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NASA NTRS1989

Precise solution for a finite set of spherical coefficients from equiangular gridded data

An important goal of geodesy is to determine the anomalous potential and its derivatives outside of the earth. Representing the surface anomalies by a series of spherical harmonics is useful since it is then possible to do a term by term solution of Laplace's equation and upward continuation. The problem of finding such a spherical harmonic series for anomaly values given on an equiangular surface grid is addressed. (This is a first step toward the more complicated problem of finding a function such that locally averaged values fit a grid of mean anomalies.) Three approaches to this fitting problem are discussed and compared: the discrete Fourier technique, the discrete integral technique, and a new approach. The peculiar nature of the equiangular grid, with its increasing density of (noisy) data toward the poles, causes each method to exhibit a different type of difficulty. The new method is shown to be practical as well as precise since the numerical conditioning problems which appear can be successfully handled by such well-known techniques as a (simple) Kalman filter.

Zucker, Paul A.↗

NASA NTRS1974

SAS-2 observations of celestial diffuse gamma radiation above 30 MeV

The small astronomy satellite, SAS-2, used a 32-deck magnetic core digitized spark chamber to study gamma rays with energies above 30 MeV. Data for four regions of the sky away from the galactic plane were analyzed. These regions show a finite, diffuse flux of gamma rays with a steep energy spectrum, and the flux is uniform over all the regions. Represented by a power law, the differential energy spectrum shows an index of 2.5 + or - 0.4. The steep SAS-2 spectrum and the lower energy data are reasonably consistent with a neutral pion gamma-ray spectrum which was red-shifted (such as that proposed by some cosmological theories). It is concluded that the diffuse celestial gamma ray spectrum observed presents the possibility of cosmological studies and possible evidence for a residual cosmic ray density, and supports the galactic superclusters of matter and antimatter remaining from baryon-symmetric big bang.

Thompson, D. J.↗

NASA NTRS1991

Numerical investigation of the flow over a double delta wing at high incidence

The vortical flowfield over a double-delta wing configuration, consisting of a sharp leading edge 76 deg sweep strake and a 40 deg sweep wing section is investigated. The governing equations are solved numerically with a partially upwind, finite-difference, factorized algorithm. The leeward side vortex system resulting from the strake and wing vortices is investigated for subsonic, high-Reynolds-number flow at various angles of incidence. At low angles of attack the strake and wing vortices remain separate over the wing section, while for flows at higher angles of attack the two vortices merge and vortex breakdown develops. Vortex breakdown appears initially at the trailing edge region of the wing section. As the angle of attack increases bursting occurs further upstream closer to the strake section. The effect of numerical grid density is investigated, and the solutions are compared with available experimental data.

Ekaterinaris, John A.↗

NASA NTRS1996

A Review of High-Order and Optimized Finite-Difference Methods for Simulating Linear Wave Phenomena

This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested.

Zingg, David W.↗

NASA NTRS2003

Validation of a High-Order Prefactored Compact Code on Nonlinear Flows with Complex Geometries

A finite-difference time domain solution of the airfoil gust problem is obtained using a high-accuracy nonlinear computational aeroacoustics code. For computational efficiency, the equations are cast in chain-rule curvilinear form, and a structured multiblock solver is used in parallel. In order to fully investigate the performance of this solver, a test matrix of eight problems are computed (two airfoil geometries, two gust frequencies, and two gust configurations). These results are compared to solutions obtained by the GUST3D frequency-domain solver both on the airfoil surface and in the far field. Grid density and domain size studies are included.

