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Results for “approximation theory”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Sudden stretching of a four layered composite plate

An approximate theory of laminated plates is developed by assuming that the extensioral and thickness mode of vibration are coupled. The mixed boundary value crack problem of a four layered composite plate is solved. Dynamic stress intensity factors for a crack subjected to suddenly applied stress are found to vary as a function of time and depend on the material properties of the laminate. Stress intensification in the region near the crack front can be reduced by having the shear modulus of the inner layers to be larger than that of the outer layers.

Sih, G. C.↗
NASA NTRS1980

Nonlinear axially symmetric circulations in a nearly inviscid atmosphere

The structure of certain axially symmetric circulations in a stably stratified, differentially heated, rotating Boussinesq fluid on a sphere is analyzed. A simple approximate theory (similar to that introduced by Schneider (1977)) is developed for the case in which the fluid is sufficiently inviscid that the poleward flow in the Hadley cell is nearly angular momentum conserving. The theory predicts the width of the Hadley cell, the total poleward heat flux, the latitude of the upper level jet in the zonal wind, and the distribution of surface easterlies and westerlies. Fundamental differences between such nearly inviscid circulations and the more commonly studied viscous axisymmetric flows are emphasized. The theory is checked against numerical solutions to the model equations.

Held, I. M.↗
NASA NTRS1981

Investigation of the effects of inlet shapes on fan noise radiation

The effect of inlet shape on forward radiated fan tone noise directivities was investigated under experimentally simplified zero flow conditions. Simulated fan tone noise was radiated to the far field through various shaped zero flow inlets. Baseline data were collected for the simplest baffled and unbaffled straight pipe inlets. These data compared well with prediction. The more general inlet shapes tested were the conical, circular, and exponential surfaces of revolution and an asymmetric inlet achieved by cutting a straight pipe inlet at an acute angle. Approximate theories were developed for these general shapes and some comparisons with data are presented. The conical and exponential shapes produced directivities that differed considerably from the baseline data while the circular shape produced directivities similar to the baseline data. The asymmetric inlet produced asymmetric directivities with significant reductions over the straight pipe data for some angles.

Clark, T. L.↗
NASA NTRS1981

The challenge of unsteady separating flows

It is noted that the general fluid dynamic problem of unsteady separation at most practical Reynolds numbers remains an unsolved one and that no completely reliable prediction techniques exist at the present time. The modern design engineer must therefore draw from a combination of approximate theories, empirical correlations of data, and finite difference programs based on uncertain physical modeling of turbulence. An attempt is made to describe the basic features of several representative classes of problems for which unsteady effects produce strong or unusual changes in the separation characteristics of the flow. The analysis concerns itself largely with external flow, and emphasis is placed on the physical phenomena involved.

Mccroskey, W. J.↗
NASA NTRS1981

Turbulence in deep radio occultations

The effects of turbulence in the focal region of spherical or weakly oblate refracting bodies on the evolute flashes associated with the crossing of the evolute of the planetary limb by an occulted spacecraft are investigated. The approximate theory of focal evolutes in oblate refractivity fields developed by Eshleman et al. (1979) is combined with a generalized weak scattering scintillation theory that includes the effect of focusing around a curved limb to obtain expressions for the scintillation index and power spectrum. Results are then applied to the radio observations of the crossing of the focal evolute of Jupiter by Voyager 1, in which no flash was detected, and to the effects of the solar coronal plasma on the gravitational lens of the sun.

Haugstad, B. S.↗
NASA NTRS1985

Conducting a thermal conductivity survey

A physically transparent approximate theory of phonon decay rates is presented starting from a pair potential model of the interatomic forces in an insulator or semiconductor. The theory applies in the classical regime and relates the 3-phonon decay rate to the third derivative of the pair potential. Phonon dispersion relations do not need to be calculated, as sum rules relate all the needed quantities directly to the pair potential. The Brillouin zone averaged phonon lifetime turns out to involve a dimensionless measure of the anharmonicity multiplied by an effective density of states for 3-phonon decay. Results are given for rare gas and alkali halide crystals. For rare gases, the results are in good agreement with more elaborate perturbation calculations. Comparison to experimental data on phonon linewidths and thermal conductivity are made.

