Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical stability”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Exponential Runge-Kutta Parareal for non-diffusive equations

Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial time-stepping methods. However, like many parallel-in-time methods it can fail to converge when applied to non-diffusive equations such as hyperbolic systems or dispersive nonlinear wave equations. Here, this paper explores the use of exponential integrators within the Parareal iteration. Exponential integrators are particularly interesting candidates for Parareal because of their ability to resolve fast-moving waves, even at the large stepsizes used by coarse propagators. This work begins with an introduction to exponential Parareal integrators followed by several motivating numerical experiments involving the nonlinear Schrödinger equation. These experiments are then analyzed using linear analysis that approximates the stability and convergence properties of the exponential Parareal iteration on nonlinear problems. The paper concludes with two additional numerical experiments involving the dispersive Kadomtsev-Petviashvili equation and the hyperbolic Vlasov-Poisson equation. These experiments demonstrate that exponential Parareal methods offer improved time-to-solution compared to serial exponential integrators when solving certain non-diffusive equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

An investigation on the structural stability of $\mathrm{ZIF}$-8 in water versus water-derived oxidative species in aqueous environment

We report the zeolitic-imidazolate-framework-8 (ZIF-8) is one of the extensively studied metal-organic frameworks (MOF) materials because of its unique structure. For its potential applicability in numerous fields, it becomes crucial to have detailed studies on the structural stability of ZIF-8, especially in aqueous environments. A number of studies have been conducted to investigate the breakdown process of the ZIF-8 structure in water; which is known as the hydrolysis of ZIF-8. However, those studies reported different opposing experimental observations on the role of water on the structural stability of ZIF-8, which created obscurity in understanding this phenomenon. This study explored the effects of different water-derived species on the structural stability of ZIF-8; specifically, examined the effects of only water and water with different oxidative species that may be generated by water molecules' dissociation under external energy or catalyst presence. To this effort, we experimentally probed the physical and chemical structural changes of ZIF-8 in DI water and three different solutions of hydrogen peroxides (H 2 O 2 ); taking H 2 O 2 as the source of oxidative species. To assess the changes in elemental compositions, chemical bonds, functional groups, crystal structure, and morphology, all the samples were analyzed by X-ray photoelectron spectroscopy (XPS), energy-dispersive x-ray (EDX) spectroscopy, Fourier Transform Infrared (FTIR) spectroscope, X-ray diffractometer (XRD), and scanning electron microscope (SEM). Significant structural changes in ZIF-8 occurred mainly in the presence of oxidative species in water. Notably, oxidative species' concentration exceeding 1 M heightened the deformation of the ZIF-8 structure.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Superheating gold beyond the predicted entropy catastrophe threshold

In their landmark study, Fecht and Johnson unveiled a phenomenon that they termed the ‘entropy catastrophe’, a critical point where the entropy of superheated crystals equates to that of their liquid counterparts. This point marks the uppermost stability boundary for solids at temperatures typically around three times their melting point. Despite the theoretical prediction of this ultimate stability threshold, its practical exploration has been prevented by numerous intermediate destabilizing events, colloquially known as a hierarchy of catastrophes, which occur at far lower temperatures. Here we experimentally test this limit under ultrafast heating conditions, directly tracking the lattice temperature by using high-resolution inelastic X-ray scattering. Our gold samples are heated to temperatures over 14 times their melting point while retaining their crystalline structure, far surpassing the predicted threshold and suggesting a substantially higher or potentially no limit for superheating. We point to the inability of our samples to expand on these very short timescales as an important difference from previous estimates. These observations provide insights into the dynamics of melting under extreme conditions.

Laser-produced plasmas↗
DOE OSTI2024

Relevance of anisotropy in the Kondo effect: Lessons from the symplectic case

A Kondo model with symplectic symmetry was recently put forward as the effective low-energy theory of a superconducting-island device coupled to multiple leads. This model, which possesses non-Fermi liquid physics and effective anyons, was argued to belong to the class of topological Kondo effects. Here, we clarify the extent of stability of its exotic fixed point using perturbative and numerical renormalization group in conjunction with bosonization and conformal field theory. In contrast to previous claims, we show that asymmetry in the coupling to the leads destabilizes the non-Fermi liquid. Other destabilizing perturbations include asymmetry in the superconducting pairing or internal energy of the individual quantum dots in the island. Nevertheless, these perturbations all generate the same relevant operators. Thus, only a small number of couplings need to be tuned individually, and these can be selected according to experimental convenience. Our results highlight a common misconception that anisotropy in single-channel Kondo couplings is always irrelevant. As demonstrated, relevant terms will emerge whenever the group generators do not span the full space of impurity operators. This calls for a more detailed inspection of models that exhibit this property, such as large-spin impurities and SO⁡( M ) Kondo models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Quasinormal modes of naked singularities in presence of nonlinear scalar fields

