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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

A Multipole Expansion Method for Analyzing Lightning Field Changes

Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q model) or a point dipole (the P model). The Q model has four unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P model has six unknown parameters and describes many intracloud (IC) discharges. In this paper we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a dme-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer-simulated sources and on natural lightning at the NASA Kennedy Space Center and U.S. Air Force Eastern Range.

Koshak, William J.↗
NASA NTRS1998

A Multipole Expansion Method for Analyzing Lightning Field Changes

Changes in the surface electric field are frequently used to infer the locations and magnitudes of lightning-caused changes in thundercloud charge distributions. The traditional procedure is to assume that the charges that are effectively deposited by the flash can be modeled either as a single point charge (the Q-model) or a point dipole (the P-model). The Q-model has 4 unknown parameters and provides a good description of many cloud-to-ground (CG) flashes. The P-model has 6 unknown parameters and describes many intracloud (IC) discharges. In this paper, we introduce a new analysis method that assumes that the change in the cloud charge can be described by a truncated multipole expansion, i.e., there are both monopole and dipole terms in the unknown source distribution, and both terms are applied simultaneously. This method can be used to analyze CG flashes that are accompanied by large changes in the cloud dipole moment and complex IC discharges. If there is enough information content in the measurements, the model can also be generalized to include quadrupole and higher order terms. The parameters of the charge moments are determined using a 3-dimensional grid search in combination with a linear inversion, and because of this, local minima in the error function and the associated solution ambiguities are avoided. The multipole method has been tested on computer simulated sources and on natural lightning at the NASA Kennedy Space Center and USAF Eastern Range.

Koshak, William J.↗
NASA NTRS1995

Sensitivity analysis in multipole-accelerated panel methods for potential flow

In the design of an airframe, the effect of changing the geometry on resulting computations is necessary for design optimization. The geometry is defined in terms of a series of design variables, including design variables to define the wing planform, tail, canard, pylon, and nacelle. Design optimization in this research is based on how these design variable affect the potential flow. The potential flow is computed as a function of the geometry and location of a series of panels describing the airframe, which are in turn a function of the design variables. Multipole accelerated panel methods improve the computational complexity of the problem and thus are an attractive approach. To utilize the methods in design optimization, it was necessary to define the appropriate sensitivity derivatives. The overhead incurred from finding the sensitivity derivatives in conjunction with the original computation should be small. This research developed the background for multipole-accelerated panel methods and the framework for finding sensitivity derivatives in the methods. Potential flow panel codes are commonly used for powered-lift aerodynamic predictions for three dimensional geometries. Given an airframe which has been discretized into a series of panels to define the airframe geometry, potential is computed as a function of the influence of all panels on all other panels. This is a computationally intensive problem for which efficient solutions are desired to improve the computational time and to allow greater resolution by use of more panels. One such solution is the use of hierarchical multipole methods which entail approximations of the effects of far-field terms. Hierarchical multipole methods have become prevalent in molecular dynamics and gravitational physics, and have been introduced into the fields of capacitance calculations, computational fluid dynamics, and electromagnetics. The methods utilize multipole expansions to describe the effect of bodies (i.e. particles, astrophysical bodies, panels, etc.) within a sphere on points distant from the sphere, where the influence diminishes as a function of distance. The expansions are exact with infinite series, however, for practical computations, the series are truncated and accuracy is selected based on the number of terms retained in the expansions. A hierarchical tree structure groups bodies together based on proximity to allow definition of multipole expansions for each group. The multipole expansions are then used to compute the effect of the bodies in a group on distant bodies.