Allen, P. B.↗
NASA NTRS1985

Integral functions of electron lateral distribution and their fluctuations in electron-photon cascades

Monte Carlo simulated lateral distribution functions for electrons of EPC developing in lead, at superhigh energies (.1-1 PeV) for depths t or = 60 c.u. delta t=1t. c.u. are presented. The higher moment characteristics, i.e., variation, asymmetry, excess, are presented along with analytical solutions for the same characteristics at fixed observation level calculated to theory approximations A and B by using numerical inversion of the Laplace transformation. The conclusion is made of a complex, usually non-Gaussian shape of the function of the particle number distribution within a circle of given radius at fixed depth.

Ivanenko, I. P.↗
NASA NTRS1986

Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems

The problem of estimating discontinuous coefficients, including locations of discontinuities, that occur in second order hyperbolic systems typical of those arising in I-D surface seismic problems is discussed. In addition, the problem of identifying unknown parameters that appear in boundary conditions for the system is treated. A spline-based approximation theory is presented, together with related convergence findings and representative numerical examples.

Lamm, P. K.↗
NASA NTRS1986

Equilibrium shapes of acoustically levitated drops

The quantitative determination of the shape of liquid drops levitated in an ultrasonic standing wave has provided experimental data on the radiation pressure-induced deformations of freely suspended liquids. Within the limits of small deviations from the spherical shape and small drop diameter relative to the acoustic wavelength, an existing approximate theory yields a good agreement with experimental evidence. The data were obtained for millimeter and submillimeter drops levitated in air under 1 g, where g is the sea level gravitational acceleration.

Trinh, E. H.↗
NASA NTRS1986

Coherent lidars based on intracavity heterodyning of echo signals

The development and technical realization of the method of laser sounding of the atmosphere based on the effects of mixing of reference and external fields of scattering inside a laser cavity are presented. An approximate theory of the method was developed on the basis of the investigations using the model of a three-mirror laser. The nonlinear effect of a wideband laser on frequency-dependent external influences of the atmosphere was investigated. The field measurements of gaseous composition of the atmosphere were performed on the basis of a given method of coherent reception using a tunable CO2 laser.

Zuev, V. E.↗
NASA NTRS1988

Effects of static equilibrium and higher-order nonlinearities on rotor blade stability in hover

The equilibrium and stability of the coupled elastic lead/lag, flap, and torsion motion of a cantilever rotor blade in hover are addressed, and the influence of several higher-order terms in the equations of motion of the blade is determined for a range of values of collective pitch. The blade is assumed to be untwisted and to have uniform properties along its span. In addition, chordwise offsets between its elastic, tension, mass, and aerodynamic centers are assumed to be negligible for simplicity. The aerodynamic forces acting on the blade are modeled using a quasi-steady, strip-theory approximation.

Crespodasilva, Marcelo R. M.↗
NASA NTRS1988

Estimation of the reaction rate for the formation of CH3O from H + H2CO - Implications for chemistry in the solar system

Troe's (1977) approximate theory is presently used in conjunction with transition state theory to estimate the rate coefficient of the reaction by which CO is reduced to CH4; attention is given to the role that may be played in the reduction process by the formation of the CH3O radical from H + H2CO. Attention is given to the implications of such a reaction (1) for the CO chemistry on Jupiter and within the solar nebula, (2) for the interpretation of such experimental results as those of Bar-Nun and Shaviv (1975) and Bar-Nun and Chang (1983), and (3) for organic synthesis in the prebiotic terrestrial atmosphere.

Yung, Yuk L.↗
NASA NTRS1988

Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems

The problem of estimating discontinuous coefficients, including locations of discontinuities, that occur in second-order hyperbolic systems typical of those arising in one-dimensional surface seismic problems, is considered. The problem of identifying unknown parameters that appear in boundary conditions for the system is addressed. A spline-based approximation theory is presented as well as related convergence findings and representative numerical examples.

