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NASA NTRS2015

Evolving Design Criteria for Very Large Aperture Space Based Telescopes and Their Influence on the Need for Integrated Tools in the Optimization Process

NASA's Advanced Mirror Technology Development (AMTD) program has been developing the means to design and build the future generations of space based telescopes. With the nearing completion of the James Webb Space Telescope (JWST), the astrophysics community is already starting to define the requirements for follow-on observatories. The restrictions of available launch vehicles and the possibilities of planned future vehicles have fueled the competition between monolithic primaries (with better optical quality) and segmented primaries (with larger apertures, but with diffraction, costs and figure control issues). Regardless of the current shroud sizes and lift capacities, these competing architectures share the need for rapid design tools. As part of the AMTD program a number of tools have been developed and tested to speed up the design process. Starting with the Arnold Mirror Modeler (which creates Finite Element Models (FEM) for structural analysis) and now also feeds these models into thermal stability analyses. They share common file formats and interchangeable results. During the development of the program, numerous trade studies were created for 4-meter and 8-meter monolithic primaries, complete with support systems. Evaluation of these results has led to a better understanding of how the specification drives the results. This paper will show some of the early trade studies for typical specification requirements such as lowest mirror bending frequency and suspension system lowest frequency. The results use representative allowable stress values for each mirror substrate material and construction method and generic material properties. These studies lead to some interesting relationships between feasible designs and the realities of actually trying to build these mirrors. Much of the traditional specifications were developed for much smaller systems, where the mass and volume of the primary where a small portion of the overall satellite. JWST shows us that as the aperture grows, the primary takes up the majority of the mass and volume and the established rules need to be adjusted. For example, a small change in lowest frequency requirement can change the cost by millions of dollars. The paper uses numerous trade studies created during the software development phase of the Arnold Mirror Modeler to illustrate the influences of system specifications on the design space. The future telescopes will require better performance, stability and documented feasibility to meet the hurdles of today's budget and schedules realities. AMTD is developing the tools, but the basic system planning mentality also has to adopt to the requirements of these very large and complex physical structures.

Arnold, William R., Sr.↗

NASA NTRS2008

3D RMHD Simulations of Magnetized Spine-Sheath Relativistic Jets

We have performed numerical simulations of weakly and strongly magnetized relativistic jets embedded in a weakly and strongly magnetized stationary or mildly relativistic (0.5c) sheath flow using the RAISHIN code. In the numerical simulations a jet with Lorentz factor gamma=2.5 is processed to break the initial equilibrium configuration. Results of the numerical simulations are compared to theoretical predictions from a normal mode analysis of the linearized RMHD equations describing a uniform axially magnetized cylindrical relativistic jet embedded in a uniform axially magnetized sheath flow. The prediction of increased stability of a weakly-magnetized system with mildly relativistic sheath flow to Kelvin-Helmholtz instabilities and the stabilization of a strongly magnetized system with mildly relativistic sheath flow is confirmed by the numerical simulations.

Mizuno, Yosuke↗

NASA NTRS2021

Detection of Transient Instabilities in Multi-Agent Systems and Swarms

In this paper, we introduce the novel concept of transient instabilities in multi-agent systems and swarms, i.e., a small disturbance leads to increasing-amplitude oscillations throughout the swarm, which results in a large number of interagent collisions. This instability is dominant in the transient phase of the system and it does not appear in the steady-state behavior of the system, as each agent uses Lyapunov-stable feedback control laws. We present a rigorous definition of transient instability in swarms, and discuss its key properties. We also present a sufficient condition to check if a swarm will be transient stable. Using both theoretical techniques and numerical results, we show that a simple Proportional-Integral-Derivative (PID) feedback-tracking control law is not suitable for these applications. We also present a robust control law for Euler- Lagrangian systems that maintains transient stability across static swarms or time-varying reconfiguration in swarms. Both theoretical results and numerical simulations are presented to demonstrate the effectiveness of our proposed approach.

Quadrelli, Marco B.↗

NASA NTRS1979

Transient unbalance response of four multilobe journal bearings

This work carries out an analysis of the transient response of four multilobe journal bearings (elliptical, offset, three-lobe, and four-lobe) subject to unbalance both below and above the linearized stability thresholds for the bearings. It extends the work of a previous paper on a balanced rotor in the same four bearing types. Transient orbits, bearing forces, and a numerical fast Fourier transform analysis of the orbits are presented. A comparison of bearing forces above the stability threshold for each bearing indicates that the elliptical bearing has the most violent whirl vibration amplitudes, while the offset bearing exhibits the least amount of subsynchronous vibration.

