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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 397 records · Page 22
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NASA NTRS1977

Approximate theory of large-amplitude wave propagation

An orbit perturbation procedure is applied to the description of monochromatic, large-amplitude, electrostatic plasma wave propagation. In the lowest-order approximation, untrapped electrons are assumed to follow constant-velocity orbits and trapped electrons are assumed to execute simple harmonic motion. The deviations of these orbits from the actual orbits are regarded as perturbations. The nonlinear damping rate and frequency shift are then obtained in terms of simple functions. The results are in good agreement with previous less approximate analyses. A significant feature of the analysis is that it treats a single wave by techniques previously applied to turbulent spectra. The analysis can consequently be extended to the case of a large-amplitude wave interacting with a lower-amplitude spectrum of waves.

Kim, H.↗
NASA NTRS1978

Applied Routh approximation

The Routh approximation technique for reducing the complexity of system models was applied in the frequency domain to a 16th order, state variable model of the F100 engine and to a 43d order, transfer function model of a launch vehicle boost pump pressure regulator. The results motivate extending the frequency domain formulation of the Routh method to the time domain in order to handle the state variable formulation directly. The time domain formulation was derived and a characterization that specifies all possible Routh similarity transformations was given. The characterization was computed by solving two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given. Additional computational problems are discussed, including an optimization procedure that can improve the approximation accuracy by taking advantage of the transformation characterization.

Merrill, W. C.↗
NASA NTRS1978

Feature selection for best mean square approximation of class densities

A criterion for linear feature selection is proposed which is based on mean square apporximation of class density functions. It is shown that for the widest possible class of approximants, the criterion reduces to Devijver's Bayesian distance. For linear approximants the criterion is equivalent to well known generalized Fisher criteria.

Peters, C.↗
NASA NTRS1973

An approximate solution for the free vibrations of rotating uniform cantilever beams

Approximate solutions are obtained for the uncoupled frequencies and modes of rotating uniform cantilever beams. The frequency approximations for flab bending, lead-lag bending, and torsion are simple expressions having errors of less than a few percent over the entire frequency range. These expressions provide a simple way of determining the relations between mass and stiffness parameters and the resultant frequencies and mode shapes of rotating uniform beams.

Peters, D. A.↗
NASA NTRS1977

Vibrational and rotational transitions in low-energy electron-diatomic-molecule collisions. I - Close-coupling theory in the moving body-fixed frame. II - Hybrid theory and close-coupling theory: An /l subscript z-prime/-conserving close-coupling approximation

A detailed vibrational-rotational (V-R) close-coupling formulation of electron-diatomic-molecule scattering is developed in which the target molecular axis is chosen to be the z-axis and the resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire interaction region. The coupled differential equation and asymptotic boundary conditions in the body-fixed frame are given for each parity, and procedures are outlined for evaluating V-R transition cross sections on the basis of the body-fixed transition and reactance matrix elements. Conditions are discussed for obtaining identical results from the space-fixed and body-fixed formulations in the case where a finite truncated basis set is used. The hybrid theory of Chandra and Temkin (1976) is then reformulated, relevant expressions and formulas for the simultaneous V-R transitions of the hybrid theory are obtained in the same forms as those of the V-R close-coupling theory, and distorted-wave Born-approximation expressions for the cross sections of the hybrid theory are presented. A close-coupling approximation that conserves the internuclear axis component of the incident electronic angular momentum (l subscript z-prime) is derived from the V-R close-coupling formulation in the moving body-fixed frame.

Choi, B. H.↗
NASA NTRS1978

An approximate inviscid radiating flow field analysis for outer planet entry probes

An approximate computational technique has been developed for predicting inviscid, radiating flows about blunt probes entering atmospheres consisting of hydrogen and helium. The technique is rapid and versatile and is well suited for performing parametric trade studies for outer planet entries. Details of the computational technique, the thermodynamic correlations, the 58-step absorption coefficient model and the analytic shock shape equations are discussed. Good comparisons of the radiative heating computed by the approximate method and by detailed calculations are obtained.