We study linear perturbations against static spherically symmetric background configurations of general relativity with a real scalar field (SF), which is minimally coupled with gravity; it is nonlinear due to the presence of the self-action potential. The background solutions have a naked singularity at the center of the configuration. The focus is on the stability of the background and fundamental frequencies of the quasinormal modes (QNM) of the axial perturbations in the Regge-Wheeler gauge. The problem is reduced to one hyperbolic master equation with an effective potential 𝑊eff, which turns out to be positive for a general non-negative SF potential; this ensures the linear stability with respect to this kind of perturbations. For numerical simulations, the SF potential was chosen in the power-law form 𝑉⁡(𝜙) ∼ 𝜙 2⁢𝑛 with 2 < 𝑛 ≤40. We extracted the fundamental frequencies of QNM for different 𝑛 and various sets of the background configuration parameters. The results show that even for a small background SF, there is a significant difference between the fundamental frequencies and ones in case of the Schwarzschild background. Furthermore, the results are also compared with the case of the Fisher-Janis-Newman-Winicour background dealing with a massless linear scalar field.

General relativity↗
DOE OSTI2026

Finite-range pairing in nuclear density functional theory

Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Many pairing functionals currently used can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational schemes diverge as the single-particle space increases, and the results depend on how marginally occupied states are incorporated. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this study, this is done by folding the pair density with Gaussians. Here, we show that a folding radius of about 1 fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications.

Nuclear density functional theory↗
DOE OSTI2024

Material Discovery and Design Principles of Perovskite Oxides for Reversible Solid Oxide Cells (R-SOC)

Reversible solid oxide cells (R-SOCs) are highly efficient devices for energy conversion and storage, capable of operating for both hydrogen utilization and production. In fuel cell mode, an R-SOC consumes hydrogen or natural gas to generate electricity, while in electrolysis mode, it produces hydrogen from steam. The discover of new materials with rapid oxygen surface exchange kinetics and enduring stability is crucial for the economically viable commercialization of R-SOCs. To facilitate this pursuit, we conducted extensive Density Functional Theory (DFT) calculations and developed Machine Learning (ML) models to predict critical catalytic properties essential for R-SOCs, such as oxygen surface exchange/diffusivity, and area-specific resistance (ASR). BaCoxFeyZrzO3-d(BFCZ)(x+y+z=1) emerged as a promising family of electrode materials with high activity and stability, validated through systematic experimental study. Moreover, a robust numerical multiphysics model was developed to optimize materials and microstructure parameters, providing the ability to predict the performance of functional R-SOCs.

Liu, Jian↗
DOE OSTI2020

Distributed Small-Signal Stability Conditions for Inverter-Based Unbalanced Microgrids

The proliferation of inverter-based generation and advanced sensing, controls, and communication infrastructure have facilitated accelerated deployment of microgrids. A coordinated network of microgrids can maintain reliable power delivery to critical facilities during extreme events. Low-inertia offered by the power-electronics–interfaced energy resources, however, can present significant challenges to ensuring stable operation of the microgrids. In this work, distributed small-signal stability conditions for inverter-based microgrids are developed that involve the droop-controller parameters and the network parameters (e.g. line impedances, loads). The distributed closed-form parametric stability conditions derived in this paper can be verified in a computationally efficient manner, facilitating reliable design and operations of networks of microgrids. Dynamic phasor models have been used to capture the effects of electromagnetic transients. Furthermore, numerical results are presented, along with PSCAD simulations, to validate the analytical stability conditions. Effects of design choices, such as the conductor types, and inverter sizes, on the small-signal stability of inverter-based microgrids are investigated to derive useful engineering insights.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Large-eddy simulation of non-vaporizing sprays using the spectral-element method

