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At least 343 records · Page 19

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NASA NTRS1982

Solar particle propagation and modulation theory

Developments related to solar flare particle propagation theory are considered, taking into account the transport equation currently employed to describe the propagation of solar flare particles. This equation does not take into consideration convection with the solar wind, drifts, and changes in particle energy. The equation was solved numerically to generate typical solar flare particle time profiles at 1 AU. The results, however, were not satisfactory. It was found that the numerical method used was apparently in error. New advances which provide approximate analytical solutions to the equation are reported. Questions of galactic cosmic ray propagation in interplanetary space are also discussed.

Lee, M. A.↗

NASA NTRS1982

An accurate and efficient method for evaluating the kernel of the integral equation relating pressure to normalwash in unsteady potential flow

This paper describes an accurate economical method for generating approximations to the kernel of the integral equation relating unsteady pressure to normalwash in nonplanar flow. The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the non elementary integrals in the kernel by exponential approximations and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. Coefficients for 8, 12, 24, and 72 term approximations are tabulated in the report. Also, since the method is automated, it can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

Desmarais, R. N.↗

NASA NTRS1989

Nonlinear evolution of the auroral electron beam

The nonlinear spatial evolution, from the source to the atmosphere, of the auroral electron beam and the beam-generated electrostatic whistler noise was studied, calculating changes in beam parameters from equations for the conservation of total particle and wave energy and momentum flux density. Wave power fluxes were calculated by numerically integrating the wave kinetic equations, and the levels of beam-generated noise were determined by using thermal levels of Cerenkov radiation as a source. It was found that beam parameters evolve on ionospheric scale lengths, and their positive slope feature in velocity space is maintained over altitudes measured in thousands of kilometers of altitude, even though they can generate wave energy density fluxes sufficient to modify the ionospheric density profile.

Maggs, James E.↗

NASA NTRS1979

Aperture amplitude and phase control of offset dual reflectors

An approximate synthesis method is presented for solving the problem of offset dual-shaped reflectors. It is shown that the equations obtained by this method are partial differential equations that can be integrated numerically, except that these equations are generally not total and therefore do not have a 'smooth' solution. However, it is demonstrated that these equations form a nearly total differential that enables one to generate a smooth subreflector by integrating the differential equations and then synthesizing a main reflector which gives an exact solution for the specified aperture phase distribution. Several important illustrative examples are treated, which validate the adequacy of the proposed method.

Galindo-Israel, V.↗

NASA NTRS1981

Influence of friction forces on the motion of VTOL aircraft during landing operations on ships at sea

Equations describing the friction forces generated during landing operations on ships at sea were formulated. These forces depend on the platform reaction and the coefficient of friction. The platform reaction depends on the relative sink rate and the shock absorbing capability of the landing gear. The friction coefficient varies with the surface condition of the landing platform and the angle of yaw of the aircraft relative to the landing platform. Landings by VTOL aircraft, equipped with conventional oleopneumatic landing gears are discussed. Simplifications are introduced to reduce the complexity of the mathematical description of the tire and shock strut characteristics. Approximating the actual complicated force deflection characteristic of the tire by linear relationship is adequate. The internal friction forces in the shock strut are included in the landing gear model. A set of relatively simple equations was obtained by including only those tire and shock strut characteristics that contribute significantly to the generation of landing gear forces.

Howard, J. C.↗

NASA NTRS1978

Long range orbital error estimation for applications satellites

A method of optimum orbital averaging was employed to study the long range accuracy potential of polar orbiting applications satellites. This approach involved the determination of the boundary conditions of one set of differential equations of motion by adjusting the initial conditions in a least square sense with the use of data generated by another set of differential equations of motion.

Bonavito, N. L.↗

NASA NTRS1988

Calculations Of Transonic Flow About A Wing

Report describes calculations of transonic airflows about wing in wind tunnel. Basic equations of flow used in study are Reynolds-averaged Navier-Stokes equations in strong conservation-law form. Equations of flow incorporated into finite-difference computer code called TNS (Transonic Navier-Stokes). Computational grid generated by solution of partial differential equations yielding smooth meshes conforming to surfaces of wing and wind tunnel.