Zoby, E. V.↗
NASA NTRS1977

The application of the Routh approximation method to turbofan engine models

The Routh approximation technique is applied in the frequency domain to a 16th order state variable turbofan engine model. The results obtained motivate the extension of the frequency domain formulation of the Routh method to the time domain to handle the state variable formulation directly. The time domain formulation is derived and a new characterization, which specifies all possible Routh similarity transformations, is given. This characterization is computed by the solution of two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described and some results are given. Additional computational problems are discussed including an optimization procedure which can improve the approximation accuracy by taking advantage of the transformation characterization.

Merrill, W. C.↗
NASA NTRS1978

On least squares approximations to indefinite problems of the mixed type

A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The method retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency, i.e., the resulting matrix system is always symmetric and positive definite. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.

Fix, G. J.↗
NASA NTRS1978

Heating due to the 9.6 micron ozone band in an inhomogeneous atmosphere - A new approximation

The Curtis-Godson (1953) method, when applied to the 9.6-micron ozone band, yields large errors. Kuriyan et al. (1977) suggested a method improving this result and yet retaining the analytic simplicity of the transmission function. In this paper, the analytic form of the derivative of the transmission function is obtained and then the heating rates are calculated with the new approximation. The errors in this case are negligibly small. Algebraic manipulation enables the reduction of this approximation to a form similar to that proposed by Goody (1964). This procedure permits interpretation of the boundary conditions in physical terms.

Kuriyan, J. G.↗
NASA NTRS1978

Compression of ephemerides by discrete Chebyshev approximations

The use of Chebyshev series in representing the ephemerides of satellites and planets in terms of truncated polynomial series is discussed. Emphasis is placed on a FORTRAN package which was developed for fitting satellite orbits. The features desired in any approximation are: (1) the ability to compress a satellite emphemeris; (2) the ability to represent a satellite ephemeris over several orbits; (3) guaranteed accuracy to within prescribed tolerance over the time interval of consideration; and (4) fast processing. These features are imposed with an eye towards adapting the approximation for use on microprocessor applications in which storage is limited and real time processing is required.

Pickard, H. M.↗
NASA NTRS1979

A Study of Linear Approximation Techniques for SAR Azimuth Processing

The application of the step transform subarray processing techniques to synthetic aperture radar (SAR) was studied. The subarray technique permits the application of efficient digital transform computational techniques such as the fast Fourier transform to be applied while offering an effective tool for range migration compensation. Range migration compensation is applied at the subarray level, and with the subarray size based on worst case range migration conditions, a minimum control system is achieved. A baseline processor was designed for a four-look SAR system covering approximately 4096 by 4096 SAR sample field every 2.5 seconds. Implementation of the baseline system was projected using advanced low power technologies. A 20 swath is implemented with approximately 1000 circuits having a power dissipation of from 70 to 195 watts. The baseline batch step transform processor is compared to a continuous strip processor, and variations of the baseline are developed for a wide range of SAR parameters.

Martinson, L. W.↗
NASA NTRS1978

A note on obtaining an approximate value for the period of a periodic solution of x-double prime = -V prime /x/

The first integral of x-double prime = - V prime (x) yields an integral for the period of a periodic solution, if such exists. In general, this integral cannot be evaluated. By means of an approximate solution along with the minimization of a mean-square error, one can obtain an approximate value for the period in terms of the amplitude of the motion. The calculated period agrees very well with the period obtained by means of numerical integration for the case of orbit-orbit resonance involving the motion of two satellites of a planet. The same method is applied to obtain an alternative derivation of the first Krylov-Bogoliuboff averaging method in nonlinear mechanics.