Predictive simulations of high-pressure sprays require accurate representation of the turbulent gaseous flow field generated by liquid jet. Typically, the accuracy that can be obtained with low-order numerical methods (e.g. finite volume, finite element) is limited by stability issues in fine grids and the order of convergence of the method. In this work, we resolve the turbulent flow field in an Eulerian manner using the high-order spectral element method, coupled with a Lagrangian parcels approach to model the atomizing liquid jet. Large eddy simulations of single-hole sprays under non-evaporative conditions were conducted and compared against experimental data from Margot et al. (2008) and Spray A data from the Engine Combustion Network. The sensitivity of liquid penetration and droplet sizes to different breakup model parameters was studied. The effect of different numerical parameters, such as polynomial order of the solution (grid resolution), on liquid penetration was also analyzed. The method achieved grid-independent results using p-refinement, achieving finer resolution (by a factor of x 1.7 - x 3.5) in the gas-phase solution than in state-of-the-art simulations using the finite-volume method. Here the results showed good agreement with experimental data, demonstrating the ability of the current method to accurately capture liquid penetration and the shape of the spray.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Stability Functions in the Stable Surface Layer Derived from the Mellor–Yamada–Nakanishi–Niino (MYNN) Scheme

It is desirable that a surface layer scheme in an atmospheric numerical model is consistent with an atmospheric boundary layer scheme incorporated in the same model. In this study, stability functions based on Monin–Obukhov similarity theory for momentum and heat, φ m and φ h , in the stable surface layer are derived from the Mellor–Yamada–Nakanishi–Niino (MYNN) scheme. The resulting stability functions are approximated by φ m = 1 + 4.8z/L and φ h = 0.74 + 6.0z/L, which can be analytically integrated with respect to height z to obtain momentum and heat fluxes, where L is the Obukhov length. The fluxes thus, obtained are compared with those acquired from stability functions in four previous studies: they are nearly the same as those from two of them, and show better agreement with observational data of the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) over sea ice than those from the other two studies. Detailed comparisons of the results of the MYNN scheme with the SHEBA data suggest that significant variations of the fluxes observed during “winter” when the ice was covered with dry snow may have been caused by those of the surface roughness around the observational site. The stability functions obtained from the MYNN scheme predict that the bulk and flux Richardson numbers approach critical values of 0.26 and 0.21, respectively, in the limit of z/L → ∞. These critical values result from the Kolmogorov hypothesis applied to the turbulent dissipation in the MYNN scheme and are considered to correspond to a transition from Kolmogorov to non-Kolmogorov turbulence.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Stability-based optimization of ACRT for the growth of CZT by the traveling heater method

Numerical modeling is employed to study the effects of several accelerated crucible rotation technique (ACRT) rotation schedules on the growth of cadmium zinc telluride (CZT) by the traveling heater method (THM). In conjunction with these analyses, a measure is developed to estimate the amplitude of disturbances associated with cellular interface growth morphologies that develop over time and across the melt-solid interface. Furthermore, this disturbance amplitude measure is used to assess the ability of ACRT to stabilize the growth interface and thereby minimize inclusion formation processes. Notably, our analyses reveal that interfacial instability is not well correlated with melt undercooling, explaining why classical ACRT approaches to reduce undercooling by mixing may not stabilize growth. Computations show that interface stability is best achieved via rotation schedules that accentuate outward Ekman flows during spin-up and, during spin-down, eliminate Taylor-Görtler flows and minimize inward Ekman flows.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A unified framework of stabilized finite element method for solving the Boltzmann transport equation

This paper presents a unified framework of stabilized finite element method for solving the Boltzmann transport equation. Unlike the traditional Petrov-Galerkin finite element method which modifies the test function to construct the stabilization term, we derive the stabilization methods from the standard Galerkin weak form with Sub-grid scale model. The basic idea of this method is to decompose the unknowns into its numerical solution and residual, with an approximation for the residual and embeds it in the Galerkin weak form to yield a stabilized variational formula. Different approximations of the residual lead to different stabilization methods, all the frequently used stabilized methods, including the Streamline Upwinding Petrov-Galerkin (SUPG) method, Galerkin/Least-Square (GLS) method, and Algebraic Sub-Grid Scale (ASGS) method can be obtained from this framework. The similarities and differences of the different approximations are compared in this paper. The numerical results show that the behaviors of the different methods area similar with the same stabilization parameter, and all these stabilized techniques can obtain a correct and stable solution. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Epitaxial stabilization of thin films of the frustrated Ge-based spinels

