Search NASA⌕ Search

SEARCH · Search NASA

Results for “spherical”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A Theoretical Study of Propagation and Extinction of Nonsteady Spherical Flame Fronts

Freely propagating expanding spherical flame fronts are studied analytically using the method of activation energy asymptotics. Effects of Lewis number (Le), curvature, heat loss, and thermal expansion on propagation rates and extinction conditions are examined. The behavior of spherical flame fronts is found to be determined primarily by the values of Le and a heat-loss parameter. Results are compared to recent experimental observations of spherical flame fronts in mixtures near the flammability limits; for Le less than 1, it is found that many of the features of these experimental results are described by the analysis presented here. For Le greater than 1, however, unrealistic dynamic behavior is predicted due to the nature of diffusive-thermal instabilities under these conditions.

Ronney, P. D.↗
NASA NTRS1991

Use of non-spherical gravity harmonics for relative motion GN/C (category 2)

Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 nm; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm and; (3) close proximity motion - the near-field motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. Limit boundaries to these regions can be precisely defined by further analysis and will be functions of the tracking measurement accuracies and the computer resources available for the solution of the algorithms. This paper analyzes the relative motion in Regions 2 and 3 above and present the derivation and discussion of the general case of non-spherical gravitational perturbed relative motion. Mathematical deviations from the numerically integrated spherical gravity case and solutions from the Clohessy-Wiltshire equations are presented in the analysis. Based upon this preliminary analysis, it is recommended that further efforts be used to assess the relative position and velocity differences in Region 2 due to non-spherical gravity harmonics and that viable GN&C algorithms be developed to include these gravity perturbations (especially the effects of the first gravity harmonic, J2).

Henderson, David M.↗
NASA NTRS1992

Analysis of rotationally symmetric arrays of apertures on conducting spherical surfaces

Rotationally symmetric arrays of circular waveguide fed apertures on conducting spherical surfaces have been analyzed. Representation of the outside electromagnetic fields in terms of spherical transmission line modes permit the array analysis to be viewed as a spherical waveguide junction discontinuity problem. The apertures, in general, carry dual polarized circular waveguide TE11 modes. Two independent formulations - the unit cell method and the eigenexcitation method that take rotational symmetry into account - are developed and are checked against each other numerically for computational accuracy. These two formulations are analytically linked as discrete Fourier series pairs. It is seen that mutual coupling along the array decays more rapidly when the polarization of excitation is perpendicular to the array plane than when it is parallel to it. This analysis has been applied in the performance analysis of the Dome Lens phased array radar antenna.

Bondyopadhyay, Probir K.↗
NASA NTRS1993

Computer program for analysis of high speed, single row, angular contact, spherical roller bearing, SASHBEAN. Volume 2: Mathematical formulation and analysis

Spherical roller bearings have typically been used in applications with speeds limited to about 5000 rpm and loads limited for operation at less than about 0.25 million DN. However, spherical roller bearings are now being designed for high load and high speed applications including aerospace applications. A computer program, SASHBEAN, was developed to provide an analytical tool to design, analyze, and predict the performance of high speed, single row, angular contact (including zero contact angle), spherical roller bearings. The material presented is the mathematical formulation and analytical methods used to develop computer program SASHBEAN. For a given set of operating conditions, the program calculates the bearings ring deflections (axial and radial), roller deflections, contact areas stresses, depth and magnitude of maximum shear stresses, axial thrust, rolling element and cage rotational speeds, lubrication parameters, fatigue lives, and rates of heat generation. Centrifugal forces and gyroscopic moments are fully considered. The program is also capable of performing steady-state and time-transient thermal analyses of the bearing system.

Aggarwal, Arun K.↗
NASA NTRS1998

Inner Core Rotation from Geomagnetic Westward Drift and a Stationary Spherical Vortex in Earth's Core

The idea that geomagnetic westward drift indicates convective leveling of the planetary momentum gradient within Earth's core is pursued in search of a differentially rotating mean state, upon which various oscillations and secular effects might be superimposed. The desired state conforms to roughly spherical boundary conditions, minimizes dissipative interference with convective cooling in the bulk of the core, yet may aid core cooling by depositing heat in the uppermost core and lower mantle. The variational calculus of stationary dissipation applied to a spherical vortex within the core yields an interesting differential rotation profile, akin to spherical Couette flow bounded by thin Hartmann layers. Four boundary conditions are required. To concentrate shear induced dissipation near the core-mantle boundary, these are taken to be: (i) no-slip at the core-mantle interface; (ii) geomagnetically estimated bulk westward flow at the base of the core-mantle boundary layer; (iii) no-slip at the inner-outer core interface; and, to describe magnetic locking of the inner core to the deep outer core; (iv) hydrodynamically stress-free at the inner-outer core boundary. By boldly assuming the axial core angular momentum anomaly to be zero, the super-rotation of the inner core relative to the mantle is calculated to be at most 1.5 deg./yr.