Leathrum, James F., Jr.↗
NASA NTRS1994

Accelerated panel methods using the fast multipole method

Panel methods are commonly used in computational fluid dynamics for the solution of potential flow problems. The methods are a numerical technique based on the surface distribution of singularity elements. The solution is the process of finding the strength of the singularity elements distributed over the body's surface. This process involves the solution of the matrix problem Pq = p' for a set of unknowns q. The Fast Multipole Method is used to directly compute q without using matrix solvers. The algorithm works in O(N) time for N points, a great improvement over standard matrix solvers. In panel methods, the surface of a body is divided into a series of quadrilateral panels. The methods involve the computation of the influence of all other panels on each individual panel. The influence is based on the surface distribution, though this can be approximated by the area for distant panels. An alternative approximation, though with arbitrary accuracy, is to develop a multipole expansion about the center of the panel to describe the effect of a given panel on distant points in space. The expansion is based on the moments of the panel, thus allow the use of various surface distributions without changing the basic algorithm, just the computation of the various moments. The expansions are then manipulated in a tree walk to develop Taylor series expansions about a point in space which describe the effect of all distant panels on any point within a volume of convergence. The effect of near panels then needs to be computed directly, but the effect of all distant panels can be computed by simply evaluating the resulting expansion. The Fast Multipole Method has been applied to panel methods for the solution of source and doublet distributions. A major feature of the algorithm is that the algorithm does not change to derive the potential and velocity for sources and doublets. The same expansions can be used for both sources and doublets. Since the velocity is related to the potential, and the doublet potential is related to the z-component of the source velocity, all values can be derived from the same expansion by taking a series of partial derivatives. This requires more expansion terms to be kept since terms are lost in the process of taking partial derivatives. Thus to maintain accuracy for the doublet computation, more terms are required than if just evaluating for sources. The resulting Fast Multipole code should then parallelize better than classical panel methods due to the locality of data dependencies found in the Fast Multipole Method. Theoretically the parallelized code should execute in O(log N) time with O(N) processors, though this is not practical. Ongoing work includes implementing the parallel accelerated panel method, including methods to improve the load balancing of the problem by taking advantage of the known geometry of panels, and to encorporate sensitivity analysis into the algorithm.

Leathrum, James F., Jr.↗
NASA NTRS1980

Errors incurred in a plane-wave-type expansion of a Gaussian beam

The multipole expansion obtained by Morita et al. (1968) of the Gaussian laser beam used to levitate an aerosol particle in order that its complete phase matrix may be measured is compared with that of Tsai and Pogorzelski (1975) in order to demonstrate the effect of the incorrect expansion used by Morita. Errors incurred by the use of an equation in which one side satisfies the scalar wave equation while the other side does not and can be reduced to a plane wave amplitude are calculated as functions of the inverse of the wave number times the beam waist, the wave number times the radial spherical coordinate and the angular spherical coordinate. Errors on the order of a few percent, considered undetectable are obtained in the squared-field amplitudes due to the expansion, however, they are found to become significant (several tens of percent) when the angle is zero. It is concluded that the expansion of Morita should only be used in the regions where the spherical angle is less than 0.01 and its product with the wave number and the radial spherical coordinate is less than unity.

Kattawar, G. W.↗
NASA NTRS1992

Magnetic field models from energetic particle data at Neptune

The locations of features in the Voyager 2 energetic particle data from Neptune are combined with uncertainties in the multipole expansion of the planetary magnetic field to derive new magnetic field models that are consistent both with various interpretations of the particle features and with the magnetic field data. While assumptions as to the origin of the features must be made, they do not provide sufficient constraints to obtain significant new information on any of the unknown multipole coefficients. However, the magnetic L shell positions of the particle features, which are interpreted primarily as absorption signatures of Neptune's satellites, can, in general, be brought into agreement with expected values.

Selesnick, R. S.↗
NASA NTRS1974

The polarizability of diatomic helium

The calculation of the electric dipole polarizability tensor of the He 2 dimer is described, and the results are used in the computation of several dielectric and optical properties of helium gas, at both high (322 K) and low (4 K) temperatures. The properties considered are the second dielectric virial coefficient, the second Kerr virial coefficient, and the depolarization ratio of the integrated intensities for the Raman scattering experiments. The thesis consists of five parts: the polarizability and various properties are defined; the calculation of the polarizability in the long-range region in terms of a quantum mechanical multipole expansion is described; the calculation of the He2 polarizability in the overlap region via coupled Hartree-Fock perturbation theory is described; the calculation of the quantum pair distribution function for both the He-3 and He-4 isotopes at 4 K is discussed; and the calculated values of the properties of helium gas are given.

Fortune, P. J.↗
NASA NTRS1975

Dispersion forces at arbitrary distances

The formalism of Boehm and Yaris is used to evaluate explicitly the leading term of the London dispersion force between closed-shell atoms. Instead of using the usual multipole expansion, which breaks down at intermediate internuclear distances, an analytic representation of the Born amplitude together with a general angular momentum analysis is used. As a result, expressions are obtained which reduce to the usual dispersion forces at large distances and are finite at all distances.

Jacobi, N.↗
NASA NTRS1976

Application of the adaptive-wall concept to three-dimensional low-speed wind tunnels

Three methods for evaluating the functional relationships required to obtain interference-free flows about a model in a wind tunnel have been developed. The first, the original multipole expansion (MPE) procedure, is based on a series of point singularities which satisfy the governing Prandtl-Glauert equation. The second, the modified MPE, provides an improved representation of finite-span wings and thereby extends the range of validity of the original MPE to larger ratios of span-to-control-surface-width. The third method is more general and is based on source distributions over the control surface. Several numerical examples are presented to help establish the range of validity of these methods. An accuracy-assessment procedure, which combines the original MPE procedure with classical wall-correction theory, has been developed to estimate the degree of interference at the model if the functional relationships are not satisfied exactly. Several numerical examples are presented for representative wings and bodies.

