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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

A calculation of Saturn's gravitational contraction history

A gravitational-contraction history is calculated for a homogeneous quasi-equilibrium Saturn model of solar composition without a rock-ice core and without allowance for the possible separation of hydrogen and helium. The calculations begin at the time when Saturn's radius was ten times its current value, and the subsequent gravitational contraction is followed for 4.5 billion years. The results obtained are given in terms of the path of the evolving model on the H-R diagram, the variation of central temperature with central density, the time variation of radius and internal luminosity, and the energy changes that take place during the evolution. These results are compared with those of similar calculations for Jupiter, and the internal structure of the evolutionary models is examined in detail. The Saturn calculations yield a radius at the current epoch that is 9% larger than the observed value and an excess luminosity comparable to that observed. It is noted that an inhomogeneous model containing a solar-mix envelope and a central rocky core has a radius equal to the observed value.

Pollack, J. B.↗
NASA NTRS1978

Calculated rate constants for the reaction ClO + O yields Cl + O2 between 220 and 1000 deg K

Classical trajectory calculations are presented for the reaction ClO + O yields Cl + O2, a reaction which is an important step in the chlorine-catalyzed destruction of ozone which is thought to occur in the 220 and 1000 K. The calculated rate constant is 4.36 x 10 to the minus 11th power exp (-191/T)cu cm molecule (-1)s(-1) and its value at 300 K is 2.3 plus or minus 10 to the 11th power cu cm molecule (-1)s(-1), about a factor of 2 lower than recent experimental data. The empirical potential energy surface used in the calculations was constructed to fit experimental data for ClO, O2 and ClOO molecules. Other important features of this potential surface, such as the barrier to reaction, were varied systematically and calculations were performed for a range of conditions to determine the best theoretical rate constants. Results demonstrate the utility of classical trajectory methods for determining activation energies and other kinetic data for important atmospheric reactions.

Jaffee, R. L.↗
NASA NTRS1978

Transonic flow over the NACA 64A006 with an oscillating flap-calculations based on the Euler equations

Exploratory calculations of transonic flows over the airfoil with a quarter-chord oscillating flap were made using a program which obtains approximate solutions to the Euler equations with an explicit, shock-capturing, finite-difference scheme. The calculations, essentially inviscid and for the airfoil at zero angle-of-attack in a free-stream, are at Mach numbers and reduced frequencies which were tested in experiments by Tijdeman. The oscillatory lifts from analogus calculations by various investigators generally agree with one another better than they agree with Tijdeman's data. Inclusion in the calculations of an approximate modelling of boundary conditions expected at slotted wind tunnel walls tends to shift some of the results closer to the experimental values.

Magnus, R. J.↗
NASA NTRS1979

Computer program to calculate three-dimensional boundary layer flows over wings with wall mass transfer

A system of computer programs for calculating three dimensional transonic flow over wings, including details of the three dimensional viscous boundary layer flow, was developed. The flow is calculated in two overlapping regions: an outer potential flow region, and a boundary layer region in which the first order, three dimensional boundary layer equations are numerically solved. A consistent matching of the two solutions is achieved iteratively, thus taking into account viscous-inviscid interaction. For the inviscid outer flow calculations, the Jameson-Caughey transonic wing program FLO 27 is used, and the boundary layer calculations are performed by a finite difference boundary layer prediction program. Interface programs provide communication between the two basic flow analysis programs. Computed results are presented for the NASA F8 research wing, both with and without distributed surface suction.

Mclean, J. D.↗
NASA NTRS1979

Effect of element density on the NASTRAN calculated mechanical and thermal stresses of a spar

A NASTRAN model of a spar was examined to determine the sensitivity of calculated axial thermal stresses and bending stresses to changes in element density of the model. The thermal stresses calculated with three different element densities resulted in drastically differing values. The position of the constraint also significantly affected the value of the calculated thermal stresses. Mechanical stresses calculated from an applied loading were insensitive to element density.

