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NASA NTRS1991

A generalized scheme for three-dimensional hyperbolic grid generation

A hyperbolic grid generation scheme formulated from grid orthogonality and cell volume specification is generalized such that high quality three-dimensional grids can be obtained for a wide variety of geometries. The speed of the scheme is one to two orders of magnitude faster than typical elliptic grid generation methods. The robustness of the scheme is significantly enhanced by several new techniques. By using a spatially variable smoothing coefficient, orthogonality and smoothness of the grid are maintained around complex concave and convex surface topologies. A metric correction procedure is employed to guarantee that the grid marches out of a corner by bisecting the angles subtended by the neighboring points. Extra robustness at severe convex corners is achieved by special local treatments. Different extrapolation methods are used to provide smoothness at floating edges and axis regions. The versatility of the new hyperbolic grid generation scheme is demonstrated by three-dimensional grids generated for external components of the intergrated Space Shuttle vehicle and the SOFIA telescope.

Chan, William M.↗

NASA NTRS2023

Three Eruptions Observed by Remote Sensing Instruments Onboard Solar Orbiter

On February 21 and March 21 – 22, 2021, the Extreme Ultraviolet Imager (EUI) onboard Solar Orbiter observed three prominence eruptions. The eruptions were associated with coronal mass ejections (CMEs) observed by Metis, Solar Orbiter’s coronagraph. All three eruptions were also observed by instruments onboard the Solar–TErrestrial RElations Observatory (Ahead; STEREO-A), the Solar Dynamics Observatory (SDO), and the Solar and Heliospheric Observatory (SOHO). Here we present an analysis of these eruptions. We investigate their morphology, direction of propagation, and 3D properties. We demonstrate the success of applying two 3D reconstruction methods to three CMEs and their corresponding prominences observed from three perspectives and different distances from the Sun. This allows us to analyze the evolution of the events, from the erupting prominences low in the corona to the corresponding CMEs high in the corona. We also study the changes in the global magnetic field before and after the eruptions and the magnetic field configuration at the site of the eruptions using magnetic field extrapolation methods. This work highlights the importance of multi-perspective observations in studying the morphology of the erupting prominences, their source regions, and associated CMEs. The upcoming Solar Orbiter observations from higher latitudes will help to constrain this kind of study better.

Coronal mass ejections↗

NASA NTRS1997

Locating the Discontinuities of a Bounded Function by the Partial Sums of its Fourier Series I: Periodical Case

A key step for some methods dealing with the reconstruction of a function with jump discontinuities is the accurate approximation of the jumps and their locations. Various methods have been suggested in the literature to obtain this valuable information. In the present paper, we develop an algorithm based on identities which determine the jumps of a 2(pi)-periodic bounded not-too-highly oscillating function by the partial sums of its differentiated Fourier series. The algorithm enables one to approximate the locations of discontinuities and the magnitudes of jumps of a bounded function. We study the accuracy of approximation and establish asymptotic expansions for the approximations of a 27(pi)-periodic piecewise smooth function with one discontinuity. By an appropriate linear combination, obtained via derivatives of different order, we significantly improve the accuracy. Next, we use Richardson's extrapolation method to enhance the accuracy even more. For a function with multiple discontinuities we establish simple formulae which "eliminate" all discontinuities of the function but one. Then we treat the function as if it had one singularity following the method described above.

Kvernadze, George↗

NASA NTRS1973

Evaluation of digitally corrected ERTS imagery

Utilizing all digital processing techniques, precision rectified ERTS multispectral imagery have been produced. Precision geometric correction is accomplished by: (1) utilizing a low order piecewise approximation to the image distortions; (2) incorporating spacecraft attitude refinement derived from ground control points utilized in a Kalman filter; (3) utilizing interpolation techniques which preserve value and slope continuity in the image data. Imagery produced is represented in a UTM projection, and has been evaluated for precision by statistical and analytical methods. Extrapolations to modest size computers indicate good throughput with no sacrifice in precision.

