Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical approximations”

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 559 records · Page 31

Iron-absorption band analysis for the discrimination of iron-rich zones

The author has identified the following significant results. Analysis of ERTS-1 images of Nevada has followed two courses: comparative lineament mapping and spectral reflectance evaluation. The comparative lineament mapping was conducted by mapping lineaments on 9 x 9 inch prints of MSS bands 5 and 7, transferring the data to a base map, and comparing the results with existing geologic maps. The most significant results are that lineaments are more numerous on the band 7 images, and approximately 100 percent more were mapped than appear on existing maps. Geologic significance of these newly mapped lineaments will not be known until they are checked in the field: many are probably faults. Spectral analysis has been limited to visual comparison among the four MSS bands. In general, higher scene contrast is shown in the near infrared bands (6 and 7) than in the visible wavelength bands (4 and 5). The economic implications of these results derive chiefly from the greater efficiency that can be obtained by using near infrared as well as visible wavelength images.

Rowan, L. C.↗

An evaluation of some special techniques for nuclear waste disposal in space

A preliminary examination is reported of several special ways for space disposal of nuclear waste material which utilize the radioactive heat in the waste to assist in the propulsion for deep space trajectories. These include use of the wastes in a thermoelectric generator (RTG) which operates an electric propulsion device and a radioisotope - thermal thruster which uses hydrogen or ammonia as the propellant. These propulsive devices are compared to the space tug and the space tug/solar electric propulsion combination for disposal of waste on a solar system escape trajectory. Such comparisons indicate that the waste-RTG approach has considerable potential provided the combined specific mass of the waste container - RTG system does not exceed approximately 150 kg/kw sub e. Several exploratory numerical calculations have been made for high earth orbit and Earth escape destinations.

Mackay, J. S.↗

Computer solutions of Wu's equations for compressible flow through turbomachines

Two computers programs, known as Matrix Through-Flow and Matrix Blade-To-Blade, for analyzing the meridional and blade-to-blade flow patterns are described. The numerical solutions are obtained by finite difference approximations to the governing Poisson-type differential equations for the stream function. Solutions for several turbomachines, giving flow patterns and velocity distributions, are included.

Smith, D. J. L.↗

Solving multiple scattering problems in planetary atmospheres

Multiple scattering problems, radiative transfer problems in planetary atmospheres within extended visible portion of the spectrum, are examined. The direct and inverse problems and the extinction coefficient are defined, along with other scattering characteristics. Albedos in semi-infinite and finite atmospheres are considered, as well as surface illumination, energy deposition, and polarization. The Eddington approximation figures prominently in the calculations. Precise numerical methods and analytical solutions are included.

Irvine, W. M.↗

On the theory of thermal runaway in the hydrogen envelope of a white dwarf

An evolutionary sequence was calculated for a white dwarf on which a hydrogen rich envelope is assumed to increase with time. The stellar models were computed by integrating numerically the system of stellar structure equations by means of the Henyey method. The accretion of matter was assumed to be quasi-static. Near the point of the chemical discontinuity, a temperature maximum is shown to arise, and hydrogen ignites; a thin shell energy source is formed which is thermally unstable. The resulting thermal runaway was investigated numerically and by means of a simple approximation based on the energy balance in the hydrogen burning shell source.

Redkoborodyy, Y. N.↗

Pioneer Solar Plasma and Magnetic Field Measurements in Interplanetary Space During August 2-17, 1972

Solar wind plasma and magnetic field measurements from Pioneers 9 and 10 during August 2-17, 1972, reveal complex and large-amplitude variations on a one-hour time scale and numerous discontinuities. During this time period an approximate radial alignment of the two spacecraft as seen from the Sun occurred with heliocentric distances of 0.8 AU for Pioneer 9 and 2.2 AU for Pioneer 10, both at 45 deg east of the Earth's solar longitude. The peak hourly average solar wind proton bulk velocity measured at Pioneer 9 was 990 km sec (exp -1) during hour 0 UT of August 5. The peak hourly average proton number density was 62 cm (exp -3) during hour 11 UT of August 3. The peak solar wind speeds are generally much reduced at Pioneer 10 compared with those observes at Pioneer 9. The peak 30 minute average magnetic field magnitude was 85 gamma during 1245 - 1315 UT of August 3. The Pioneer 9 data indicate passage of four fast forward interplanetary shocks, and one slow forward interplanetary shock.

