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Results for “Approximation methods”

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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Plate measurement techniques and reduction methods used by the West German satellite observers, and resulting consequences for the observation

The West German tracking stations are equipped with ballistic cameras. Plate measurement and plate reduction must therefore follow photogrammetric methods. Approximately 100 star positions and 200 satellite positions are measured on each plate. The mathematical model for spatial rotation of the bundle of rays is extended by including terms for distortion and internal orientation of the camera as well as by providing terms for refraction which are computed for the measured coordinates of the star positions on the plate. From the measuring accuracy of the plate coordinates it follows that the timing accuracy for the exposures has to be about one millisecond, in order to obtain a homogeneous system.

Deker, H.↗
NASA NTRS1972

The estimation of galactic cosmic ray penetration and dose rates

This study is concerned with approximation methods that can be readily applied to estimate the absorbed dose rate from cosmic rays in rads - tissue or rems inside simple geometries of aluminum. The present work is limited to finding the dose rate at the center of spherical shells or behind plane slabs. The dose rate is calculated at tissue-point detectors or for thin layers of tissue. This study considers cosmic-rays dose rates for both free-space and earth-orbiting missions.

Burrell, M. O.↗
NASA NTRS1972

Locally nonsimilar solutions for radiating shock layer about smooth axisymmetric bodies

Locally nonsimilar solutions for nongray radiating shock layers about smooth axisymmetric bodies have been obtained based on a newly developed approximate method. Good agreement is found with numerical solutions for inviscid cases (both radiating and nonradiating) and with series solutions for the radiating viscous case. For the inviscid case, the effect of radiative cooling is to destroy the entropy layer; at a distance far from the stagnation point, the shock layer is nearly isothermal. For the viscous case, the radiative wall flux approaches that of the inviscid case at a distance far downstream of the stagnation point. The method can also treat surface mass injection.

Chou, Y. S.↗
NASA NTRS1972

Evaluation of one-dimensional approximations for radiative transport in blunt body shock layers

One-dimensional approximations for the nongray radiative flux and flux divergence in radiating shock layers about a blunt entry body are compared with an exact three-dimensional treatment. A coupled radiative-gasdynamic analysis of the shock layer flow about the entire body provided the thermodynamic field used in these comparisons. In terms of calculating the total energy lost by the shock layer, the one-dimensional approximations to the radiative flux divergence are accurate to within a few percent. In terms of calculating the surface flux, the one-dimensional approximations introduce the largest errors of approximately 15 percent near the stagnation point. The source of these errors is the slab-like geometric representation of the shock layer inherent in all one-dimensional models. Finally, for both the radiative flux and its divergence, the tangent slab approximation provides more accurate results than differential approximation methods.

Wilson, K. H.↗
NASA NTRS1972

Vortex equations: Singularities, numerical solution, and axisymmetric vortex breakdown

A method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows. The method approximates the axial velocity and circulation profiles by series of exponentials having (N + 1) and N free parameters, respectively. Formal integration results in a set of (2N + 1) ordinary differential equations for the free parameters. The governing equations are shown to have an infinite number of discrete singularities corresponding to critical values of the swirl parameters. The computations point to the controlling influence of the inner core flow on vortex behavior. They also confirm the existence of two particular critical swirl parameter values: one separates vortex flow which decays smoothly from vortex flow which eventually breaks down, and the second is the first singularity of the quasi-cylindrical system, at which point physical vortex breakdown is thought to occur.

Bossel, H. H.↗
NASA NTRS1972

A numerical study of electromagnetic scattering from ocean like surfaces

The integral equations describing electromagnetic scattering from one dimensional conducting surfaces are formulated and numerical results are presented. The results are compared with those obtained using approximate methods such as physical optics, geometrical optics, and perturbation theory. The integral equation solutions show that the surface radius of curvature must be greater than 2.5 wavelengths for either the physical optics or geometric optics to give satisfactory results. It has also been shown that perturbation theory agrees with the exact fields as long as the root mean square surface roughness is less than one-tenth of a wavelength.

Lentz, R. R.↗
NASA NTRS1972

Anode heat transfer for a flowing argon plasma at elevated electron temperature.

Theoretical investigation of heat transfer from a preionized gaseous plasma flowing over an anode surface at an elevated electron temperature in the presence of an electric field normal to the surface. A laminar boundary layer is considered in which only the velocity profile is locally similar and fluid properties are assumed to change uniformly in the gas flow direction. Results obtained by an approximation method show that for moderate current densities, the velocity and temperature distributions are insensitive to current. In addition, the effect of elevated electron temperature is negligible on convective heat transfer, but is significant for the overall heat transfer due to the enthalpy transport by current. Total heat flux to the anode is obtained by evaluating the Nusselt number and adding terms due to the potential drop in the sheath and the surface work function.