Lass, H.↗
NASA NTRS1979

Approximations for proton excitation - Erratum and extension

Kastner (1977) proposed relatively simple approximations for proton excitation in coronal ions, which yield both excitation rate coefficients and excitation cross sections. An error in Kastner's expression for one of the partial excitation rate coefficients is corrected. The expression for excitation cross section is extended to higher energies, and the resulting expression for the other partial rate coefficient is given. Results obtained with the corrected and extended total excitation rate coefficient are presented for several representative transitions in Ca XIII, Ca XV, Fe X, Fe XIII, Fe XIV, Fe XVIII, and S X. The corrected and extended approximation is expected to yield excitation rates reliably within 50%.

Kastner, S. O.↗
NASA NTRS1979

Rotational excitation of symmetric top molecules by collisions with atoms. II - Infinite order sudden approximation

The infinite order sudden (IOS) approximation is extended to rotational excitation of symmetric tops by collisions with atoms. After development of a formalism for 'primitive' or 'one-ended' tops, proper parity-adapted linear combinations describing real rotors are considered and modifications needed for asymmetric rigid rotors are noted. The generalized spectroscopic relaxation cross sections are discussed. IOS calculations for NH3-He and H2CO-He are performed and compared with more accurate calculations, and the IOS approximation is found to provide a reasonably accurate description.

Green, S.↗
NASA NTRS1979

Radiative transfer in spherical dust shells using a generalized two-stream Eddington approximation

Application of a generalized two-stream Eddington approximation to the problem of radiative transfer in extended, spherically symmetric dust shells is presented. It is assumed that the radiation field can be characterized by the mean intensity, the flux, and a positionally dependent direction cosine specifying the division into two solid-angle ranges. The direction cosine is not specified a priori and is a function of the geometry, opacity, and emissivity in the dust shell. A multiple-grain-size multiple-temperature-distribution dust shell is postulated in which isotropic and anisotropic scattering as well as absorption and thermal reemission are allowed. A program has been developed that solves for the multiple temperature distributions by applying the constraint of radiative equilibrium to each grain size, and then calculates emergent fluxes. Results of one such calculation are presented for a model dust shell having a maximum optical depth (approximately 41) in the visible, clearly showing large optical extinction and a moderate infrared excess.

Haisch, B. M.↗
NASA NTRS1978

A sequential method for spline approximation with variable knots

In this paper we describe a method for approximating a waveform by a spline. The method is quite efficient, as the data are processed sequentially. The basis of the approach is to view the approximation problem as a question of estimation of a polynomial in noise, with the possibility of abrupt changes in the highest derivative. This allows us to bring several powerful statistical signal processing tools into play. We also present some initial results on the application of our technique to the processing of electrocardiograms, where the knot locations themselves may be some of the most important pieces of diagnostic information.

Mier Muth, A. M.↗
NASA NTRS1978

Computational test of the infinite order sudden approximation for excitation of linear rigid rotors by collisions with atoms

The infinite order sudden approximation for excitation of linear rigid rotors by collisions with atom is tested by comparing integral state-to-state cross sections with accurate close coupling and coupled states results. The systems studied are HCl-Ar, HCl-He, CO-He, HCN-He, CS-H2 and OCS-H2. With the exception of diatomic hydrides (e.g., HCl) which have atypically large rotational constants the method is found to be very accurate to remarkably low collision energies. This approximation should generally be extremely useful for thermal energy collisions.

Green, S.↗
NASA NTRS1979

Approximate convective heating equations for hypersonic flows

Laminar and turbulent heating-rate equations appropriate for engineering predictions of the convective heating rates about blunt reentry spacecraft at hypersonic conditions are developed. The approximate methods are applicable to both nonreacting and reacting gas mixtures for either constant or variable-entropy edge conditions. A procedure which accounts for variable-entropy effects and is not based on mass balancing is presented. Results of the approximate heating methods are in good agreement with existing experimental results as well as boundary-layer and viscous-shock-layer solutions.

Zoby, E. V.↗