Mihalov, J. D.↗

Theory of a cylindrical probe in a collisionless magnetoplasma

A theory is presented for a cylindrical electrostatic probe in a collisionless plasma in the case where the probe axis is inclined at an angle to a uniform magnetic field. The theory is applicable to electron collection, and under more restrictive conditions, to ion collection. For a probe at space potential, the theory is exact in the limit where probe radius is much less than Debye length. At attracting probe potentials, the theory yields an upper bound and an adiabatic limit for current collection. At repelling probe potentials, it provides a lower bound. The theory is valid if the ratios of probe radius to Debye length and probe radius to mean gyroradius are not simultaneously large enough to produce extrema in the probe sheath potential. The numerical current calculations are based on the approximation that particle orbits are helices near the probe, together with the use of kinetic theory to relate velocity distributions near the probe to those far from it. Probe characteristics are presented for inclination angles from 0 to 90 deg and for probe-radius mean-gyroradius ratios from 0.1 to infinity. For an angle of 0 deg, the end-effect current is calculated separately.

Laframboise, J. G.↗

Microturbulence, systematic motions, and line formation in molecular clouds

Microturbulence and systematic motions are viewed as simplifying assumptions made to facilitate treatment of line formation in molecular clouds, and line intensities calculated in the two approximations are compared to estimate how uncertainties about the actual line-broadening mechanism affect the interpretation of molecular emission lines. For lines formed by two-level molecules in an isothermal homogeneous cloud, the alternative assumptions lead to peak and integrated line intensities which agree within the differences (up to a factor of 3) associated with the ignorance of cloud geometry. New multilevel calculations for CO in the same cloud model bear out the generality of this result. It follows that, within the geometrical uncertainties, the Sobolev (1960) approximation may be used confidently in the numerous applications for which this simple cloud model suffices.

White, R. E.↗

Three dimensional steady and unsteady asymmetric flow past wings of arbitrary planforms

The nonlinear discrete vortex method is extended to treat the problem of asymmetric flows past a wing with leading edge separation, including steady and unsteady flows. The problem is formulated in terms of a body fixed frame of reference and the nonlinear-discrete vortex method is modified accordingly. Although the method is general, only examples of flows past delta wings are presented due to the availability of experimental data as well as approximate theories. Comparison of results with experimental results for a delta wing undergoing a steady rolling motion at zero angle of attack demonstrate the superiority of the present method over existing approximate theories in obtaining highly accurate loads. Numerical results for yawed wings at large angles of attack are also presented. In all cases, total load coefficients, pressure distributions, and shapes of the free vortex sheets are shown.

Kandil, O. A.↗

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Daniele, C. J.↗

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

Lee, S. S.↗

The largest H II regions in M101

Coordinated millimeter, infrared, and ultraviolet observations of the five brightest H II regions in M101 are presented. A CO complex has been found to be associated with NGC 5461 which is much more massive than any Milky Way counterpart. A narrow line width has been observed which suggests that the molecular complex may consist of numerous fragments with a volume filling fraction approximately 0.01. NGC 5461 also shows a 10 micron and 20 micron excess which is similar to that of galactic H II regions. The ultraviolet observations show that the 2200 A dust feature is greatly attenuated in all of the H II regions but least of all in NGC 5461. The near-infrared flux densities and B-gamma line strengths are consistent with the hypothesis that a significant fraction of the infrared emission is free-free.