Holst, Terry L.↗

NASA NTRS1993

Development of deterministic transport methods for low energy neutrons for shielding in space

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in aluminum. As an external verification, the results from MGSLAB and MGSEMI were compared to ANISN/PC, a routinely used neutron transport code, showing excellent agreement. In an application to an aluminum shield, the FN method seems to generate reasonable results.

Ganapol, Barry↗

NASA NTRS1980

An investigation of dynamic-analysis methods for variable-geometry structures

Selected space structure configurations were reviewed in order to define dynamic analysis problems associated with variable geometry. The dynamics of a beam being constructed from a flexible base and the relocation of the completed beam by rotating the remote manipulator system about the shoulder joint were selected. Equations of motion were formulated in physical coordinates for both of these problems, and FORTRAN programs were developed to generate solutions by numerically integrating the equations. These solutions served as a standard of comparison to gauge the accuracy of approximate solution techniques that were developed and studied. Good control was achieved in both problems. Unstable control system coupling with the system flexibility did not occur. An approximate method was developed for each problem to enable the analyst to investigate variable geometry effects during a short time span using standard fixed geometry programs such as NASTRAN. The average angle and average length techniques are discussed.

Austin, F.↗

NASA NTRS1977

Fundamental electronic mechanisms limiting the performance of solar cells

Attention is focused on distortion in the energy band, and carrier recombination and generation rates (lifetimes), as the two dominant mechanisms. Spatial dependences associated with these two mechanisms, in the direction normal to the surface illuminated by the sun and in the direction tangential to that surface, are also emphasized as crucial factors in governing the efficiency of solar cells. Electronic parameters for the set of differential equations characterizing transport, recombination, and generation of carriers, and interband and band-bound transition rates, are studied.

Lindholm, F. A.↗

NASA NTRS1989

The theory of magnetohydrodynamic wave generation by localized sources. II - Collisionless dissipation of wave packets

The dispersion equation of Barnes (1966) is used to study the dissipation of asymptotic wave packets generated by localized periodic sources. The solutions of the equation are linear waves, damped by Landau and transit-time processes, in a collisionless warm plasma. For the case of an ideal MHD system, most of the waves emitted from a source are shown to cancel asympotically through destructive interference. The modes transporting significant flux to asymptotic distances are found to be Alfven waves and fast waves with theta (the angle between the magnetic field and the characteristics of the far-field waves) of about 0 and about pi/2.

Collins, William↗

NASA NTRS1983

Adaptive grids generated by elliptic systems

It is pointed out that a finite difference grid which moves with the solution of the partial differential equation being solved can improve the accuracy and efficiency of a numerical algorithm. This technique is particularly advantageous in the solution of problems involving boundary layers or shocks where a poorly chosen grid may give a numerical solution which is useless because of poor resolution or extreme oscillations. The present investigation is concerned with the development of a scheme which does not excessively distort the grid. The grid generation algorithm is based on the numerical solution of a system of elliptic differential equations. Holst and Brown (1981) have used a preliminary solution to move points on the boundary of the physical region and then resolved the problem on a new grid generated by an elliptic system. In the current investigation, the grid movement and the solution will develop simultaneously. The solution is used to modify the generating equations, thereby controlling the grid point distributions.

Mastin, C. W.↗

NASA NTRS1980

Viscous compressible flow about blunt bodies using a numerically generated orthogonal coordinate system

A numerical solution to the Navier-Stokes equations was obtained for blunt axisymmetric entry bodies of arbitrary shape in supersonic flow. These equations are solved on a finite difference mesh obtained from a simple numerical technique which generates orthogonal coordinates between arbitrary boundaries. The governing equations are solved in time dependent form using Stetter's improved stability three step predictor corrector method. For the present application, the metric coefficients were obtained numerically using fourth order accurate, finite difference relations and proved to be totally reliable for the highly stretched mesh used to resolve the thin viscous boundary layer. Solutions are obtained for a range of blunt body nose shapes including concavities.

Graves, R. A., Jr.↗

NASA NTRS1990

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Slack, David C.↗

NASA NTRS1993

Hypersonic stagnation line merged layer flow on blunt axisymmetric bodies of arbitrary shape

The problem of hypersonic stagnation line merged-layer flow of variously shaped blunt asisymmetric bodies is here formulated in such a way as to allow analytical calculations for bodies generated by a conic section. The governing equations encompass, apart from the usual parameters, the eccentricity of the conic section that generates the body-of-revolution for the effect of body shape on the solution obtained. The stagnation-point surface pressure increases as the favorable pressure gradient decreases, in the course of a change of body shape from spherical to hyperboloid.

