using pressure and current profile information the NN can act as a forward Grad–Shafranov equilibrium solver. This forward-mode version is envisioned to be implemented in the suite of tools for simulation of plasma scenarios. The reconstruction-mode version gives some performance improvements compared to the online reconstruction code real-time EFIT, especially when vessel eddy currents are significant. Here, we report strong performance for all NNs indicating that the models could reliably be used within closed-loop simulations or other applications. Some limitations are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