Hixon, R.↗

NASA NTRS1974

A redetermination of the galactic H I half-thickness and a discussion of some dynamical consequences

We have redetermined the half-thickness of the neutral hydrogen layer of our Galaxy over a significant portion of the disk (R, distance from the galactic center between 1.4 and 16.8 kpc). Four high-resolution 21-cm surveys were employed, and corrections were made for the effects of finite optical depth in the 21-cm line. We find that the half-thickness is approximately constant for R from 4.5 to 10 kpc and averages 260 pc for 0 to 90 deg long and 230 pc for 270 to 360 deg long. Using this thickness in conjunction with a recent galactic mass model, we are able to determine the quantity Q over a large portion of the galactic disk, where Q-squared is the ratio at the galactic plane of the sum of the gas, magnetic, and cosmic-ray pressures to the gas density.

Jackson, P. D.↗

NASA NTRS1983

The collapse of the local, Spitzer-Haerm formulation and a global-local generalization for heat flow in an inhomogeneous, fully ionized plasma

The breakdown of the classical (CBES) field aligned transport relations for electrons in an inhomogeneous, fully ionized plasma as a mathematical issue of radius of convergence is addressed, the finite Knudsen number conditions when CBES results are accurate is presented and a global-local (GL) way to describe the results of Coulomb physics moderated conduction that is more nearly appropriate for astrophysical plasmas are defined. This paper shows the relationship to and points of departure of the present work from the CBES approach. The CBES heat law in current use is shown to be an especially restrictive special case of the new, more general GL result. A preliminary evaluation of the dimensionless heat function, using analytic formulas, shows that the dimensionless heat function profiles versus density of the type necessary for a conduction supported high speed solar wind appear possible.

Scudder, J. D.↗

NASA NTRS2013

MHD Simulations of the Plasma Flow in the Magnetic Nozzle

The magnetohydrodynamic (MHD) flow of plasma through a magnetic nozzle is simulated by solving the governing equations for the plasma flow in the presence of an static magnetic field representing the applied nozzle. This work will numerically investigate the flow and behavior of the plasma as the inlet plasma conditions and magnetic nozzle field strength are varied. The MHD simulations are useful for addressing issues such as plasma detachment and to can be used to gain insight into the physical processes present in plasma flows found in thrusters that use magnetic nozzles. In the model, the MHD equations for a plasma, with separate temperatures calculated for the electrons and ions, are integrated over a finite cell volume with flux through each face computed for each of the conserved variables (mass, momentum, magnetic flux, energy) [1]. Stokes theorem is used to convert the area integrals over the faces of each cell into line integrals around the boundaries of each face. The state of the plasma is described using models of the ionization level, ratio of specific heats, thermal conductivity, and plasma resistivity. Anisotropies in current conduction due to Hall effect are included, and the system is closed using a real-gas equation of state to describe the relationship between the plasma density, temperature, and pressure.A separate magnetostatic solver is used to calculate the applied magnetic field, which is assumed constant for these calculations. The total magnetic field is obtained through superposition of the solution for the applied magnetic field and the self-consistently computed induced magnetic fields that arise as the flowing plasma reacts to the presence of the applied field. A solution for the applied magnetic field is represented in Fig. 1 (from Ref. [2]), exhibiting the classic converging-diverging field pattern. Previous research was able to demonstrate effects such as back-emf at a super-Alfvenic flow, which significantly alters the shape of the magnetic field in both the near- and far-field regions. However, in that work the downstream domain was constrained to a channel of constant cross-sectional area. In the present work we seek to address this issue by modeling the downstream region with a domain that permits free expansion of the plasma, permitting a better evaluation of the downstream effects the applied field has on the plasma. The inlet boundary conditions and applied magnetic field values will also be varied to determine the effect the initial plasma energy content and applied magnetic field energy density have on the near- and far-field plasma properties on the MHD code. This will determine the effect of inlet boundary conditions on the results downstream and address issues related to the restrictive numerical domain previously used.