Blitz, L.↗

Numerical computations on one-dimensional inverse scattering problems

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

Dunn, M. H.↗

Numerical computations on one-dimensional inverse scattering problems

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

Dunn, M. H.↗

Microwave radiances from precipitating clouds containing aspherical ice, combined phase, and liquid hydrometeors

A numerical algorithm based on Eddington's second approximation to the equation of radiative transfer has been developed in order to compute the radiances with horizontal and vertical polarization that emerge from precipitating clouds. This algorithm yields a rapid solution to problems pertaining to clouds with vertically inhomogeneous structure. Precipitating clouds containing liquid, mixtures of phases, and ice hydrometeors are modelled. It is shown that the lower-frequency radiances are sensitive to liquid precipitation at low altitudes while the higher-frequency radiances are more sensitive to the ice hydrometeors at the cloud tops. The extinction coefficients of aspherical hydrometeors are presented as a function of rainfall rates. The fact that vertically polarized radiances are warmer than horizontally polarized ones at high rainfall rates, with the difference diminishing at lower frequencies, is due to aspherical ice hydrometeors in the upper regions of precipitating clouds.

Wu, R.↗

A refined shear deformation theory for the analysis of laminated plates

A refined, third-order plate theory that accounts for the transverse shear strains is presented, the Navier solutions are derived for certain simply supported cross-ply and antisymmetric angle-ply laminates, and finite-element models are developed for general laminates. The new theory does not require the shear correction factors of the first-order theory (i.e., the Reissner-Mindlin plate theory) because the transverse shear stresses are represented parabolically in the present theory. A mixed finite-element model that uses independent approximations of the generalized displacements and generalized moments, and a displacement model that uses only the generalized displacements as degrees of freedom are developed. The displacement model requires C sup 1-continuity of the transverse deflection across the inter-element boundaries, whereas the mixed model requires a C sup 0-element. Also, the mixed model does not require continuous approximations (between elements) of the bending moments. Numerical results are presented to show the accuracy of the present theory in predicting the transverse stresses. Numerical results are also presented for the nonlinear bending of plates, and the results compare well with the experimental results available in the literature.

Reddy, J. N.↗

Postbuckling of laminated anisotropic panels

A two-part study of the buckling and postbuckling of laminated anisotropic plates with bending-extensional coupling is presented. The first part involves the development and application of a modified Rayleigh-Ritz analysis technique. Modifications made to the classical technique can be grouped into three areas. First, known symmetries of anisotropic panels are exploited in the selection of approximation functions. Second, a reduced basis technique based on these same symmetries is applied in the linear range. Finally, geometric boundary conditions are enforced via an exterior penalty function approach, rather than relying on choice of approximation functions to satisfy these boundary conditions. Numerical results are presented for both the linear and nonlinear range, with additional studies made to determine the effect of variation in penalty parameter and number of basis vectors. In the second part, six panels possessing anisotropy and bending-extensional coupling are tested. Detailed comparisons are made between experiment and finite element results in order to gain insight into the postbuckling and failure characteristics of such panels. The panels are constructed using two different lamination sequences, and panels with three different aspect ratios were constructed for each lamination sequence.

Jeffrey, Glenda L.↗

Trajectory characteristics and heating of hypervelocity projectiles having large ballistic coefficients

A simple, approximate equation describing the velocity-density relationship (or velocity-altitude) has been derived from the flight of large ballistic coefficient projectiles launched at high speeds. The calculations obtained by using the approximate equation compared well with results for numerical integrations of the exact equations of motion. The flightpath equation was used to parametrically calculate maximum body decelerations and stagnation pressures for initial velocities from 2 to 6 km/s. Expressions were derived for the stagnation-point convective heating rates and total heat loads. The stagnation-point heating was parametrically calculated for a nonablating wall and an ablating carbon surface. Although the heating rates were very high, the pulse decayed quickly. The total nose-region heat shield weight was conservatively estimated to be only about 1 percent of the body mass.

Tauber, Michael E.↗