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At least 253 records · Page 14

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NASA NTRS1975

Pressure perturbation in EHD contacts due to an ellipsoidal asperity

The pressure fluctuations around an ellipsoidal asperity tip at the inlet region of an elastohydrodynamic contact is determined by solving a perturbed Reynolds equation assuming that the asperity shape is unaffected by the perturbed pressure. Results are presented as the amplitude of the perturbed pressure as a function of ellipticity ratio, maximum Hertzian pressure, nominal EHD film thickness, asperity size, asperity height, and pressure viscosity coefficient. For the case of simple sliding between a smooth surface and a stationary asperity, a comparison is also made between the results for large ellipticity ratios and the pressure fluctuations obtained by using a previous line contact EHD analysis for a two-dimensional asperity ridge. The agreement is found to be close for moderate Hertzian pressure and relatively thick EHD film thickness.

Chow, L. S. H.↗

NASA NTRS1976

On the equations governing the electromagnetic perturbations of the Kerr black hole

Teukolsky's (1973) radial wave equation for electromagnetic perturbations about a rotating black hole is transformed into a one-dimensional wave equation with a real and short-range potential. A general technique for transforming one wave equation into another is described, and it is shown how an equation with a complex potential can be transformed into one with a purely real potential. These general techniques are then used to transform Teukolsky's equation into a wave equation whose potential is purely real and of short range. This equation is found to provide a simple formulation of the concepts of superradiant scattering and the conservation of energy underlying the present electromagnetic perturbations. It is noted that the techniques employed are general enough to be applicable when the spin weight is plus or minus 2, making a 'real-potential' formulation of the problem of gravitational perturbations about a Kerr black hole most likely.

Detweiler, S.↗

NASA NTRS1977

A perturbation solution for interlaminar stresses in bidirectional laminates

The paper considers a thin elastic bidirectional symmetric composite laminate subjected to a uniform axial strain. All interlaminar stresses are determined by a zeroth-order perturbation analysis of the governing equations. The method of solution considers the laminate to be composed of an interior region (removed from the free edge) and a boundary layer region. The interior region is analyzed by dropping terms related to powers of the thickness-to-width ratio in the dimensionless elasticity equations. The boundary layer region is studied by introducing a stretching transformation to the governing equations. A uniform solution is then formed by satisfying Prandtl's matching principle of perturbation theory. Results for a four-layer bidirectional graphite-epoxy laminate are compared with existing finite-difference results. It is shown that the perturbation analysis provides more insight into the stress distribution near the free edge.

Hsu, P. W.↗

NASA NTRS1977

Perturbation solutions for blade-to-blade surfaces of a transonic compressor

The paper describes a perturbation method for turbomachinery calculations, particularly where it is necessary to carry out a number of calculations for closely-related flows such as are needed in a parametric study. The method is applied for solving a model problem involving blade-to-blade surfaces of a transonic compressor. Basically, the method makes use of a previously calculated base solution to determine first-order changes in the flow field due to variations in one or more of a variety of geometrical or flow field parameters. The fundamental assumption associated with the perturbation solution is that the magnitude of the deviations from the base solution lies within the range of a linear perturbation analysis. Comparisons are made for results obtained, by varying the thickness ratio of an unstaggered nonlifting cascade composed of biconvex profiles in a flow with an oncoming freestream Mach number of 0.60.

Stahara, S. S.↗

NASA NTRS1977

Application of perturbation methods to improve analytical model correlation with test data

A linear perturbation method developed by White (1972) to improve the correlation between analytical models and experimental data is applied to modeling of the Viking Propulsion Subsystem (VPS), flown successfully as part of the Viking Spacecraft launch of 1975. Analytical models and modal test data developed for the VPS are employed in the application; a set of mathematically generated data and a corresponding perturbed analytical model, representative of actual flight hardware, are also subjected to the White method. It is found that the linear perturbation method does not yield a single unique improved model.

Garba, J. A.↗

NASA NTRS1978

Interactions of simultaneous perturbations of stratospheric photochemistry

The combined effects of two specific ozone perturbation mechanisms are examined. The need to look back to predictions of the near past as well as the future as a means of testing model results is emphasized. The two perturbations examined are that due to chlorofluoromethane (CFM) release and that due to the air pollutants CO and nitrogen oxide. A steady-state model is used to investigate the characteristics of the stratospheric-tropospheric photochemical system for differing levels of CO and nitrogen oxide fluxes at the ground and for simultaneously changing the stratospheric from CFM release. Two basic scenarios chosen to illustrate the competing effects of the two types of perturbation use the time-dependence for chlorine radical buildup calculated for constant continued release of CFM's.