Allaire, P. E.↗

DOE OSTI2021

Computational general relativistic force-free electrodynamics: I. Multi-coordinate implementation and testing

General relativistic force-free electrodynamics is one possible plasma-limit employed to analyze energetic outflows in which strong magnetic fields are dominant over all inertial phenomena. The amazing images of black hole (BH) shadows from the Galactic Center and the M87 galaxy provide a first direct glimpse into the physics of accretion flows in the most extreme environments of the universe. The efficient extraction of energy in the form of collimated outflows or jets from a rotating BH is directly linked to the topology of the surrounding magnetic field. We aim at providing a tool to numerically model the dynamics of such fields in magnetospheres around compact objects, such as BHs and neutron stars. To do so, we probe their role in the formation of high energy phenomena such as magnetar flares and the highly variable teraelectronvolt emission of some active galactic nuclei. In this work, we present numerical strategies capable of modeling fully dynamical force-free magnetospheres of compact astrophysical objects. Here, we provide implementation details and extensive testing of our implementation of general relativistic force-free electrodynamics in Cartesian and spherical coordinates using the infrastructure of the E INSTEIN T OOLKIT . The employed hyperbolic/parabolic cleaning of numerical errors with full general relativistic compatibility allows for fast advection of numerical errors in dynamical spacetimes. Such fast advection of divergence errors significantly improves the stability of the general relativistic force-free electrodynamics modeling of BH magnetospheres.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Research on the Influence Mechanism of the High‐Steep Slope on the Deformation Characteristics of Bridge Substructure

With the development of the Chinese railway, the high‐steep slope is irreversible to be faced; especially under severe conditions such as heavy rainfall and earthquake, this kind of slope is prone to geological disasters, which seriously affects the safety and stability of the bridge substructure. Aiming to this, long‐term monitorization and numerical analysis were carried out in this research, and the influence mechanism of the high‐steep slopes on the stress and deformation characteristics of the bridge structure was studied. The research results show that under the effect of rainfall and earthquake, the original stress balance in the high‐steep slope is broken, and the possibility of landslide thrust increases; under the comprehensive impact of residual landslide thrust, traction force at slope foot, vertical gravity of bridge slab and vehicle, and the bridge cap will deform. Besides, the deformation of the bridge pier exceeds the allowable lateral displacement of the top of the bridge pier, reaching 111.7%∼112.4% of the limit, which seriously affects the stability of the bridge structure and the safety of the railway service. Therefore, by increasing the support strength of the slope foot and the diameter of the bridge pile foundation, the traction force of the slope foot can be reduced, and the sliding resistance of the bridge pile foundation can be improved so as the safety of the bridge structure can be promoted.

Zhang, Yufang (ORCID:0000000348912060)↗

NASA NTRS1992

The stability of a trailing-line vortex in compressible flow

We consider the inviscid stability of the Batchelor (1964) vortex in a compressible flow. The problem is tackled numerically and also asymptotically, in the limit of large (aximuthal and streamwise) wavenumbers, together with large Mach numbers. The nature of the solution passes through different regimes as the Mach number increases, relative to the wavenumbers. At very high wavenumbers and Mach numbers, the mode which is present in the incompressible case ceases to be unstable, while new 'center mode' forms, whose stability characteristics, are determined primarily by conditions close to the vortex axis. We find that generally the flow becomes less unstable as the Mach number increases, and that the regime of instability appears generally confined to disturbances in a direction counter to the direction of the rotation of the swirl of the vortex. Throughout the paper, comparison is made between our numerical results and results obtained from the various asymptotic theories.

Stott, Jillian A. K.↗

NASA NTRS1988

Stability of semidiscrete approximations for hyperbolic initial-boundary-value problems: Stationary modes

Spatially discrete difference approximations for hyperbolic initial-boundary-value problems (IBVPs) require numerical boundary conditions in addition to the analytical boundary conditions specified for the differential equations. Improper treatment of a numerical boundary condition can cause instability of the discrete IBVP even though the approximation is stable for the pure initial-value or Cauchy problem. In the discrete IBVP stability literature there exists a small class of discrete approximations called borderline cases. For nondissipative approximations, borderline cases are unstable according to the theory of the Gustafsson, Kreiss, and Sundstrom (GKS) but they may be Lax-Richtmyer stable or unstable in the L sub 2 norm on a finite domain. It is shown that borderline approximation can be characterized by the presence of a stationary mode for the finite-domain problem. A stationary mode has the property that it does not decay with time and a nontrivial stationary mode leads to algebraic growth of the solution norm with mesh refinement. An analytical condition is given which makes it easy to detect a stationary mode; several examples of numerical boundary conditions are investigated corresponding to borderline cases.