Rifman, S. S.↗

NASA NTRS1975

Glauber exchange amplitudes

The extrapolation method of Ochkur, valid for intermediate energies (about 50 eV), is applied to the exchange form of the Glauber amplitudes. In the case of elastic scattering of electrons from hydrogen atoms at 54.4 Ev the 'post' and 'prior' forms of the exchange amplitude are equivalent, whereas for the case of inelastic scattering there is a minute discrepancy between the two forms of the amplitude. The results are compared with the close-coupling calculation. The investigation is expected to be useful for optically forbidden exchange-allowed transitions due to electron impact at intermediate energies.

Madan, R. N.↗

NASA NTRS1979

Polarizabilities of highly ionized atoms

An extrapolation method based on a screening approximation, applied to available initial values of polarizability for low stages of ionization, is used to obtain dipole and quadrupole polarizabilities for more highly ionized members of many isoelectronic sequences. It is suggested that the derived screening constants x sub L and limiting ratios F sub L may have significant physical meaning, especially the latter which may have an interpretation in terms of hydrogenic polarizabilities.

Kastner, S. O.↗

NASA NTRS1983

Abundance of cosmic-ray elements from sulfur to nickel as a function of atmospheric depth

The measured elemental composition of cosmic rays with charge Z from 16-28 as a function of atmospheric depth was compared with a propagation calculation including energy loss. The resulting composition at the top of the atmosphere has better precision than previously possible on balloon borne experiments, and agrees well with the only satellite data available in this charge range. The extrapolation method also provides checks on assumed cross-sections for interactions of cosmic rays in air.

Crane, J. H.↗

NASA NTRS1984

Simulation and assimilation of satellite altimeter data at the oceanic mesoscale

An improved "objective analysis' technique is used along with an altimeter signal statistical model, an altimeter noise statistical model, an orbital model, and synoptic surface current maps in the POLYMODE-SDE area, to evaluate the performance of various observational strategies in catching the mesoscale variability at mid-latitudes. In particular, simulated repetitive nominal orbits of ERS-1, TOPEX, and SPOT/POSEIDON are examined. Results show the critical importance of existence of a subcycle, scanning in either direction. Moreover, long repeat cycles ( 20 days) and short cross-track distances ( 300 km) seem preferable, since they match mesoscale statistics. Another goal of the study is to prepare and discuss sea-surface height (SSH) assimilation in quasigeostrophic models. Restored SSH maps are shown to meet that purpose, if an efficient extrapolation method or deep in-situ data (floats) are used on the vertical to start and update the model.

Demay, P.↗

NASA NTRS1990

Numerical study of shock-wave/boundary layer interactions in premixed hydrogen-air hypersonic flows

A computational study of shock wave/boundary layer interactions involving premixed combustible gases, and the resulting combustion processes is presented. The analysis is carried out using a new fully implicit, total variation diminishing (TVD) code developed for solving the fully coupled Reynolds-averaged Navier-Stokes equations and species continuity equations in an efficient manner. To accelerate the convergence of the basic iterative procedure, this code is combined with vector extrapolation methods. The chemical nonequilibrium processes are simulated by means of a finite-rate chemistry model for hydrogen-air combustion. Several validation test cases are presented and the results compared with experimental data or with other computational results. The code is then applied to study shock wave/boundary layer interactions in a ram accelerator configuration. Results indicate a new combustion mechanism in which a shock wave induces combustion in the boundary layer, which then propagates outwards and downstream. At higher Mach numbers, spontaneous ignition in part of the boundary layer is observed, which eventually extends along the entire boundary layer at still higher values of the Mach number.

Yungster, Shaye↗

NASA NTRS1991

Numerical study of shock-wave/boundary layer interactions in premixed hydrogen-air hypersonic flows

Yungster, Shaye↗

NASA NTRS1991

Long term integrity for space station power systems

A study was made of the High Temperature Design Codes ASME N47, British R5, and the French RCC-MR Rules. It is concluded that all these codes provide a good basis of design for space application. The new British R5 is the most complete since it deals with the problem of defects. The ASME N47 was subjected longer to practical application and scrutiny. A draft code is introduced, and a proposed draft for high temperature design in which attempts were made to identify gaps and improvements is suggested. The design is limited by creep characteristics. In these circumstances, life is strongly affected by the selected value of the factor of safety. The factor of safety of primary loads adopted in the codes is 1.5. Maybe a lower value of 1.25 is permissible for use in space. Long term creep rupture data for HAYNES 188 is deficient and it is suggested that extrapolation methods be investigated.