Jenkins, J. M.↗
NASA NTRS1979

SCF treatment of charge polarization effects in intermediate-energy electron scattering calculations with applications to N2

Converged rotational close coupling calculations of differential, integral, and momentum-transfer cross sections are obtained for seven model potentials for electron-N2 scattering at an impact energy of 30 eV. The model potentials involve a static potential calculated by the INDO/1s or INDOXI/1s method, and exchange potential calculated by the semiclassical exchange approximation from the INDO/1s or INDOXI/1s unperturbed electron density and a polarization potential. The polarization potentials used include the Buckley-Burke semiempirical one and various modifications of the INDOXI and INDO SCF (self-consistent-field) adiabatic polarization potentials. Without adjustment of parameters, good agreement is obtained with the angle dependence of the experimentally measured sum of the elastic and rotational excitation differential cross sections; however, the absolute value of the calculated cross sections is about 20-30% larger than the measured values in the best case, perhaps indicating that the model potentials are too strong or should have a nonzero imaginary part.

Onda, K.↗
NASA NTRS1979

High resolution atmospheric transmission calculations down to 28.7 km in the 200-243-nm spectral range

Decrease in stratospheric ozone absorption and increase in oxygen absorption with decreasing wavelength combine to produce a window of maximum atmospheric transmission near 210 nm. Since solar radiation in this spectral region dissociates molecular oxygen, the deep atmospheric penetration at this wavelength is of particular aeronomical interest. High resolution calculations of the transmittance down to 28.65 km were made for the 200-243-nm spectral range in this window region, in support of a stratospheric balloon flight from Fort Churchill in July 1974. The calculations were made by dividing the atmosphere into layers which were chosen so that each could be assumed homogeneous; optical depths were calculated separately for each of these layers and then summed to obtain the over-all transmittance of the atmosphere. Absorption by molecular oxygen (line and continuum) and by ozone was included, as well as extinction through Rayleigh scattering by air molecules. The calculated transmittances were combined with high altitude (above 100-km) rocket measurements of the sun-center spectrum and center-to-limb variations to give residual high resolution solar spectral flux for several altitudes and solar zenith angles.

Cann, M. W. P.↗
NASA NTRS1979

Extensions to the classical calculation of the effect of mutual shadowing in diffuse reflection

The classical method for accounting for the mutual shadowing among closely packed particles in multiple scattering calculations is extended in the following ways. (1) By modeling the particle distribution by a Poisson process with a varying density parameter, a 'Van der Waals' type approximation allows extension to a greater fractional volume density, D. In this case it is only required that D squared be much less than 1 instead of D being much less than 1. (2) In the case that the particle distribution is not uniform the classical calculation may be weighted by the pair correlation function of the distribution. (3) The use of the Markov chain formalism for radiative transfer allows inclusion of the effect of shadowing for two orders of scattering. For conditions such as might apply in Saturn's rings, the inclusion of this effect makes less than a 0.1% difference in the calculated phase curves, compared to previous calculations which have included shadowing only in the first scattering. The latter are thus shown to be quite accurate.

Esposito, L. W.↗
NASA NTRS1980

Comparison of calculated and measured model rotor loading and wake geometry

The calculated blade bound circulation and wake geometry are compared with measured results for a model helicopter rotor in hover and forward flight. Hover results are presented for rectangular tip and ogee tip planform blades. The correlation is quite good when the measured wake geometry characteristics are used in the analysis. Available prescribed wake geometry models are found to give fair predictions of the loading, but they do not produce a reasonable prediction of the induced power. Forward flight results are presented for twisted and untwisted blades. Fair correlation between measurements and calculations is found for the bound circulation distribution on the advancing side. The tip vortex geometry in the vicinity of the advancing blade in forward flight was predicted well by the free wake calculation used, although the wake geometry did not have a significant influence on the calculated loading and performance for the cases considered.