Warming, Robert F.↗

NASA NTRS2006

Stability of Supersonic Boundary Layers Over Blunt Wedges

Receptivity and stability of supersonic boundary layers over blunt flat plates and wedges are numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 10(exp 6)/inch. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. Computations are performed for a flat plate with leading edge thicknesses of 0.0001, 0.001, 0.005 and 0.01 inches that give Reynolds numbers based on the leading edge thickness ranging from 1000 to 10000. Calculations are also performed for a wedge of 10 degrees half angle with different leading edge radii 0.001 and 0.01 inches. The linear stability results showed that the bluntness has a strong stabilizing effect on the stability of two-dimensional boundary layers. The transition Reynolds number for a flat plate with a leading edge thickness of 0.01 inches is about 3.5 times larger than it is for the Blasius boundary layer. It was also revealed that boundary layers on blunt wedges are far more stable than on blunt flat plates.

Balakumar, Ponnampalam↗

NASA NTRS1993

Linear instability of curved free shear layers

The linear inviscid hydrodynamic stability of slightly curved free mixing layers is studied in this paper. The disturbance equation is solved numerically using a shooting technique. Two mean velocity profiles that represent stably and unstably curved free mixing layers are considered. Results are shown for cases of five curvature Richardson numbers. The stability characteristics of the shear layer are found to vary significantly with the introduction of the curvature effects. The results also indicate that, in a manner similar to the Goertler vortices observed in a boundary layer along a concave wall, instability modes of spatially developing streamwise vortex pairs may appear in unstable curved mixing layers.

Liou, William W.↗

NASA NTRS1993

Linear instability of curved free shear layers

Liou, William W.↗

DOE OSTI2024

Dynamic flux surrogate-based partitioned methods for interface problems

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. In conclusion, we provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.

Dynamic mode decomposition (DMD)↗

DOE OSTI2022

On the effects of reactant stratification and wall curvature in non-premixed rotating detonation combustors

The optimization of non-premixed rotating detonation combustors (RDCs) requires improved understanding of the coupled effects of reactant stratification, fluid property gradients, and complex shock-wave interactions on the detonation wave structure within annular geometries. In the current work, simultaneous orthogonal views of chemiluminescence and hydroxyl planar laser-induced fluorescence (PLIF) are utilized to establish the existence of a dual-wave system characterized by leading and trailing detonation waves that are closely coupled by the local flow physics. These features are persistent over a wide range of mass flow rates and are consistent with prior observations of non-premixed rotating detonations in annular geometries. The detailed instantaneous time sequences are compared with a 3D reactive unsteady Reynolds averaged Navier-Stokes (URANS) simulation to more clearly elucidate the in-situ combustion dynamics and the sensitivity to reactant inlet conditions. It is found that the dual-wave system results from unburned reactants that survive the leading detonation wave in the injector near field and are consumed within a trailing azimuthal reflected-shock combustion (ARSC) zone. By contrast, the injector far field is characterized by rapid mixing due to a sudden drop to subsonic conditions, and the bifurcated detonation wave structure collapses into a stronger, single-wave detonation front with higher overall pressure ratio as compared with the dual-wave system. While each RDC will have different inflow, mixing, and combustion characteristics, the underlying interactions between the stratified reactants and azimuthal wave dynamics identified through the combination of advanced MHz-rate diagnostics and 3D numerical simulations have important implications for the study of detonation wave stability, mode transition, and combustion efficiency in non-premixed annular RDCs.

3D URANS↗

DOE OSTI2025

Spin-State and Reorganization Energy Considerations for Metal-Centered Photoredox Catalysis

Transition-metal complexes featuring metal-centered excited states have recently emerged as mechanistically distinct platforms for selective photochemistry, including photoredox catalysis. Among these, Co(III) complexes have demonstrated productive photoinduced electron transfer via the 3 T 1 metal-centered state. In contrast, photoreactivity from the 5 T 2 metal-centered state in Fe(II) polypyridyl complexes remains limited. Building on our prior report concerning reactivity associated with the 5 T 2 state in [Fe(tren(py) 3 )] 2+ (tren(py) 3 = tris(2-pyridylmethyliminoethyl)-amine), we introduced stronger-field ligands in an effort to increase excited-state energies of Fe(II) polypyridyl complexes and enhance reactivity. Despite achieving nanosecond-scale excited-state lifetimes and favorable thermodynamic driving forces, no photoreactivity was observed. Reinvestigation of the observations previously reported for [Fe(tren(py) 3 )] 2+ revealed interactions between the metal complex and the substrate in their respective ground states that mimicked dynamic quenching of the chromophore, prompting a reassessment of mechanistic considerations inherent in leveraging reductive chemistry from the 5 T 2 excited state of Fe(II). Our analysis indicates that electron transfer from the 5 T 2 excited state of a low-spin d6 metal is subject to significant barriers both in terms of reorganization energies and spin conservation that undermines its ability to act as an electron donor for photoredox catalysis. In contrast, ligand fields that are sufficient to stabilize the 3 T 1 excited state have available to them numerous spin-allowed and, in certain cases, near-barrierless pathways to engage in excited-state electron transfer (both oxidative and reductive depending on the identity of the metal). These results highlight the critical role of spin-state changes and their associated reorganization energy requirements in metal-centered photoredox catalysis.