Smith, T. E. R.↗

NASA NTRS2019

Simultaneous Localization and Mapping for Satellite Rendezvous and Proximity Operations Using Random Finite Sets

Future space missions require that spacecraft have the capability to autonomously navigate non-cooperative environments for rendezvous and proximity operations (RPO). Current relative navigation filters can have difficulty in these situations, diverging due to complications with data association, high measurement uncertainty, and clutter, particularly when detailed a priori maps of the target object or spacecraft do not exist. The goal of this work is to demonstrate the feasibility of random finite set (RFS) filters for spacecraft relative navigation and pose estimation. The approach is to formulate satellite relative navigation and pose estimation as a simultaneous localization and mapping (SLAM) problem, in which an observer spacecraft seeks to simultaneously estimate the location of features on a target object or spacecraft as well as its relative position, velocity and attitude. This work utilizes a filter developed using the framework of RFS which are well suited to multi-target SLAM operations, avoiding data association entirely. Relevant RPO scenarios with simulated flash LIDAR measurements are tested with a Probability Hypothesis Density (PHD) RFS filter embedded in a particle filter to obtain a feature map of a target and a relative pose estimate between the target and observer. Preliminary results show that an RFS-based filter can successfully perform SLAM in a spacecraft relative navigation scenario with no a priori map of the target. These results demonstrate the feasibility of RFS filtering for spacecraft relative navigation and motivate future studies which may expand to tracking space objects for space situational awareness, as well as relative navigation around small bodies.

Schlenker, Lauren↗

NASA NTRS2019

Simultaneous Localization and Mapping for Satellite Rendezvous and Proximity Operations using Random Finite Sets

Schlenker, Lauren↗

NASA NTRSDate not supplied

Machine Learning Approaches for Rare-Earth Silicate Environmental Barrier Coating Thermochemical and Thermomechanical Property Predictions

Environmental barrier coatings (EBCs) are a necessary enabling technology for the transition from superalloys to silicon carbide (SiC) ceramic matrix composites (CMCs) in gas turbine engines for increased efficiency and decreased fuel costs. SiC-based CMCs are prone to oxidation-based degradation in the engine hot section, and rare-earth (RE) silicates are promising candidates for EBCs due to their close thermal expansion match to the composite substrate and oxidation resistance. However, the design of EBCs is hindered by the large chemical space of candidate materials and the difficulty in obtaining material properties for engineering optimization. This is especially difficult as research continues into mixed-cation or “high-entropy” RE silicates. First-principles computational methods such as density functional theory (DFT) are highly effective at calculating material properties to guide coating design but are limited by their computational cost. Atomistic simulations have the potential to both accelerate property calculations and expand the properties able to be calculated due to their lower computational compared to DFT. However, they require interatomic potentials (IAPs) specific to the material system of interest, and, to our knowledge, there are no suitable IAPs for RE silicates. Machine learning (ML) is a promising technique to accelerate material property predictions indirectly by generating IAPs for atomistic simulations or via direct prediction. In this work, we present two ML approaches to accelerate the calculation of RE silicate properties relevant to EBC design: 1) a ML-derived interatomic potential (IAP) for atomistic simulations of yttrium disilicate (Y2Si2O7) from DFT training data, and 2) a neural network (NN) model to directly predict thermochemical properties of RE silicates and oxides directly from easily obtainable unit cell parameters. Classical MD simulations using the IAP yield lattice properties and bond lengths in good agreement with both DFT and experimental results from x-ray diffraction. Thermodynamic properties calculated using the finite-displacement phonon method and quasi-harmonic approximation were orders of magnitude faster than DFT with good agreement to the DFT results. The IAP was also used to calculate properties such as coefficient of thermal expansion (CTE) that require large simulation supercells and are therefore difficult with DFT. The IAP correctly predicted the anisotropic nature of the CTE in three different phases of Y2Si2O7. The NN model predicts constant pressure heat capacity, Cp, orders of magnitude faster than DFT calculations, which can enable its use as a surrogate model for multiscale simulations. The two methods presented in this work demonstrate the utility of ML for accelerating the prediction of RE silicate properties, which can in turn accelerate EBC design and optimization.