Voorhies, Coerte V.↗
NASA NTRS1999

Ocean Domains and Maximum Degree of Spherical Harmonic and Orthonormal Expansions

Ocean domains used for the orthonormal (ON) systems are studied to determine the maximum degree of spherical harmonic and orthonormal expansions that can be constructed. Although it was shown that one domain was restricted to degree 24, others were shown could be constructed to determine expansions to at least degree 36. Since 1991 the maximum degree expansion used for several Ohio State studies has been 24. In this report it is shown that the maximum degree for the ocean domain used by Wang and Rapp [1994] was 32 and 29 for the domain used by Rapp, Zhang, Yi [1996]. A modification of the former domain was developed (D1e) that enabled a solution to degree 36 to be determined. A modification of the Rapp, Zhang, Yi domain (D7d) enabled a degree 30 solution to be made. Combination coefficients were developed for domain D1e, to degree 36, and to degree 30 for domain D7d. The degree 30 spherical harmonic expansion provided by Pavlis [1998] of the POCM_4B dynamic ocean topography (DOT), and the degree 30 part of the degree 360 expansion [Rapp. 1998] of the POCM_4B model was converted to an ON expansion valid for the D7d domain. The degree 36 part of the degree 360 expansion was converted to the ON expansion for the D1e domain. The square root of the degree variances of the various solutions were compared. The root mean square value of DOT from the Pai,lis expansion, after conversion to the ON system, was + or - 66.52 cm (D7d domain). The value from the degree 30 part of the 360 expansion was + or - 66.65 cm. The value based on the actual POCM-4B data, in the D7d domain, was + or - 66.74 cm showing excellent agreement with the ON results. If the spherical harmonic coefficients had been used the implied root mean square value was + or - 60.76 cm [Pavlis] and + or -59.70 cm [Rapp].

Rapp, R.↗
NASA NTRS1999

Inner Core Rotation from Geomagnetic Westward Drift and a Stationary Spherical Vortex in Earth's Core

The idea that geomagnetic westward drift indicates convective leveling of the planetary momentum gradient within Earth's core is pursued in search of a differentially rotating mean state, upon which various oscillations and secular effects might be superimposed. The desired state conforms to roughly spherical boundary conditions, minimizes dissipative interference with convective cooling in the bulk of the core, yet may aide core cooling by depositing heat in the uppermost core and lower mantle. The variational calculus of stationary dissipation applied to a spherical vortex within the core yields an interesting differential rotation profile akin to spherical Couette flow bounded by thin Hartmann layers. Four boundary conditions are required. To concentrate shear induced dissipation near the core-mantle boundary, these are taken to be: (i) no-slip at the core-mantle interface; (ii) geomagnetically estimated bulk westward flow at the base of the core-mantle boundary layer; (iii) no-slip at the inner-outer core interface; and, to describe magnetic locking of the inner core to the deep outer core, (iv) hydrodynamically stress-free at the inner-outer core boundary. By boldly assuming the axial core angular momentum anomaly to be zero, the super-rotation of the inner core is calculated to be at most 1.5 degrees per year.

Voorhies, C. V.↗
NASA NTRS2000

TOA Lightning Location Retrieval on Spherical and Oblate Spheroidal Earth Geometries

A simple linear algebraic solution is introduced for retrieving the location and time-of-occurrence of lightning ground strikes on a spherical Earth from a network of four or more time-of-arrival (TOA) sensors. Since the solution accounts for Earth curvature, it represents an extension to earlier planar model results described by Koshak et al. A test of the retrieval method is provided using computer-simulated data sets. The method is easy to comprehend and completely avoids reference to the mathematics of spherical hyperbolas such as discussed by Lewis. A quasi-analytic extension to the spherical Earth solution is provided for an oblate spheroidal Earth geometry, and the importance/relevance of oblate effects are discussed. Future application of these methods in support of the North American National Lightning Detection Network (NALDN) described by Cummins et al. is desirable, but additional theoretical investigations are required to incorporate magnetic bearing information into the present solution process.

Koshak, W. J.↗
NASA NTRS1995

Heliospheric Termination Shock Motion Due to Fluctuations in the Solar Wind Upstream Conditions: Spherically Symmetric Model

Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gas dynamic model to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary, and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit Total Variation Diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations, and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the heliopause boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a "ringing" of the outer heliosphere.

Ratkiewicz, R.↗
NASA NTRS1993

Antenna system providing a spherical radiation pattern

An antenna system provides a substantially spherical radiation pattern about a structure located above ground level, by locating the individual radiation pattern of each of a plurality of individual antennae, each positioned to have a radiation pattern covering only a portion of the desired sphere, and then applying all antenna signals, during either transmission or reception time intervals, through space-diversity and/or time-diversity apparatus, to cause the patterns of all of the antennae to combine into the desired substantially-spherical pattern. The antennae may have substantially hemispherical patterns, with each antenna of a pair thereof being directed in a direction generally opposite to the other antenna of that pair. Time domain multiple access (TDMA) operation of a master system station, with transmission in different time slots for different portions of the coverage sphere, and selection of the strongest received signal from among all of the plurality N of signals simultaneously received by the plurality N of antennae, can provide the desired spherical radiation pattern in both the transmission and reception modes of operation.

