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Results for “Perturbative 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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

A numerical method for relating two- and three-dimensional pressure distributions on transonic wings

This paper presents a preliminary design method for determining a wing's design pressure distribution and geometry based on airfoil normal Mach numbers and airfoil loading. In this method, the perturbation velocities in supercritical regions are computed from airfoil transonic normal Mach numbers and include the influence of local sweep, taper, and three-dimensional induced velocities, so that the appearance and strength of shocks can be expected to resemble those of the airfoil. The velocities in subcritical wing regions are scaled first with simple sweep theory, and then to achieve the desired load distribution. The method was applied to the design of an oblique flying wing, using a linear potential method. The required wing area could be reduced by 14 percent using this method rather than simple sweep theory.

Kroo, Ilan↗
NASA NTRS1988

Scattering of electromagnetic waves from a periodic surface with random roughness

Equations for the scattering of electromagnetic waves from a randomly perturbed periodic surface have been formulated using the extended boundary condition method and solved using the small perturbation method. Surface currents and scattered fields are solved for up to the second order. The results indicate that as the correlation length of the random roughness increases, the bistatic scattering patterns of the scattered fields show several beams associated with each Bragg diffraction direction of the periodic surface. The beam shape becomes broader with smaller correlation length. Results obtained using the Kirchhoff approximation are found to agree well with the present results for the hh and vv polarized backscattering coefficients for small angles of incidence.

Yueh, H. A.↗
NASA NTRS1972

A study of numerical methods for computing reentry trajectories for shuttle-type space vehicles

The reuseable exterior insulation system (REI) is studied to determine the optimal reentry trajectory for a space shuttle, which minimizes the heat input to the fuselage. The REI is composed of titanium, covered by a surface insulation material. The method of perturbation functions was used to generate the trajectories, and proved to be an effective technique for generating families of solutions, once an initial trajectory has been obtained.

Source record↗
NASA NTRS1972

Hydrogen atom in intense magnetic field.

The structure of a hydrogen atom situated in an intense magnetic field is investigaged. Three approaches are employed. An elementary Bohr picture establishes a crucial magnetic field strength, H sub a approximately equal to 5 x 10 to the 9th G. Fields in excess of H sub a are intense in that they are able to modify the characteristic atomic scales of length and binding energy. A second approach solves the Schrodinger equation by a combination of variational methods and perturbation theory. It yields analytic expressions for the wave functions and energy eigenvalues. A third approach determines the energy eigenvalues by reducing the Schrodinger equation to a one-dimensional wave equation, which is then solved numerically. Energy eigenvalues are tabulated for field strengths of 2 x 10 to the 10th G and 2 x 10 to the 12th G. It is found that at 2 x 10 to the 12th G the lowest energy eigenvalue is changed from -13.6 to about -180 eV in agreement with previous variational computations.

Canuto, V.↗
NASA NTRS1973

Investigation into the propagation of Omega very low frequency signals and techniques for improvement of navigation accuracy including differential and composite omega

An analysis of Very Low Frequency propagation in the atmosphere in the 10-14 kHz range leads to a discussion of some of the more significant causes of phase perturbation. The method of generating sky-wave corrections to predict the Omega phase is discussed. Composite Omega is considered as a means of lane identification and of reducing Omega navigation error. A simple technique for generating trapezoidal model (T-model) phase prediction is presented and compared with the Navy predictions and actual phase measurements. The T-model prediction analysis illustrates the ability to account for the major phase shift created by the diurnal effects on the lower ionosphere. An analysis of the Navy sky-wave correction table is used to provide information about spatial and temporal correlation of phase correction relative to the differential mode of operation.

Source record↗
NASA NTRS1975

Computational study of nonlinear plasma waves. I - Simulation model and monochromatic wave propagation. II - Sideband instability and satellite growth

A hybrid plasma simulation model is described and applied to the study of electrostatic wave propagation in a one-dimensional Maxwellian plasma with periodic boundary conditions. The model employs a cloud-in-cell scheme which can drastically reduce the fluctuations in particle simulation models and greatly ease the computational difficulties of the Vlasov equation approach. A grid in velocity space is introduced and the particles are represented by points in the x-v phase space. The model is tested first in the absence of an applied signal and then in the presence of a small-amplitude perturbation. The method is also used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories.

Matsuda, Y.↗
NASA NTRS1975

A uniformly valid solution for motion about the interior libration point of the perturbed elliptic-restricted problem

Bounded motion about Lagrange collinear libration points is considered for a perturbed elliptic-restricted problem. A practical application is the motion of a satellite near a libration point collinear with the sun and the earth-moon barycenter. Such a system is treated here as an earth-sun-satellite elliptic restricted problem with lunar perturbations. The method of dual time scales is utilized to develop a uniformly valid three-dimensional analytical solution to the satellite's equations of motion. The analytical development applies somewhat generally to that class of four-body problems where the second primary mass is much greater than the first, and the third primary mass is much greater than the second.

Richardson, D. L.↗
NASA NTRS1979

Analytic theory of orbit contraction due to atmospheric drag

Theory of space vehicle flight in near vacuum and in a planetary atmosphere is unified for the case of a spherically symmetric atmosphere with exponential variation of density with height. Dimensionless equations of motion are established that bridge the gap between satellite theory and entry theory. Integration is done by Poincare's method of perturbations. Solutions for the dimensionless semimajor axis are numerically obtained.