machine learning↗

NASA NTRS1983

Fluid signatures of rotational discontinuities at Earth's magnetopause

Fluid signatures in the MHD approximation at rotational discontinuities (RD) of finite width called rotational shear layers (RSL) are examined for general flow and magnetic geometries. Analytical and geometrical arguments illustrate that the fluid speed can either go up or down across an RSL for a fixed normal mass flux. The speed profile may or may not be monotonic depending on the boundary conditions. The flow velocity may or may not be field aligned or ""jetting'' as a result of traversing the RSL. In general, significant ""convection'' is expected in the layer. The observable signatures of (MHD) RSL's depend on 7 (boundary condition) parameters are (1) the mass density, (2 to 5) the incident normal and transverse components of the magnetic field and fluid velocity, (6) the angle epsilon between the incident tangential flow velocity and tangential magnetic field, and (7) the size of the magnetic angular rotation implemented by the layer delta phi.

Scudder, J. D.↗

NASA NTRS1984

Fluid signatures of rotational discontinuities at the earth's magnetopause

Fluid signatures in the MHD approximation at rotational discontinuities (RD) of finite width called rotational shear layers (RSL) are examined for general flow and magnetic geometries. Analytical and geometrical arguments illustrate that the fluid speed can either go up or down across an RSL for a fixed normal mass flux. The speed profile may or may not be monotonic depending on the boundary conditions. The flow velocity may or may not be field aligned or 'jetting' as a result of traversing the RSL. In general, significant 'convection' is expected in the layer. The observable signatures of (MHD) RSL's depend on 7 (boundary condition) parameters are (1) the mass density, (2 to 5) the incident normal and transverse components of the magnetic field and fluid velocity, (6) the angle epsilon between the incident tangential flow velocity and tangential magnetic field, and (7) the size of the magnetic angular rotation implemented by the layer delta phi.

Scudder, J. D.↗

NASA NTRS1973

Vertical distribution of vibrational energy of molecular nitrogen in a stable auroral red arc and its effect on ionospheric electron densities

Previous solutions of the problem of the distribution of vibrationally excited molecular nitrogen in the thermosphere have either assumed a Boltzmann distribution and considered diffusion as one of the loss processes or solved for the energy level populations and neglected diffusion. Both of the previous approaches are combined by solving the time dependent continuity equations, including the diffusion process, for the first six energy levels of molecular nitrogen for conditions in the thermosphere corresponding to a stable auroral red arc. The primary source of molecular nitrogen excitation was subexcitation, and inelastic collisions between thermal electrons and molecular nitrogen. The reaction rates for this process were calculated from published cross section calculations. The loss processes for vibrational energy were electron and atomic oxygen quenching and vibrational energy exchange. The coupled sets of nonlinear, partial differential equations were solved numerically by employing finite difference equations.

Newton, G. P.↗

NASA NTRS1985

The non-hydrostatic figures of the terrestrial planets

Solid state creep being exponentially dependent on temperature must dominate the mechanical behavior of the mantles of terrestrial planets beneath their lithospheres. General arguments suggest that the lithospheres of the Moon and Mars are about 200 km thick; the Earth, Venus and Mercury much less. Short wavelength gravity anomalies are explained by the finite strength of the lithosphere: the lunar mascons being an example. The good correlation of the Venus and Mars gravity anomalies with topography up to spherical harmonics of degrees 10-15 is in striking contrast to the lack of correlation between the long wavelength components of the geoid and the continent-ocean distribution or even the plates. Attempts have been made to explain the former correlations by isostatic models but the depths of compensation seem implausible. Low degree harmonics of the gravity fields of the terrestrial planets as is certainly the case in the Earth must arise from the density variations driving solid state convection. In the case of Venus the less dense differentiated materials of the highlands seems to be positioned over the singular points of the convection pattern. Thus the correlated gravity field does not arise from the highlands but from the density difference in the convecting interior. In the Earth lack of correlation seems to arise from the fact that the plates have moved relative to the convection pattern the last 100 M yr.