Lamm, Patricia K.↗
NASA NTRS1989

CSM research: Methods and application studies

Computational mechanics is that discipline of applied science and engineering devoted to the study of physical phenomena by means of computational methods based on mathematical modeling and simulation, utilizing digital computers. The discipline combines theoretical and applied mechanics, approximation theory, numerical analysis, and computer science. Computational mechanics has had a major impact on engineering analysis and design. When applied to structural mechanics, the discipline is referred to herein as computational structural mechanics. Complex structures being considered by NASA for the 1990's include composite primary aircraft structures and the space station. These structures will be much more difficult to analyze than today's structures and necessitate a major upgrade in computerized structural analysis technology. NASA has initiated a research activity in structural analysis called Computational Structural Mechanics (CSM). The broad objective of the CSM activity is to develop advanced structural analysis technology that will exploit modern and emerging computers, such as those with vector and/or parallel processing capabilities. Here, the current research directions for the Methods and Application Studies Team of the Langley CSM activity are described.

Knight, Norman F., Jr.↗
NASA NTRS1983

Aerodynamically-driven condensate layer thickness distributions on isothermal cylindrical surfaces

A simple yet rather general mathematical model is presented for predicting the distribution of condensate layer thickness when aerodynamic shear is the dominant mechanism of liquid flow along the surface. The Newtonian condensate film is treated using well-known thin-layer (lubrication theory) approximations, and condensate supply is taken to be the result of either convective diffusion or inertial impaction. Illustrative calculations for a circular cylinder in a crossflow at Re = 100,000 reveal the consequences of alternate condensate arrival mechanisms and the existence of thicker reverse-flow films behind the position of gas boundary-layer separation. The present formulation is readily generalized to include transient liquid layer flows on noncircular objects of variable surface temperature, as encountered in turbine-blade materials testing or operation.

Rosner, D. E.↗
NASA NTRS1989

Interactive boundary-layer calculations of a transonic wing flow

Results obtained from iterative solutions of inviscid and boundary-layer equations are presented and compared with experimental values. The calculated results were obtained with an Euler code and a transonic potential code in order to furnish solutions for the inviscid flow; they were interacted with solutions of two-dimensional boundary-layer equations having a strip-theory approximation. Euler code results are found to be in better agreement with the experimental data than with the full potential code, especially in the presence of shock waves, (with the sole exception of the near-tip region).

Kaups, Kalle↗
NASA NTRS1989

Hybrid method in light scattering by an arbitrary particle

A hybrid method for light scattering by an arbitrary particle using the scattering-order formulation of the coupled dipole method is described. An arbitrary particle is divided into two or more segments, and the field scattered by the particle is obtained from the fields scattered by each segment together with the field due to interactions among segments. An exact or approximate theory is used to calculate the scattered field from each segment, and interactions are included using the scattering-order formulation of the coupled dipole method. Calculations show that for certain particles, this hybrid approach can require fewer computations and give more accurate results than the scattering-order method.

Singham, Shermila Brito↗
NASA NTRS1989

Computers boost structural technology

Derived from matrix methods of structural analysis and finite element methods developed over the last three decades, computational structures technology (CST) blends computer science, numerical analysis, and approximation theory into structural analysis and synthesis. Recent significant advances in CST include stochastic-based modeling, strategies for performing large-scale structural calculations on new computing systems, and the integration of CST with other disciplinary modules for multidisciplinary analysis and design. New methodologies have been developed at NASA for integrated fluid-thermal structural analysis and integrated aerodynamic-structure-control design. The need for multiple views of data for different modules also led to the development of a number of sophisticated data-base management systems. For CST to play a role in the future development of structures technology and in the multidisciplinary design of future flight vehicles, major advances and computational tools are needed in a number of key areas.

Noor, Ahmed K.↗