Frustrated magnets can host numerous exotic many-body quantum and topological phenomena. GeNi 2 O 4 is a three-dimensional S=1 frustrated magnet with an unusual two-stage transition to the two-dimensional antiferromagnetic ground state, while GeCu 2 O 4 is a high-pressure phase with a strongly tetragonally elongated spinel structure and magnetic lattice formed by S=1/2 CuO 2 linear chains with frustrated interchain exchange interactions and exotic magnetic behavior. Here, we report on the thin-film epitaxial stabilization of these two compounds. The developed growth mode, surface morphology, crystal structure, and copper valence state were characterized by in situ reflection high-energy electron diffraction, atomic force microscopy, x-ray reflectivity, x-ray diffraction, x-ray photoelectron spectroscopy, and resonant x-ray absorption spectroscopy. Our results pave an alternative route to the comprehensive investigation of the puzzling magnetic properties of these compounds and the exploration of emergent features driven by strain.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Numerical Simulations of Flow-Induced Deflections in MITR LEU Fuel Plate Due to Channel Size Disparity

The hydromechanical stability of the fuel plates in parallel coolant channels of a Materials Testing Reactor (MTR) fuel element design is of great importance to the safety of research and test reactors. Previous analytical, experimental, and numerical efforts focused on parallel channels with the same or similar size; also, in the prior numerical simulations, the fuel plate was often assumed to be perfectly flat. This work presents the results of a fluid-structure interaction simulation performed to evaluate the flow-induced deflections of the fuel plates in the low-enriched uranium (LEU, <20 wt% 235 U) fuel element design for the conversion (from highly enriched uranium) of the Massachusetts Institute of Technology Reactor (MITR-II, also referred to as MITR). Various manufacturing and assembly tolerances of the MITR LEU elements are considered in the analysis, and the effects of channel size disparity, nonideal plate shape, and flow rate uncertainty are investigated. Results show that, for all cases analyzed, the deflection occurs toward the larger channel, and the change in any channel stripe remains small (less than 0.021 mm) compared to fabrication tolerances. In addition to simulation work, a hydraulic performance test of the MITR LEU fuel element is currently planned to support conversion to the use of LEU fuel.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Sorption kinetics and stability of conventional adsorbents for mercury remediation

In-situ remediation of mercury at numerous contaminated sites worldwide is a challenging and costly endeavor due to the persistency of this contaminant. In this study, we evaluated eight commercially available sorbent media ranging from carbon-, clays- and silica-based materials (PBC– Biochar, eSorb – Sorbster, nsPAC – Powdered Activated Carbon, fsPAC – Powdered Activated Carbon with Mackinawite, F300 – Filtrasorb 300, Si-SH – Silica Thiol, eBind – RemBind, Q-Clay – Organoclay PM-199), for their effectiveness in sorbing mercury (Hg 2+ ) and mercury complexed with dissolved organic matter (Hg-DOM). Under the chosen experimental conditions of this study, results showed that in the absence of DOM, the kinetic rates of Hg 2+ sorption onto the evaluated sorbents were in the order of 0.31 min-1 (Si-SH) to 2.98 min -1 (nsPAC), whereas in the presence of DOM, the rates varied from 0.16 min-1 (F300) to 0.95 min -1 (nsPAC). The measured sorption capacity for Hg 2+ in the absence of DOM varied from 3.02 mg/g (Q-Clay) to 35.15 mg/g (Si-SH), whereas in the presence of DOM, calculated partition coefficient (KD) ranged from 69.7 mL/g (Q-Clay) to 41,510 mL/g (Si-SH). Furthermore, kinetic data suggest liquid film diffusion was the rate-limiting steps governing mercury sorption onto the studied media. Overall, the obtained study parameters (kinetics/isotherm) are particularly important in informing robust engineering designs for deployment of the vast majority of evaluated sorbents. Thus, sorbent-based strategies offer viable solutions for cost-effective cleanup of mercury at industrially contaminated sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Numerical integration in the virtual element method with the scaled boundary cubature scheme

Abstract The virtual element method (VEM) is a stabilized Galerkin method on meshes that consist of arbitrary (convex and nonconvex) polygonal and polyhedral elements. A crucial ingredient in the implementation of low‐ and high‐order VEM is the numerical integration of monomials and nonpolynomial functions over such elements. In this article, we apply the recently proposed scaled boundary cubature (SBC) scheme to compute the weak form integrals in various virtual element formulations over polygonal and polyhedral meshes. In doing so, we demonstrate the flexibility of the approach and the accuracy that it delivers on a broad suite of boundary‐value problems in 2D and 3D over polytopes with affine faces as well as on elements with curved boundaries. In addition, the use of the SBC scheme is exemplified in an enriched Poisson formulation of the VEM in which weakly singular functions are required to be integrated. This study establishes the SBC method as a simple, accurate and efficient integration scheme for use in the VEM.

Chin, Eric B.↗