Johnson, W.↗
NASA NTRS1980

Calculation of Water Drop Trajectories to and About Arbitrary Three-Dimensional Bodies in Potential Airflow

Calculations can be performed for any atmospheric conditions and for all water drop sizes, from the smallest cloud droplet to large raindrops. Any subsonic, external, non-lifting flow can be accommodated; flow into, but not through, inlets also can be simulated. Experimental water drop drag relations are used in the water drop equations of motion and effects of gravity settling are included. Seven codes are described: (1) a code used to debug and plot body surface description data; (2) a code that processes the body surface data to yield the potential flow field; (3) a code that computes flow velocities at arrays of points in space; (4) a code that computes water drop trajectories from an array of points in space; (5) a code that computes water drop trajectories and fluxes to arbitrary target points; (6) a code that computes water drop trajectories tangent to the body; and (7) a code that produces stereo pair plots which include both the body and trajectories. Code descriptions include operating instructions, card inputs and printouts for example problems, and listing of the FORTRAN codes. Accuracy of the calculations is discussed, and trajectory calculation results are compared with prior calculations and with experimental data.

Norment, H. G.↗
NASA NTRS1980

Comparison of calculated and measured helicopter rotor lateral flapping angles

Calculated and measured values of helicopter rotor flapping angles in forward flight are compared for a model rotor in a wind tunnel and an autogiro in gliding flight. The lateral flapping angles can be accurately predicted when a calculation of the nonuniform wake-induced velocity is used. At low advance ratios, it is also necessary to use a free wake geometry calculation. For the cases considered, the tip vortices in the rotor wake remain very close to the tip-path plane, so the calculated values of the flapping motion are sensitive to the fine details of the wake structure, specifically the viscous core radius of the tip vortices.

Johnson, W.↗
NASA NTRS1979

Tropospheric UV flux calculations and photolysis rates for use with zonally and diurnally averaged models

A computationally fast and efficient method for calculating solar UV fluxes in the troposphere is developed. Calculated fluxes compare favorably with more rigorous multiple scattering results, and qualitatively correct behavior of the direct and diffuse flux components is maintained. In view of the relatively large uncertainties in other aspects of tropospheric photochemical models, the use of approximate UV flux calculations appears warranted. The technique is applied to the calculation of photolysis rates for twelve significant photolytic reactions of nine species.

Matloff, G. L.↗
NASA NTRS1979

Calculational investigation of impact cratering dynamics - Early time material motions

Early time two-dimensional finite difference calculations of laboratory-scale hypervelocity (6 km/sec) impact of 0.3 g spherical 2024 aluminum projectiles into homogeneous plasticene clay targets were performed and the resulting material motions analyzed. Results show that the initial jetting of vaporized target material is qualitatively similar to experimental observation. The velocity flow field developed within the target is shown to have features quite similar to those found in calculations of near-surface explosion cratering. Specific application of Maxwell's analytic Z-Model (developed to interpret the flow fields of near-surface explosion cratering calculations), shows that this model can be used to describe the flow fields resulting from the impact cratering calculations, provided that the flow field center is located beneath the target surface, and that application of the model is made late enough in time that most of the projectile momentum has been dissipated.

Thomsen, J. M.↗
NASA NTRS1980

A model of CO-CH4 global transport/chemistry. II - Preliminary calculation by 1 dimensional model

Calculations of the one-dimensional CO-CH4 transport/chemistry model were performed to investigate the sensitivity of the OH vertical profile to various factors. The boundary conditions at the earth's surface and the tropopause are discussed. The results show that the liquid-phase or soil-phase resistance dominates the mass transfer of both CO and CH4 between the atmosphere and the earth's surface. At the tropopause, the CO and CH4 fluxes are set approximately equal to the value at the previous time step in the numerical calculation. Photolysis rate coefficients that increase with altitude modified the OH vertical profile so that the maximum value was at midtroposphere altitudes. Increasing the CO concentration caused a decrease of the OH concentration, and the OH profile was very sensitive to the NO(x) profiles. The calculated OH profiles are compared with those from other investigations and also with some available measurements. Although the available measurements of the OH profiles are limited, the calculated OH profiles agree fairly well with them.