Erickson, J. C., Jr.↗
NASA NTRS1981

On the utility of finite element theory for computational fluid dynamics

An implicit finite element numerical solution algorithm is derived for the compressible Navier-Stokes equations expressed in generalized coordinates. The theoretical basis utilizes a Galerkin-Weighted Residuals formulation, and extremization of approximation error within the context of a multipole expansion. A von Neumann analysis for a simplified form indicates the algorithm fourth- to sixth-order phase accurate, with third-order dissipation for the elementary linear element construction. Performance is improved for the algorithm constructed using quadratic interpolation. Numerical experiments for shocked duct flows are employed to optimize the several algorithm parameters. Additional numerical solutions validate algorithm accuracy and utility for aerodynamics applications.

Baker, A. J.↗
NASA NTRS1986

An atlas of photospheric magnetic field observations and computed coronal magnetic fields: 1976-1985

Daily magnetogram observations of the large-scale photospheric magnetic field have been made at the John M. Wilcox Solar Observatory at Stanford since May of 1976. These measurements provide a homogeneous record of the changing solar field through most of solar cycle 21. Using the photospheric data, the configuration of the coronal and heliospheric fields can be calculated using a Potential Field-Source Surface model. This provides a three-dimensional picture of the heliospheric field evolution during the solar cycle. This paper announces the publication of UAG Report No. 94, an Atlas containing the complete set of synoptic charts of the measured photospheric magnetic field, the computed field at the source surface, and the coefficients of the multipole expansion of the coronal field. The general underlying structures of the solar and heliospheric fields, which determine the environment for solar-terrestrial relations and provide the context within which solar activity related events occur, can be approximated from these data.

Hoeksema, J. T.↗
NASA NTRS2000

Fast Particle Methods for Multiscale Phenomena Simulations

We are developing particle methods oriented at improving computational modeling capabilities of multiscale physical phenomena in : (i) high Reynolds number unsteady vortical flows, (ii) particle laden and interfacial flows, (iii)molecular dynamics studies of nanoscale droplets and studies of the structure, functions, and evolution of the earliest living cell. The unifying computational approach involves particle methods implemented in parallel computer architectures. The inherent adaptivity, robustness and efficiency of particle methods makes them a multidisciplinary computational tool capable of bridging the gap of micro-scale and continuum flow simulations. Using efficient tree data structures, multipole expansion algorithms, and improved particle-grid interpolation, particle methods allow for simulations using millions of computational elements, making possible the resolution of a wide range of length and time scales of these important physical phenomena.The current challenges in these simulations are in : [i] the proper formulation of particle methods in the molecular and continuous level for the discretization of the governing equations [ii] the resolution of the wide range of time and length scales governing the phenomena under investigation. [iii] the minimization of numerical artifacts that may interfere with the physics of the systems under consideration. [iv] the parallelization of processes such as tree traversal and grid-particle interpolations We are conducting simulations using vortex methods, molecular dynamics and smooth particle hydrodynamics, exploiting their unifying concepts such as : the solution of the N-body problem in parallel computers, highly accurate particle-particle and grid-particle interpolations, parallel FFT's and the formulation of processes such as diffusion in the context of particle methods. This approach enables us to transcend among seemingly unrelated areas of research.

Koumoutsakos, P.↗
NASA NTRS1986

Delta excitations and shell-model information in heavy-ion, charge-exchange reactions

We calculate total cross sections for coherent pion production using localized plane-wave approximations for the shell-structure of valence nucleons that are excited to delta particles in the intermediate state in the (12C, 12B) and (12C, 12N) charge-exchange, heavy-ion reactions. We find comparable agreement to projectile downshift data for 12C(12C, 12B)12N. Then we improve the formalism by replacing the localized plane wave bound states with harmonic oscillator states which are imbedded in a multipole expansion approach and calculate pion differential cross sections to test for the sensitivity of the spectra to the single-particle mass parameter.

NASA Program Space Medicine↗
NASA NTRS2005

Dusty Plasmas in Planetary Magnetospheres Award

This is my final report for the grant Dusty Plasmas in Planetary Magnetospheres. The funding from this grant supported our research on dusty plasmas to study: a) dust plasma interactions in general plasma environments, and b) dusty plasma processes in planetary magnetospheres (Earth, Jupiter and Saturn). We have developed a general purpose transport code in order to follow the spatial and temporal evolution of dust density distributions in magnetized plasma environments. The code allows the central body to be represented by a multipole expansion of its gravitational and magnetic fields. The density and the temperature of the possibly many-component plasma environment can be pre-defined as a function of coordinates and, if necessary, the time as well. The code simultaneously integrates the equations of motion with the equations describing the charging processes. The charging currents are dependent not only on the instantaneous plasma parameters but on the velocity, as well as on the previous charging history of the dust grains.