Leckie, F. A.↗

NASA NTRS1992

Rational approximations from power series of vector-valued meromorphic functions

Let F(z) be a vector-valued function, F: C yields C(sup N), which is analytic at z = 0 and meromorphic in a neighborhood of z = 0, and let its Maclaurin series be given. In this work we developed vector-valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyzed some of the algebraic and analytic properties of the rational approximations thus obtained, and showed that they were akin to Pade approximations. In particular, we proved a Koenig type theorem concerning their poles and a de Montessus type theorem concerning their uniform convergence. We showed how optical approximations to multiple poles and to Laurent expansions about these poles can be constructed. Extensions of the procedures above and the accompanying theoretical results to functions defined in arbitrary linear spaces was also considered. One of the most interesting and immediate applications of the results of this work is to the matrix eigenvalue problem. In a forthcoming paper we exploited the developments of the present work to devise bona fide generalizations of the classical power method that are especially suitable for very large and sparse matrices. These generalizations can be used to approximate simultaneously several of the largest distinct eigenvalues and corresponding eigenvectors and invariant subspaces of arbitrary matrices which may or may not be diagonalizable, and are very closely related with known Krylov subspace methods.

Sidi, Avram↗

NASA NTRS1999

Sputtering Threshold Energies of Heavy Ions

Sputter erosion in ion thrusters has been measured in lifetests at discharge voltages as low as 25 V. Thruster operation at this discharge voltage results in component erosion rates sufficiently low to satisfy most mission requirements. It has been recognized that most of the internal sputtering in ion thrusters is done by doubly charged ions. Knowledge of the sputtering threshold voltage of a xenon molybdenum system would be beneficial in understanding the sputtering process as well as making more accurate calculations of the sputtering rates of ion thruster components. Sputtering threshold energies calculated from various formulations found in the literature results in values ranging from 28 to 200 eV. It is evident that some of these formulations cannot be relied upon to provide sputtering thresholds with any degree of accuracy. This paper re-examines the threshold energies measurements made in the early sixties by Askerov and Sena, and Stuart and Wehner. The threshold voltages as derived by Askerov and au have been reevaluated by using a different extrapolation method of sputter yields at low ion energies. The resulting threshold energies are in general similar to those measured by Stuart and Wehner. An empirical relationship is derived,for mercury and xenon ions for the ratio of the sputtering threshold energy to the sublimation energy as a function of the ratio of target to ion atomic mass.

Mantenieks, Maris A.↗

NASA NTRS1999

X-33 Experimental Aeroheating at Mach 6 Using Phosphor Thermography

The goal of the NASA Reusable Launch Vehicle (RLV) technology program is to mature and demonstrate essential, cost effective technologies for next generation launch systems. The X-33 flight vehicle presently being developed by Lockheed Martin is an experimental Single Stage to Orbit (SSTO) demonstrator that seeks to validate critical technologies and insure applicability to a full scale RLV. As with the design of any hypersonic vehicle, the aeroheating environment is an important issue and one of the key technologies being demonstrated on X-33 is an advanced metallic Thermal Protection System (TPS). As part of the development of this TPS system, the X-33 aeroheating environment is being defined through conceptual analysis, ground based testing, and computational fluid dynamics. This report provides an overview of the hypersonic aeroheating wind tunnel program conducted at the NASA Langley Research Center in support of the ground based testing activities. Global surface heat transfer images, surface streamline patterns, and shock shapes were measured on 0.013 scale (10-in.) ceramic models of the proposed X-33 configuration in Mach 6 air. The test parametrics include angles of attack from -5 to 40 degs, unit Reynolds numbers from 1x106 to 8x106/ft, and body flap deflections of 0, 10, and 20 deg. Experimental and computational results indicate the presence of shock/shock interactions that produced localized heating on the deflected flaps and boundary layer transition on the canted fins. Comparisons of the experimental data to laminar and turbulent predictions were performed. Laminar windward heating data from the wind tunnel was extrapolated to flight surface temperatures and generally compared to within 50 deg F of flight prediction along the centerline. When coupled with the phosphor technique, this rapid extrapolation method would serve as an invaluable TPS design tool.