Jain, Amolak S.↗

NASA NTRS1992

Evolution of the shock front and turbulence structures in the shock/turbulence interaction

The interaction of a weak shock front with isotropic turbulence has been investigated using Direct Numerical Simulation (DNS). Two problems were considered: the ability of the field equation (the equation for a propagating surface) to model the shock; and a quantitative study of the evolution of turbulence structure using the database generated by Lee et al. Field equation model predictions for front shape have been compared with DNS results; good agreement is found for shock wave interaction with 2D turbulence and for a single steady vorticity wave. In the interaction of 3D isotropic turbulence with a normal shock, strong alignment of vorticity with the intermediate eigenvector of the rate of strain tensor (S(sup *)(sub ij) = S(sub ij) - (1/3)(delta(sub ij))(S(sub kk))) is seen to develop upstream of the shock and to be further amplified on passage through the shock. Vorticity tends to align at 90 deg to the largest eigenvector, but there is no preferred alignment with the smallest eigenvector. Upstream of the shock, the alignments continue to develop even after the velocity derivative skewness saturates. There is a significant tendency, which increases with time throughout the computational domain, for velocity to align with vorticity. The alignment between velocity and vorticity is strongest in eddy regions and weakest in convergence regions.

Kevlahan, N.↗

NASA NTRS2006

Various Ambiguities in Re-constructing Laser Pulse Parameters

We think that mode lock laser pulses are generated by the summation process that take place between the monochromatic EM filed frequencies as if they interact with each other as shown in equation 1. In reality, the pulse generation is a collaborative interaction process between EM fields and various material medium. When we carry out the actual mode lock analysis, we do take into account of interpaly between all the temporal dynamics of the cavity gain medium, cavity round trip time and the response time of the intra cavity element (saturable absorber, Kerr medium, etc.). that really enforces the locking of the phase of the cavity spontaneous emissions. On a conceptual level, this simplistic representation of the mode locking by Eq.1 ignores all these critical physical processes. When we try to analyze a pulsed field, again we start by representing it very much like this equation, even though we can only detect the square modulus of this complex field and loose a lot of phase related information to the detectors quantum whims and their time constants. The key parameters for a light pulse are as follows. Foremost is the (i) carrier frequency, which cannot be described or imagined without its state of undulation expressed as its (ii) phase. Next is our imagined time finite (iii) carrier envelope that provides the temporal boundary of the field amplitude strength of the undulating E-field. The final parameter is the (iv) state of polarization or the unique plane along which the strength of the E-field gradient undulates. None of these filed characteristics are made self-evident to us by the fields themselves. We do not see light. Light does not see light. Light beams pass through each other without altering each others energy distribution unless there are interacting material molecules (dipoles) within the physical volume of superposition of the beams. In contrast, we can sense the material particles. Material particles sense each other and they cannot pass through each other without interacting with (scattering from) each other. Thus the interpretation of the superposition phenomenon of multiple fields on detectors should not be lumped under the mysterious "wave-particle duality" philosophy. The phenomenon of superposition can be understood better when we focus on the actual process experienced by the detecting dipoles when allowed by QM rules, they respond to and sum all the induced stimulations due to all the superposed fields followed by the proportionate energy absorption giving rise to the fringes we observe. We will present various experimental results to illustrate our arguments. Our position is that such detector behavior driven interpretations rather than the generally implied field-field interaction driven explanations, will help us better understand the ultimate nature of light and hence invent better and newer devices and instruments.

Roychoudhuri, Chandrasekhar↗

NASA NTRS1985

Adding computationally efficient realism to Monte Carlo turbulence simulation

Frequently in aerospace vehicle flight simulation, random turbulence is generated using the assumption that the craft is small compared to the length scales of turbulence. The turbulence is presumed to vary only along the flight path of the vehicle but not across the vehicle span. The addition of the realism of three-dimensionality is a worthy goal, but any such attempt will not gain acceptance in the simulator community unless it is computationally efficient. A concept for adding three-dimensional realism with a minimum of computational complexity is presented. The concept involves the use of close rational approximations to irrational spectra and cross-spectra so that systems of stable, explicit difference equations can be used to generate the turbulence.

Campbell, C. W.↗