Vinh, N. X.↗
NASA NTRS1984

Scattering of electrons from neon atoms

Scattering of electrons from neon atoms is investigated by the polarized-orbital method. The perturbed orbitals calculated with use of the Sternheimer approximation lead to the polarizability 2.803 a(0)-cube in fairly good agreement with the experimental value 2.66 a(0)-cube. Phase shifts for various partial waves are calculated in the exchange, exchange-adiabatic, and polarized-orbital approximations. They are compared with the previous results. The calculated elastic differential, total, and momentum-transfer cross sections are compared with the experimental results. The polarized-orbital approximation yields results which show general improvement over the exchange-adiabatic approximation.

Dasgupta, A.↗
NASA NTRS1986

Test of the Hipparcos payload in the Liege vacuum facility focal

The Liege thermal vacuum optical bench (FOCAL) was used to control the mechanical stability of the structure of the European Space Agency's HIPPARCOS astrometry payload. The payload is designed to measure angles of .001 arcsec between stars during 2.5 years and this accuracy can only be reached with the extreme stability of the device. The structure of the payload is made of carbon fiber; it is thermally stabilized with an accuracy of .01 degrees C. During the test, the payload is enclosed in a shell made of shrouds having a geometry close to the shading structure of the spacecraft. The shroud temperatures are defined by the conditions in orbit, e.g., the spacecraft is spinning in front of the Sun with a period of two hours and the temperature of the shrouds is cycled around the payload with a 2 hour period. In order to avoid disturbances by vibrations, the payload is put on an adapter interfaced with the optical bench and the seismic block; the shrouds are supported by a carrier with no direct interface with the table. This method avoids perturbances brought about by the cooling fluid of the shrouds.

Jamar, C.↗
NASA NTRS1987

Torsion effect on fully developed flow in a helical pipe

Two techniques, a series expansion method of perturbed Poiseuille flow valid for low Dean numbers and a solution of the complete Navier-Stokes equation applicable to intermediate Dean values, are used to investigate the torsion effect on the fully developed laminar flow in a helical pipe of constant circular cross section. For the secondary flow patterns, the results show that the presence of torsion can produce a significant effect if the ratio of the curvature to the torsion is of order unity. The secondary flow is distorted in these cases. It is noted that the torsion effect is, however, usually small, and that the secondary flow has the usual pattern of a pair of counter-rotating vortices of nearly equal strength.

Kao, Hsiao C.↗
NASA NTRS1987

Sliding regimes on slow manifolds of systems with fast actuators

In this article the slow manifold of a system with actuator parasitics is used as a sliding surface on which a Variable Structure Controller recovers the qualitative properties of the reduced order, closed loop system obtained from an ideal actuator-based feedback controller design. Illustrative examples are presented, where (1) the simplicity of reduced order singular perturbation design methods; and (2) the robustness of Variable Structure sliding modes, are advantageously combined.

Sira-Ramirez, Hebertt↗
NASA NTRS1988

Planetary detection techniques - An overview

Interest in the search for planets around other stars is due to its connection with SETI, the desire to understand the formation of stars and planetary systems, and curiosity about the earth's place in the cosmic neighborhood. Proposed techniques include direct imaging, detection of transits, and detection of stellar radial velocity and positional perturbations. Each method has advantages and is effective at detecting different kinds of planets. It is concluded that the fundamental questions in this field should be answered during the next decade.

Scargle, J. D.↗
NASA NTRS1989

Time-resolved simplified chemical kinetics modelling using computational singular perturbation

A CO-CH4-air reaction system is used to demonstrate the computational singular perturbation (CSP) method for deriving time-resolved simplified chemical kinetics models. CSP provides a programmable algorithm to group the given collection of elementary reactions into reaction groups which are ordered according to their speed. The concept of Importance Index k(m)exp s is introduced: k(m)exp s is defined to be a number between 0 and 1 which measures the importance of the m-th reaction group to the s-th reactant and can readily be computed from data generated by CSP. It is suggested that the robustness of the solutions of the reaction system can be qualitatively assessed by inspecting the Importance Index data.

Lam, S. H.↗
NASA NTRS1989

Numerical investigation of the control of the secondary instability process in boundary layers

A numerical model has been developed for investigating boundary layer transition control for a flat plate boundary layer. Active control of a periodically forced boundary layer in an incompressible fluid is studied using surface heating techniques. The spatially evolving boundary layer is simulated. The Navier-Stokes and energy equations are integrated using a fully implicit finite difference/spectral method. Temperature perturbations are introduced locally along finite heater strips to directly attenuate the instability waves in the flow. A feedback control loop is employed in which a downstream sensor is used to monitor wall shear stress fluctuations. Active control of small amplitude two-dimensional and three-dimensional disturbances is numerically simulated. With proper phase control, in-phase reinforcement and out-of-phase attenuation are demonstrated. A receptivity study of the localized temperature perturbations is made. It is shown that narrow heater strips are more receptive in that they maximize the amplitude level of the disturbances in the flow. Active control of the early stages of the fundamental breakdown process is also numerically simulated. Control is achieved with either two-dimensional or three-dimensional control inputs.

Kral, L. D.↗
NASA NTRS1990

Reduced and simplified chemical kinetics for air dissociation using Computational Singular Perturbation

The Computational Singular Perturbation CSP methods is employed (1) in the modeling of a homogeneous isothermal reacting system and (2) in the numerical simulation of the chemical reactions in a hypersonic flowfield. Reduced and simplified mechanisms are constructed. The solutions obtained on the basis of these approximate mechanisms are shown to be in very good agreement with the exact solution based on the full mechanism. Physically meaningful approximations are derived. It is demonstrated that the deduction of these approximations from CSP is independent of the complexity of the problem and requires no intuition or experience in chemical kinetics.

Goussis, D. A.↗