Horvath, Thomas J.↗

NASA NTRS1996

The Hot Bands of Methane Between 5 and 10(micro)m

Experimental line intensities of 1727 transitions arising from nine hot bands in the pentad-dyad system of methane are fitted to first and second order using the effective dipole moment expansion in the polyad scheme. The observed bands are V3-V2, V3-V4, V1-V2, V1-V4, 2V4-V4, V2+V4-V2, V2+V4-V4, 2V2-V4, and the intensities are obtained from long-path spectra recorded with the Fourier transform spectrometer located at Kitt Peak National Observatory. For the second order model, some of the 27 intensity parameters are not linearly independant, and so two methods (extrapolation and effective parameters) are propopsed to model the intensities of the hot bands.

methane hot bands dipole moment expansion Kitt Pea↗

NASA NTRS2010

Pair Identity and Smooth Variation Rules Applicable for the Spectroscopic Parameters of H2O Transitions Involving High-J States

Two basic rules (i.e. the pair identity and the smooth variation) applicable for H2O transitions involving high-J states have been discovered. The origins of these rules are the properties of the energy levels and wavefunctions of H2O states with the quantum number J above certain boundaries. As a result, for lines involving high-J states in individually defined groups, all their spectroscopic parameters (i.e. the transition wavenumber, intensity, pressure-broadened half-width, pressure-induced shift, and temperature exponent) must follow these rules. One can use these rules to screen spectroscopic data provided by databases and to identify possible errors. In addition, by using extrapolation methods within the individual groups, one is able to predict the spectroscopic parameters for lines in this group involving very high-J states. The latter are required in developing high-temperature molecular spectroscopic databases such as HITEMP.

Ma, Q.↗

NASA NTRS2014

Mode I Cohesive Law Characterization of Through-Crack Propagation in a Multidirectional Laminate

A method is proposed and assessed for the experimental characterization of through-the-thickness crack propagation in multidirectional composite laminates with a cohesive law. The fracture toughness and crack opening displacement are measured and used to determine a cohesive law. Two methods of computing fracture toughness are assessed and compared. While previously proposed cohesive characterizations based on the R-curve exhibit size effects, the proposed approach results in a cohesive law that is a material property. The compact tension specimen configuration is used to propagate damage while load and full-field displacements are recorded. These measurements are used to compute the fracture toughness and crack opening displacement from which the cohesive law is characterized. The experimental results show that a steady-state fracture toughness is not reached. However, the proposed method extrapolates to steady-state and is demonstrated capable of predicting the structural behavior of geometrically-scaled specimens.

Bergan, Andrew C.↗

NASA NTRS2015

ER-2 High Altitude Solar Cell Calibration Flights

Evaluation of space photovoltaics using ground-based simulators requires primary standard cells which have been characterized in a space or near-space environment. Due to the high cost inherent in testing cells in space, most primary standards are tested on high altitude fixed wing aircraft or balloons. The ER-2 test platform is the latest system developed by the Glenn Research Center (GRC) for near-space photovoltaic characterization. This system offers several improvements over GRC's current Learjet platform including higher altitude, larger testing area, onboard spectrometers, and longer flight season. The ER-2 system was developed by GRC in cooperation with NASA's Armstrong Flight Research Center (AFRC) as well as partners at the Naval Research Laboratory and Air Force Research Laboratory. The system was designed and built between June and September of 2014, with the integration and first flights taking place at AFRC's Palmdale facility in October of 2014. Three flights were made testing cells from GRC as well as commercial industry partners. Cell performance data was successfully collected on all three flights as well as solar spectra. The data was processed using a Langley extrapolation method, and performance results showed a less than half a percent variation between flights, and less than a percent variation from GRC's current Learjet test platform.

ER-2↗