Sickles, II, Louis↗
NASA NTRS1997

Spherical mirror grazing incidence x-ray optics

An optical system for x-rays combines at least two spherical or near spherical mirrors for each dimension in grazing incidence orientation to provide the functions of a lens in the x-ray region. To focus x-ray radiation in both the X and the Y dimensions, one of the mirrors focusses the X dimension, a second mirror focusses the Y direction, a third mirror corrects the X dimension by removing comatic aberration and a fourth mirror corrects the Y dimension. Spherical aberration may also be removed for an even better focus. The order of the mirrors is unimportant.

Cash, Jr., Webster C.↗
NASA NTRS2008

A Three-Dimensional Analytic Model for the Scattering of a Spherical Bush

Advanced climate models require a more realistic description of canopy radiation with reasonable computational efficiency. This paper develops the mathematics of scattering from a spherical object conceptualized to be a spherical bush to provide a building block that helps to address this need of climate models. It is composed of a homogeneous distribution of individual smaller objects that scatter isotropically. In the limit of small optical depth, incident radiation will scatter isotropically as the sum of that scattered by all the individual scatterers, but at large optical depth the radiation leaving the spherical bush in a given direction is reduced by mutual shadowing of the smaller objects. In the single scattering limit, the scattering phase function and so the albedo are obtained by simple but accurate analytic expressions derived from analytic integration and numerical evaluation. Except in the limit of thin canopies, the scattering and hence albedos are qualitatively and quantitatively different than those derived from 1-D modeling.

Dickinson, Robert E.↗
NASA NTRS2007

On the Propagation and Interaction of Spherical Blast Waves

The characteristics and the scaling laws of isolated spherical blast waves have been briefly reviewed. Both self-similar solutions and numerical solutions of isolated blast waves are discussed. Blast profiles in the near-field (strong shock region) and the far-field (weak shock region) are examined. Particular attention is directed at the blast overpressure and shock propagating speed. Consideration is also given to the interaction of spherical blast waves. Test data for the propagation and interaction of spherical blast waves emanating from explosives placed in the vicinity of a solid propellant stack are presented. These data are discussed with regard to the scaling laws concerning the decay of blast overpressure.

Kandula, Max↗
NASA NTRS2014

Non-Spherical Microcapsules for Increased Core Content Volume Delivery

The goal of this project was to advance microencapsulation from the standard spherical microcapsule to a non-spherical, high-aspect ratio (HAR), elongated microcapsule. This was to be accomplished by developing reproducible methods of synthesizing or fabricating robust, non-spherical, HAR microcapsules. An additional goal of this project was to develop the techniques to the point where scale-up of these methods could be examined. Additionally, this project investigated ways to apply the microencapsulation techniques developed as part of this project to self-healing formulations.

Technology Portfolio System↗
NASA NTRS2014

Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.

corona↗
NASA NTRS2016

Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Polarization↗
NASA NTRS2018

Spherical Occulter Coronagraph Cubesat

The present invention relates to a space-based instrument which provides continuous coronal electron temperature and velocity images, for a predetermined period of time, thereby improving the understanding of coronal evolution and how the solar wind and Coronal Mass Ejection transients evolve from the low solar atmosphere through the heliosphere for an entire solar rotation. Specifically, the present invention relates to using a 6U spherical occulter coronagraph CubeSat, and a relative navigational system (RNS) that controls the position of the spacecraft relative to the occulting sphere. The present invention innovatively deploys a free-flying spherical occulter, and after deployment, the actively controlled CubeSat will provide an inertial formation flying with the spherical occulter and Sun.

Davila, Joseph M.↗
NASA NTRS2023

Quantification of Global Cloud Properties with Use of Spherical Harmonic Functions

Spherical harmonic (SH) expansion is a useful tool to study any variable that has valid values at all latitudes and longitudes. The variable can be quantified as a sum of different spherical harmonic components, which are the spherical harmonic functions multiplied by their expansion coefficients. We find that the SH components of cloud radiative effect (CRE) have correlations with El Niño-Southern Oscillation (ENSO) and the Hadley Circulation (HC). In particular, the expansion degree 2 (l = 2) SH power spectrum component anomaly of CRE is strongly correlated with ENSO. The two dipole patterns appearing in the l = 2 SH component anomaly map can be reasonably explained by a known mechanism of ENSO’s impact on cloud properties. The l = 3 and l = 5 SH power spectrum components are correlated with HC intensity, whereas the l = 6 and l = 8 components are correlated with HC latitudinal widths. In ENSO warm and cold phases, the HC-correlated SH components have opposite anomalies, which suggests the impact of ENSO on HC. This study illustrates that the SH expansion technique provides a different perspective to study the impacts of large-scale atmospheric circulation on global cloud properties and radiative effects.

clouds↗