Kitada, T.↗
NASA NTRS1981

Quantum chemical calculation of the equilibrium structures of small metal atom clusters

A decomposition of the molecular energy is presented that is motivated by the atom superposition and electron delocalization physical model of chemical binding. The energy appears in physically transparent form consisting of a classical electrostatic interaction, a zero order two electron exchange interaction, a relaxation energy, and the atomic energies. Detailed formulae are derived in zero and first order of approximation. The formulation extends beyond first order to any chosen level of approximation leading, in principle, to the exact energy. The structure of this energy decomposition lends itself to the fullest utilization of the solutions to the atomic sub problems to simplify the calculation of the molecular energy. If nonlinear relaxation effects remain minor, the molecular energy calculation requires at most the calculation of two center, two electron integrals. This scheme thus affords the prospects of substantially reducing the computational effort required for the calculation of molecular energies.

Kahn, L. R.↗
NASA NTRS1981

Calculation of two-dimensional inlet flow fields by an implicit method including viscous effects: User's manual

Inlet flow fields for airbreathing missiles are calculated by the adaptation of a two dimensional computational method developed for the flow around airfoils. A supersonic free stream is assumed to allow the forebody calculation to be uncoupled from the inlet calculation. The inlet calculation employs an implicit, time marching finite difference procedure to solve the thin layer Navier-Stokes equations formulated in body fitted coordinates. The mathematical formulation of the problem and the solution algorithm are given. Numerical stability and accuracy as well as the initial and boundary conditions used are discussed. Instructions for program use and operation along with the overall program logic are also given.

Biringen, S.↗
NASA NTRS1981

Theoretical calculation of low-lying states of NaAr and NaXe

Potential curves as well as dipole moments and linking transition moments are calculated for the ground X 2 Sigma + and low lying excited A 2 Pi, B 2 Sigma +, C 2 Sigma +, (4) 2 Sigma +, (2) 2 Pi and (1) 2 Delta states of NaAr and NaXe. Calculations are performed using a self-consistent field plus configuration-interaction procedure with the core electrons replaced by an ab initio effective core potential. The potential curves obtained are found to be considerably less repulsive than the semiempirical curves of Pascale and Vandeplanque (1974) and to agree well with existing experimental data, although the binding energies of those states having potential minima due to van der Waals interactions are underestimated. Emission bands are also calculated for the X 2 Sigma + - C 2 Sigma + excimer transitions of NaAr and NaXe using the calculated transition moments and potential curves, and shown to agree well with experiment on the short-wavelength side of the maximum.

Laskowski, B. C.↗
NASA NTRS1981

A formula for calculating theoretical photoelectron fluxes resulting from the He/+/ 304 A solar spectral line

A simplified method for the evaluation of theoretical photoelectron fluxes in the upper atmosphere resulting from the solar radiation at 304 A is presented. The calculation is based on considerations of primary and cascade (secondary) photoelectron production in the two-stream model, where photoelectron transport is described by two electron streams, one moving up and one moving down, and of loss rates due to collisions with neutral gases and thermal electrons. The calculation is illustrated for the case of photoelectrons at an energy of 24.5 eV, and it is noted that the 24.5-eV photoelectron flux may be used to monitor variations in the solar 304 A flux. Theoretical calculations based on various ionization and excitation cross sections of Banks et al. (1974) are shown to be in generally good agreement with AE-E measurements taken between 200 and 235 km, however the use of more recent, larger cross sections leads to photoelectron values a factor of two smaller than observations but in agreement with previous calculations. It is concluded that a final resolution of the photoelectron problem may depend on a reevaluation of the inelastic electron collision cross sections.

Richards, P. G.↗