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At least 181 records · Page 10

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NASA NTRS1975

A method for calculating a real-gas two-dimensional nozzle contour including the effects of gamma

A method for calculating two-dimensional inviscid nozzle contours for a real gas or an ideal gas by the method of characteristics is described. The method consists of a modification of an existing nozzle computer program. The ideal-gas nozzle contour can be calculated for any constant value of gamma. Two methods of calculating the center-line boundary values of the Mach number in the throat region are also presented. The use of these three methods of calculating the center-line Mach number distribution in the throat region can change the distance from the throat to the inflection point by a factor of 2.5. A user's guide is presented for input to the computer program for both the two-dimensional and axisymmetric nozzle contours.

Johnson, C. B.↗

NASA NTRS1975

Calculation of arbitrary-order diffraction efficiencies of thick gratings with arbitrary grating shape

A method for calculating arbitrary-order diffraction efficiencies of thick, lossless transmission gratings with arbitrary periodic grating shapes has been developed. A Fourier-series representation of the grating is employed, along with a coupled-mode theory of diffraction. For illustration, numerical values of the diffraction efficiencies at the first three Bragg angles are calculated for sinusoidal, square-wave, triangular, and saw-tooth gratings. Numerical results for the same grating shapes with the same parameters are also calculated for comparison, by extending Burckhardt's numerical method for analyzing thick sinusoidal gratings. The comparison shows that the coupled-mode theory provides results with relative computational ease and results that are in agreement with calculations obtained by extending the more-rigorous Burckhardt theory to nonsinusoidal grating shapes and to higher-order Bragg angles.

Su, S. F.↗

NASA NTRS1975

Calculation of the flow on a blunted cone at high angle of attack

A new technique for calculating the entire flow-field on spherically blunted circular cones at high angles of attack and high Reynolds numbers is described. The calculations are based on a single-layer system of three-dimensional parabolic equations which are approximations to the full steady Navier-Stokes equations. Initial conditions at the sphere-cone tangency plane are provided by using an inviscid time-dependent solution added to a viscous nonsimilar boundary layer solution. Calculated results are compared with experimental heat transfer and pressure data for a 15 deg half-angle cone with a 1-in. spherical nose at 15 deg angle of attack. The free-stream Mach number is 10.6, and the free-stream Reynolds number is 1,200,000 per foot. Excellent agreement between the calculated and experimental data for both pressure and heat transfer is obtained.

Lubard, S. C.↗

NASA NTRS1975

Calculation of autoionization of He and H/-/ using the projection-operator formalism

Improved calculations are reported for the first several autoionization states of the lower symmetries of He and H(-). Unshifted energies are calculated by diagonalizing QHQ using a Hylleraes basis with more terms than previously used; shifts, widths, and photoabsorption shape parameters are obtained with the additional use of exchange-approximate nonresonant continuum functions. Previous calculations of H(-) resonances are reviewed and slightly augmented by applying various nonresonant continua and correcting small errors. A comparison is made between the calculations and experimental results and is found to be very satisfactory except for the lowest 1P autoionization state of He, which is shown to need a more accurate experimental determination.

Bhatia, A. K.↗

NASA NTRS1975

Calculations of the radiative and dynamical state of the Venus atmosphere

Results are reported for accurate multiple-scattering calculations to determine the solar-energy deposition profile in the atmosphere of Venus. It is found that most of the absorbed energy is deposited in the main cloud-layer region, located at altitudes above 35 km, and that the ground receives approximately 3% of the energy absorbed in toto by Venus. Using these results, vertical temperature profiles are computed under conditions of pure radiative equilibrium and radiative-convective equilibrium. Since the latter results satisfactorily match the temperature structure determined from various spacecraft observations, it is inferred that the greenhouse effect can account for the high surface temperature. Aerosols make an important contribution to the infrared opacity in these calculations. Preliminary three-dimensional calculations of the general circulation of the atmosphere are discussed which incorporate the results of the radiative calculations.

Pollack, J. B.↗

NASA NTRS1976

Calculations of the Electron Energy Distribution Function in a Uranium Plasma by Analytic and Monte Carlo Techniques

Electron energy distribution functions were calculated in a U235 plasma at 1 atmosphere for various plasma temperatures and neutron fluxes. The distributions are assumed to be a summation of a high energy tail and a Maxwellian distribution. The sources of energetic electrons considered are the fission-fragment induced ionization of uranium and the electron induced ionization of uranium. The calculation of the high energy tail is reduced to an electron slowing down calculation, from the most energetic source to the energy where the electron is assumed to be incorporated into the Maxwellian distribution. The pertinent collisional processes are electron-electron scattering and electron induced ionization and excitation of uranium. Two distinct methods were employed in the calculation of the distributions. One method is based upon the assumption of continuous slowing and yields a distribution inversely proportional to the stopping power. An iteration scheme is utilized to include the secondary electron avalanche. In the other method, a governing equation is derived without assuming continuous electron slowing. This equation is solved by a Monte Carlo technique.