Butler, D. M.↗

NASA NTRS1979

A study of the application of singular perturbation theory

A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

Mehra, R. K.↗

NASA NTRS1979

Singular perturbations and the sounding rocket problem

In this paper, Goddard's problem of maximizing the final altitude of a sounding rocket (a singular problem of optimal control) is analyzed using singular perturbation methods. The problem is first cast in singular perturbation form and then solved to zero order by adding boundary-layer corrections to the reduced solution. For a quadratic drag law, a closed-form solution is obtained, although consideration of a numerical example indicates that this solution is not useful for practical sounding rockets. However, use of state variable transformations allows a very accurate numerical approximation to be constructed. It is concluded that application of singular perturbation methods to the well-known sounding rocket problem indicates that these methods may have utility in dealing with singular problems of optimal control.

Ardema, M. D.↗

NASA NTRS1980

Spontaneous emission of radiation from localized Langmuir perturbation

The radiation at the first and second harmonics of the electron plasma frequency from localized Langmuir oscillations is computed for a field-free plasma. The localized perturbations are assumed to have cylindrical symmetry about the direction of propagation of the localized perturbation. It is shown that when the wavelengths of the excited modes are much greater than the scale lengths of the Langmuir perturbation, a quadrupole radiation pattern is recovered for emission at twice the electron plasma frequency. An application to type III solar radio bursts is discussed briefly.

Freund, H. P.↗

NASA NTRS1981

A rapid perturbation procedure for determining nonlinear flow solutions: Application to transonic turbomachinery flows

Perturbation procedures and associated computational codes for determining nonlinear flow solutions were developed to establish a method for minimizing computational requirements associated with parametric studies of transonic flows in turbomachines. The procedure that was developed and evaluated was found to be capable of determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameter. Coordinate straining is employed to account for the movement of discontinuities and maxima of high gradient regions due to the perturbation. The development and results reported are for the single parameter perturbation problem. Flows past both isolated airfoils and compressor cascades involving a wide variety of flow and geometry parameter changes are reported. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure.

Stahara, S. S.↗

NASA NTRS1980

Magnetohydrodynamic perturbations of Robertson-Walker universes and of anisotropic Bianchi type-I universes

Magnetohydrodynamic (MHD) perturbations in flat Robertson-Walker universes were analyzed, emphasizing their effects on galaxy formation. The Newtonian approximation is used. There is no increase in the growth rates beyond those of the usual perturbed Robertson-Walker models; the MHD modes extract as much energy as they contribute. Some global properties of fully MHD Bianchi I relativistic models are analyzed including vorticity, fluid accelerations, and dissipative effects. The time dependence of perturbations of a fully MHD diagonal Bianchi I cosmology is studied, with an enhanced growth rate of the density contrast of t found which is still not exponential Jeans-type growth. This indicates that a more detailed analysis is needed if a solution to the galaxy formation problem in MHD cosmologies is to be found.

Fennelly, A. J.↗

NASA NTRS1981

Perturbation of transonic flow with shocks

A general formulation of the perturbation problem is studied, and a new approach, perturbation sequence expansion, is introduced for handling shock disturbances. The method is applied to unsteady effects, three-dimensional corrections to axisymmetric and two-dimensional flows, and wind tunnel corrections. The perturbation equations are nonlinear and can be solved by shock capturing methods.

Hafez, M.↗

NASA NTRS1982

The effect of perturbations of convective energy transport on the luminosity and radius of the Sun

The response of solar models to perturbations of the efficiency of convective energy transport is studied for a number of cases. Such perturbations primarily effect the shallow superadiabatic layer of the convective envelope (at depth of approx. 1000 km below the photosphere). Independent of the details of the perturbation scheme, the resulting change in the solar radius is always very small compared to the change in luminosity. This appears to be true for any physical mechanism of solar variability which operates in the outer layers of the convection zone. Changes of the solar radius have been inferred from historical observations of solar eclipses. Considering the constraints on concurrent luminosity changes, this type of solar variability must be indicative of changes in the solar structure at substantial depths below the superadiabatic layer of the convective envelope.