Bose, T. K.↗
NASA NTRS1972

The inverse scattering problem for transmission lines

A number of exact and approximate methods for solving the inverse scattering problem for transmission lines are reviewed. In particular, the application to transmission lines of Marcenko's version of the Gelfand-Levitan exact method for the quantum mechanical problem is compared with a more direct approach based on a different version of the Gelfand-Levitan method. In addition, some aspects of the lack of uniqueness of solutions are discussed, and some open questions related to the inverse scattering problem are suggested.

Kay, I.↗
NASA NTRS1972

Time-dependent Structural Analysis of Metal-epoxy Composites

In an effort to reduce structural weight while maintaining structural integrity on the space shuttle and other proposed space vehicles, various composite materials are being evaluated to determine their applicability and reliability in load carrying situations. While most of the composites being considered for structural components are of the metal-metal type, there are some applications for which metal-epoxy composites are proposed. An approximate method is presented to analyze plane stress orthotropic linear viscoelastic problems under isothermal conditions. A computer program which is based on the method was used to solve a simple uniaxial creep problem for a Maxwell type material. This solution is presented and compared with the analytical solution.

Dehoff, P. H.↗
NASA NTRS1972

Shielding of manned space vehicles against protons and alpha particles

The available information on the shielding of manned space vehicles against protons and alpha particles is summarized. The emphasis is placed on shielding against Van Allen belt protons and against solar-flare protons and alpha particles, but information on shielding against galactic cosmic rays is also presented. The approximation methods for use by nonexperts in the space shielding field are those that are standard in the space shielding literature.

Alsmiller, R. G., Jr.↗
NASA NTRS1973

Signal-to-noise ratios in coherent soft limiters

Expressions for the output signal-to-noise power ratio of a bandpass soft limiter followed by a coherent detection device are presented and discussed. It is found that a significant improvement in the output signal-to-noise ratio at low input SNRs can be achieved by such soft limiters as compared to hard limiters. This indicates that the soft limiter may be of some use in the area of threshold extension. Approximation methods for determining output signal-to-noise spectral densities are also presented.

Lesh, J. R.↗
NASA NTRS1972

Optimum performance of static propellers and rotors.

A criterion for the optimum performance of static propellers and hovering helicopter rotors is developed. Numerical results are presented for the optimum radial distributions of circulation and inflow at the propeller disk and relating the optimum power coefficient and the figure of merit to the thrust coefficient. It is shown that the present theory, which fully accounts for the effect of slipstream rotation, predicts optimum distributions of circulation and inflow that differ significantly from those based on approximate methods.

Wu, J. C.↗
NASA NTRS1973

Refraction of acoustic duct waveguide modes by exhaust jets.

The refraction of acoustic duct waveguide modes emitted from the open end of a semiinfinite rectangular duct by a jet-like exhaust flow is studied theoretically. The problem is formulated as a Wiener-Hopf problem and is ultimately solved by an approximate method due to Carrier and Koiter. Continuity of transverse acoustic particle displacement and of acoustic pressure is assumed at the jet/still-air interface. The solution exhibits several features of the acoustics of moving media such as a source convection effect, zones of relative silence, and simple refraction. Plots of far-field directivity patterns are presented for several cases and show refraction effects to be important even at modest exhaust Mach numbers of order 0.3. Only subsonic exhaust Mach numbers are considered.

Mani, R.↗
NASA NTRS1973

Role of pressure transients in the detection and identification of lunar surface gas sources.

The dynamic behavior of neutral gases emitted from lunar surface sources is investigated. Pressure transients to be expected from several types of possible lunar surface sources are constructed. An approximate method is developed to estimate the source-sensor separation distance and the amount of effluent release. The case for which the source location and effluent molecular weight can be determined from ancillary data is discussed. It is shown that, if such data are available, pressure transients detected by either Apollo lunar surface experiment package ion spectrometers or cold cathode gages can be used to determine the release rate and the total amount of effluent release from the source.

Hall, F. G.↗
NASA NTRS1974

Signal-to-noise ratios in coherent soft limiters

Expressions for the output signal-to-noise power ratio of a bandpass soft limiter followed by a coherent detection device are presented and discussed. It is found that a significant improvement in the output signal-to-noise ratio (SNR) at low input SNR's can be achieved by such soft limiters as compared to hard limiters. This indicates that the soft limiter may be of some use in the area of threshold extension. Approximation methods for determining output signal-to-noise spectral densities are also presented.

Lesh, J. R.↗
NASA NTRS1974

Analysis of bilinear stochastic systems

Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes is considered. After defining the systems of interest, the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems are discussed. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.

Willsky, A. S.↗
NASA NTRS1975

Estimation and Analysis of Nonlinear Stochastic Systems

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

Marcus, S. I.↗