Horanyi, Mihaly↗
NASA NTRS2012

An Analysis of the Rapidly Rotating Bp star HD 133880

HD 133880 is a rapidly rotating chemically peculiar B-type (Bp) star (nu sin i approx = 103km/s) and is host to one of the strongest magnetic fields of any Ap/Bp star. A member of the Upper Centaurus Lupus association, it is a star with a well-determined age of 16 Myr. 12 new spectra, four of which are polarimetric, obtained from the FEROS, ESPaDOnS and HARPS instruments, provide sufficient material from which to re-evaluate the magnetic field and obtain a first approximation to the atmospheric abundance distributions of He, O, Mg, Si, Ti. Cr, Fe, Ni, Pr and Nd. An abundance analysis was carried out using ZEEMAN, a program which synthesizes spectral line profiles for stars with permeating magnetic fields. The magnetic field structure was characterized by a colinear multipole expansion from the observed variations of the longitudinal and surface fields with rotational phase. Both magnetic hemispheres are clearly visible during the stellar rotation, and thus a three-ring abundance distribution model encompassing both magnetic poles and magnetic equator with equal spans in colatitude was adopted. Using the new magnetic field measurements and optical photometry together with previously published data, we refine the period of HD 133880 to P = 0.877 476 +/- 0.000009 d. Our simple axisymmetric magnetic field model is based on a predominantly quadrupolar component that roughly describes the field variations. Using spectrum synthesis, we derived mean abundances for O, Mg, Si, Ti, Cr, Fe and Pr. All elements; except Mg, are overabundant compared to the Son. Mg appears to be approximately uniform over the stellar surface, while all other elements are more abundant in the negative magnetic hemisphere than in the positive magnetic hemisphere. In contrast to most Ap/Bp stars which show an underabundance in 0, in HD 133880 this element is clearly overabundant compared to the solar abundance ratio. In studying the Ha and Paschen lines in the optical spectra, we could not unambiguously detect information about the magnetosphere of HD 133880. However, radio emission data at both 3 and 6 cm suggest that the magnetospheric plasma is held in rigid rotation with the star by the magnetic field and further supported against collapse by the rapid rotation. Subtle differences in the shapes of the optically thick radio light curves at 3 and 6 cm suggest that the large-scale magnetic field is not fully axisymmetric at large distances from the star.

Bailey, J. D.↗
NASA NTRSDate not supplied

An Extension of the Truncated Ingard-Myers Impedance Boundary Condition for High Mach Number Grazing Flows

The Ingard-Myers impedance boundary condition is widely recognized to be prone to hydrodynamic Kelvin-Helmholtz-type instability, primarily due to its use of a vortex sheet to model the flow at the boundary. Recently, a stabilized approximation of the Ingard-Myers condition, called the Truncated Ingard-Myers Impedance Boundary Condition (TIMIBC), has been introduced. This approximation offers a good representation of the Ingard-Myers condition for grazing flows characterized by low to mid subsonic Mach numbers. This paper explores an extension of the TIMIBC, referred to as TIMIBC-ext, designed for liners in grazing flows with high subsonic Mach numbers. The TIMIBC-ext introduces a tunable parameter and demonstrates that by judiciously selecting the parameter value, the accuracy of the TIMIBC can be improved for either upstream or downstream propagating waves in grazing flows with high subsonic Mach numbers. Consequently, the TIMIBC-ext represents an enhancement to the TIMIBC when the location of the source relative to the liner (upstream or downstream) is known. Time domain implementations of the TIMIBC-ext are also provided, employing a multipole expansion model for the impedance function. A numerical example is provided to assess the performance of the TIMIBC-ext, comparing computational results with measurements from a recent set of measurements in the NASA Langley Grazing Flow Impedance Tube.

time domain acoustic scattering↗
NASA NTRS1974

Some improvements in DNA interaction calculations

Calculations are made on specific DNA-type complexes using refined expressions for electrostatic and polarization energies. Dispersion and repulsive terms are included in the evaluation of the total interaction energy. It is shown that the expansion of the electrostatic potential to include multipole moments up to octopole is necessary to achieve convergence of first-order energies. Polarization energies are not as sensitive to this expansion. The calculations also support the usefulness of the hard sphere model for DNA hydrogen bonds and indicate how stacking interactions are influenced by second-order energies.

Egan, J. T.↗