Endal, A. S.↗

NASA NTRS1981

Theoretical and lidar studies of the density response of the mesospheric sodium layer to gravity wave perturbations

The density response of atmospheric layers to gravity waves is developed in two forms, an exact solution and a perturbation series solution. The degree of nonlinearity in the layer density response is described by the series solution whereas the exact solution gives insight into the nature of the responses. Density perturbation in an atmospheric layer are shown to be substantially greater than the atmospheric density perturbation associated with the propagation of a gravity wave. Because of the density gradients present in atmospheric layers, interesting effects were observed such as a phase reversal in the linear layer response which occurs near the layer peak. Once the layer response is understood, the sodium layer can be used as a tracer of atmospheric wave motions. A two dimensional digital signal processing technique was developed. Both spatial and temporal filtering are utilized to enhance the resolution by decreasing shot noise by more han 10 dB. Many of the features associated with a layer density response to gravity waves were observed in high resolution density profiles of the mesospheric sodium layer. These include nonlinearities as well as the phase reversal in the linear layer response.

Shelton, J. D.↗

NASA NTRS1982

The effect of perturbation of convective energy transport on the luminosity and radius of the sun

The response of solar models to perturbations of the efficiency of convective energy transport is studied. Such perturbations primarily affect the shallow superadiabatic layer of the convective envelope. Independent of the details of the perturbation scheme, the resulting change in the solar radius is always very small compared to the change in luminosity. This appears to be true for any physical mechanism of solar variability which operates in the outer layers of the convection zone. Changes of the solar radius have been inferred from historical observations of solar eclipses in 1715 and 1925. Considering the constraints on concurrent luminosity changes, this type of solar variability must be indicative of changes in the solar structure at substantial depths below the superadiabatic layer of the convective envelope.

Endal, A. S.↗

NASA NTRS1983

Perturbed particle disks

The velocity ellipsoid in a particle disk near an isolated satellite resonance is determined by solving the Boltzmann moment equations, and solutions are obtained that are stationary functions of the azimuthal angle in a coordinate frame which rotates with the pattern speed of the perturbation potential. The magnitude of the deformation rate tensor in a perturbed particle disk is bounded from above by an expression which includes the orbital angular velocity, the optical depth, and a dimensionless constant of order unity. It is also found that, in sufficiently perturbed regions, there are ranges of azimuthal angle over which the radial component of the angular momentum flux is negative. It is also possible for the angular momentum luminosity to be negative. These results are pertinent to the understanding of sharp edges and density wave decay in planetary rings.

Borderies, N.↗

NASA NTRS1984

Implementation of uniform perturbation method for potential flow past axisymmetric and two-dimensional bodies

The aerodynamic characteristics of potential flow past an axisymmetric slender body and a thin airfoil are calculated using a uniform perturbation analysis method. The method is based on the superposition of potentials of point singularities distributed inside the body. The strength distribution satisfies a linear integral equation by enforcing the flow tangency condition on the surface of the body. The complete uniform asymptotic expansion of its solution is obtained with respect to the slenderness ratio by modifying and adapting an existing technique. Results calculated by the perturbation analysis method are compared with the existing surface singularity panel method and some available analytical solutions for a number of cases under identical conditions. From these comparisons, it is found that the perturbation analysis method can provide quite accurate results for bodies with small slenderness ratio. The present method is much simpler and requires less memory and computation time than existing surface singularity panel methods of comparable accuracy.

Wong, T. C.↗

NASA NTRS1984

An analytic solution for the orbital perturbations of the Venus Radar Mapper due to gravitational harmonics

Hill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a non-spherical body. The rotation of the central planet about its spin-axis is not considered in the analysis. The perturbations are restricted to the planetary gravitational harmonics only. An extremely simple algorithm is derived to transform the spherical harmonic potentials to the orbital coordinate system, and the resulting accelerations are shown to be simply trigonometric functions of the true anomaly. With the principal matrix solution for the differential equations of the adjoint system given in closed form, the orthogonality of the trigonometric functions makes it possible to obtain an analytic solution for the non-homogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying well-known results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.

Vijayaraghavan, A.↗