Bathke, C. G.↗

NASA NTRS1976

Calculation of subsonic and supersonic steady and unsteady aerodynamic forces using velocity potential aerodynamic elements

Expressions for calculation of subsonic and supersonic, steady and unsteady aerodynamic forces are derived, using the concept of aerodynamic elements applied to the downwash velocity potential method. Aerodynamic elements can be of arbitrary out of plane polygon shape, although numerical calculations are restricted to rectangular elements, and to the steady state case in the supersonic examples. It is suggested that the use of conforming, in place of rectangular elements, would give better results. Agreement with results for subsonic oscillating T tails is fair, but results do not converge as the number of collocation points is increased. This appears to be due to the form of expression used in the calculations. The methods derived are expected to facilitate automated flutter analysis on the computer. In particular, the aerodynamic element concept is consistent with finite element methods already used for structural analysis. The method is universal for the complete Mach number range, and, finally, the calculations can be arranged so that they do not have to be repeated completely for every reduced frequency.

Haviland, J. K.↗

NASA NTRS1976

A computer program to calculate the longitudinal aerodynamic characteristics of wing-flap configurations with externally blown flaps

A vortex lattice lifting-surface method is used to model the wing and multiple flaps. Each lifting surface may be of arbitrary planform having camber and twist, and the multiple-slotted trailing-edge flap system may consist of up to ten flaps with different spans and deflection angles. The engine wakes model consists of a series of closely spaced vortex rings with circular or elliptic cross sections. The rings are normal to a wake centerline which is free to move vertically and laterally to accommodate the local flow field beneath the wing and flaps. The two potential flow models are used in an iterative fashion to calculate the wing-flap loading distribution including the influence of the waves from up to two turbofan engines on the semispan. The method is limited to the condition where the flow and geometry of the configurations are symmetric about the vertical plane containing the wing root chord. The calculation procedure starts with arbitrarily positioned wake centerlines and the iterative calculation continues until the total configuration loading converges within a prescribed tolerance. Program results include total configuration forces and moments, individual lifting-surface load distributions, including pressure distributions, individual flap hinge moments, and flow field calculation at arbitrary field points.

Mendenhall, M. R.↗

NASA NTRS1976

Hybrid theory and calculation of e-N2 scattering

A theory of electron-molecule scattering is developed which is a synthesis of close-coupling and adiabatic-nuclei theories. Specifically, the theory is close-coupling with respect to vibrational degrees of freedom and adiabatic-nuclei with respect to rotation. It can be applied to any number of partial waves required; the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations is given which indicates those partial waves and energy domains requiring the various approximations. The theory allows all cross sections (pure rotational, vibrational, simultaneous vibration-rotation, differential, and total) to be calculated, and explicit formulas for all these cross sections are given. The theory is applied to low-energy e-N2 scattering. The fixed-nuclei results are such that the criterion shows clearly that vibrational close coupling is necessary, but only for the Pi sub g partial wave. It is found that the close-coupling calculation for this wave gives rise to the substructure as well as the gross structure of the 2.4-eV resonance and that vibrational excitation cross sections are about twice as large as previously inferred.

Chandra, N.↗

NASA NTRS1976

Twilight helium 10,830-A calculations and observations

The 10,830-A column emission rates from metastable He(2 3S) atoms in the upper atmosphere are calculated and compared with other calculations and observations. It is shown that the calculated emission rates agree well with the observed emission rates provided that the cross sections for loss of He(2 3S) by Penning ionization on atomic oxygen is near 5 A 2 and not 44 A 2 as previously measured. It is assumed that the local and conjugate photoelectron fluxes above 300 km are about double those calculated. The dawn/dusk intensity ratio observed in New Mexico, Brazil and Peru is accounted for by changes in the ambient thermal electron concentration in Brazil and Peru and by changes in plasmasphere opacity to conjugate point electrons for New Mexico and to some extent for Brazil. The rate at which He-4 would escape from the earth if sufficient energy were imparted to the He-4 atoms during the Penning reaction was recalculated and found to be inadequate by an order of magnitude to balance the terrestrial production.

Tinsley, B. A.↗

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.↗