charge transfer↗

DOE OSTI2020

False metals, real insulators, and degenerate gapped metals

This paper deals with a significant family of compounds predicted by simplistic electronic structure theory to be metals but are, in fact, insulators. This false metallic state has been traditionally attributed in the literature to reflect the absence of proper treatment of electron-electron correlation (“Mott insulators”) whereas, in fact, even mean-field like density functional theory describes the insulating phase correctly if the restrictions posed on the simplistic theory are avoided. Such unwarranted restrictions included different forms of disallowing symmetry breaking described in this article. As the science and technology of conductors have transitioned from studying simple elemental metals such as Al or Cu to compound conductors such as binary or ternary oxides and pnictides, a special class of degenerate but gapped metals has been noticed. Their presumed electronic configurations show the Fermi level inside the conduction band or valence band, yet there is an “internal band gap” between the principal band edges. The significance of this electronic configuration is that it might be unstable toward the formation of states inside the internal band gap when the formation of such states costs less energy than the energy gained by transferring carriers from the conduction band to these lower energy acceptor states, changing the original (false) metal to an insulator. The analogous process also exists for degenerate but gapped metals with the Fermi level inside the valence band, where the energy gain is defined by transfer of electrons from the donor level to the unoccupied part of the valence band. We focus here on the fact that numerous electronic structure methodologies have overlooked some physical factors that could stabilize the insulating alternative, predicting instead false metals that do not really exist (note that this is in general not a physical phase transition, but a correction of a previous error in theory that led to a false prediction of a metal). Such errors include: (i) ignoring spin symmetry breaking, such as disallowing magnetic spin ordering in CuBi2O4 or disallowing the formation of polymorphous spin networks in paramagnetic LaTiO 3 and YTiO 3 ; (ii) ignoring structural symmetry breaking, e.g., not enabling energy-lowering bond disproportionation (Li-doped TiO 2 , SrBiO 3 , and rare-earth nickelates), or not exploring pseudo-Jahn–Teller-like distortions in LaMnO 3 , or disallowing spontaneous formation of ordered vacancy compounds in Ba 4 As 3 and Ag 3 Al 22 O 34 ; and (iii) ignoring spin–orbit coupling forcing false metallic states in CaIrO 3 and Sr 2 IrO 4 . The distinction between false metals vs real insulators is important because (a) predicting theoretically that a given compound is metal even though it is found to be an insulator often creates the temptation to invoke high order novel physical effects (such as correlation in d-electron Mott insulators) to explain what was in effect caused by a more mundane artifact in a lower-level mean-field band theory, (b) recent prediction of exotic physical effects such as topological semimetals were unfortunately based on the above compounds that were misconstrued by theory to be metal, but are now recognized to be stable insulators not hosting exotic effects, and (c) practical technological applications based on stable degenerate but gapped metals such as transparent conductors or electrides for catalysis must rely on the systematically correct and reliable theoretical classification of metals vs insulators.

36 MATERIALS SCIENCE↗

NASA NTRS1966

A study of pulsation in RR Lyrae models.

Nonlinear calculations of intermediate amplitude to analyze stability of pulsating stars of varying composition, mass, luminosity, etc, using numerical integration of motion equations

STELLAR MASS↗

NASA NTRS1972

An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing

An implicit finite-difference scheme is developed for the fully coupled solution of the viscous, radiating stagnation-streamline equations, including strong blowing. Solutions are presented for both air injection and injection of carbon-phenolic ablation products into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative-transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized in the study. With minimum number of assumptions for the initially unknown parameters and profile distributions, convergent solutions to the full stagnation-line equations are rapidly obtained by a method of successive approximations. Damping of selected profiles is required to aid convergence of the solutions for massive blowing. It is shown that certain finite-difference approximations to the governing differential equations stabilize and improve the solutions. Detailed comparisons are made with the numerical results of previous investigations. Results of the present study indicate lower radiative heat fluxes at the wall for carbonphenolic ablation than previously predicted.

Garrett, L. B.↗

NASA NTRS1973

Deformation and burst of a liquid droplet freely suspended in a linear shear field

A theoretical method is presented for predicting the deformation and the conditions for breakup of a liquid droplet freely suspended in a general linear shear field. This is achieved by expanding the solution to the creeping-flow equations in powers of the deformation parameter epsilon and using linear stability theory to determine the onset of bursting. When compared with numerical solutions and with the available experimental data, the theoretical results are generally found to be of acceptable accuracy although, in some cases, the agreement is only qualitative.

Barthes-Biesel, D.↗