Runcorn, S. K.↗

NASA NTRS1987

Ultra-high-energy cosmic rays in a galactic wind and its termination shock

Results are reported from numerical modeling of the acceleration and transport of ultra-high-energy cosmic rays in a galactic wind and its termination shock. A two-dimensional (azimuthally symmetric) wind and spiral magnetic field, with a spherical termination shock, where the velocity drops suddenly, is assumed. The time-dependent cosmic-ray transport equation, including all major transport effects is solved using an implicit finite-difference scheme. Particles are injected as the shock of low energy, and the subsequent evolution of the distribution function is followed. Iron nuclei are readily accelerated at the shock to energies up to 100 billion GeV, and protons to 10 billion GeV. A major effect aiding the acceleration of these particles is the spiral of the magnetic field carried out by the wind, caused by the rotation of the Galaxy, with the result that the shock is nearly normal over most of its area. Increasing the magnetic field or rotation rate increases the maximum energy attainable. Anisotropies and energy densities of the particles are also discussed. It is concluded that the process is consistent with observations of ultra-high-energy cosmic rays.

Jokipii, J. R.↗

NASA NTRS1992

Saturated fluorescence measurements of the hydroxyl radical in laminar high-pressure C2H6/O2/N2 flames

Saturation of a transition of the OH molecule in high-pressure flames is demonstrated by obtaining saturation curves in C2H6/O2/N2 laminar flames at 1, 6.1, 9.2, and 12.3 atm. Quantitative fluorescence measurements of OH number density at pressures to 12.3 atm are presented. To assess the efficacy of the balanced cross-rate model for high-pressure flames, laser-saturated fluorescence measurements, which were calibrated in an atmospheric-pressure flame, are compared with absorption measurements at 3.1 and 6.1 atm. At 3.1 atm the absorption and fluorescence measurements compare well. At 6.1 atm, however, the concentrations given by lasre-saturated fluorescence are about 25 percent lower than the absorption values, indicating some depletion of the laser-coupled levels beyond that at atmospheric pressure. By using a reasonable estimate for the finite sensitivity to quenching, it is anticipated that fluorescence measurements that are calibrated at 1 atm can be applied to flames at about 10 atm with absolute errors within +/- 50 percent.

Carter, Campbell D.↗

NASA NTRS2000

Development of Individually Addressable Micro-Mirror-Arrays for Space Applications

We have been developing a 32 x 32 prototype array of individually addressable Micro-Mirrors capable of operating at cryogenic temperature for Earth and Space Science applications. Micro-Mirror-Array technology has the potential to revolutionize imaging and spectroscopy systems for NASA's missions of the 21st century. They can be used as programmable slits for the Next Generation Space Telescope, as smart sensors for a steerable spectrometer, as neutral density filters for bright scene attenuation etc. The, entire fabrication process is carried out in the Detector Development Laboratory at NASA, GSFC. The fabrication process is low temperature compatible and involves integration of conventional CMOS technology and surface micro-machining used in MEMS. Aluminum is used as the mirror material and is built on a silicon substrate containing the CMOS address circuit. The mirrors are 100 microns x l00 microns in area and deflect by +/- 10 deg induced by electrostatic actuation between two parallel plate capacitors. A pair of thin aluminum torsion straps allow the mirrors to tilt. Finite-element-analysis and closed form solutions using electrostatic and mechanical torque for mirror operation were developed and the results were compared with laboratory performance. The results agree well both at room temperature and at cryogenic temperature. The development demonstrates the first cryogenic operation of two-dimensional Micro-Mirrors with bi-state operation. Larger arrays will be developed meeting requirements for different science applications. Theoretical analysis, fabrication process, laboratory test results and different science applications will be described in detail.

Dutta, Sanghamitra B.↗