Earth satellite orbit computations. part i- diliberto theory final report
Earth satellite orbit computations - Diliberto general perturbation method application in improved coordinate system
COORDINATE SYSTEM↗
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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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Dielectric constant of vegetation at 8.5 GHz
Measurement of dielectric constant of vegetation at microwave frequencies by cavity perturbation method
MICROWAVE FREQUENCY↗
Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations, Phase 2
A comparison with NASA conducted simulator studies has shown that the approximate digital method for computing rotor blade flapping responses to random inputs, tentatively suggested in Phase I Report, gives with increasing rotor advance ratio the wrong trend. Consequently, three alternative methods of solution have been considered and are described: (1) an approximate method based on the functional relation between input and output double frequency spectra, (2) a numerical method based on the system responses to deterministic inputs and (3) a perturbation approach. Among these the perturbation method requires the least amount of computation and has been developed in two forms - the first form to obtain the response correlation function and the second for the time averaged spectra of flapping oscillations.
Hohenemser, K. H.↗
Application of the methods of celestial mechanics to the rigid body problem Final report, 1 Jul. 1965 - 1 Jun. 1966
Celestial mechanics perturbation methods applied to problem of describing motion of rigid artificial earth satellite about its center of mass
CELESTIAL MECHANICS↗
Propagation of sound in turbulent media
Perturbation methods commonly used to study the propagation of acoustic waves in turbulent media are reviewed. Emphasis is on those techniques which are applicable to problems involving long-range propagation in the atmosphere and ocean. Characteristic features of the various methods are illustrated by applying them to particular problems. It is shown that conventional perturbation techniques, such as the Born approximation, yield solutions which contain secular terms, and which therefore have a relatively limited range of validity. In contrast, it is found that solutions obtained with the aid of the Rytov method or the smoothing method do not contain secular terms, and consequently have a much greater range of validity.
Wenzel, A. R.↗
Reanalysis information for eigenvalues derived from a differential equation analysis formulation
The investigation reported demonstrates that in the case considered perturbation methods can be used in a straightforward manner to obtain reanalysis information. A perturbation formula for the buckling loads of a general shell of revolution is derived. The accuracy of the obtained relations and their range of application is studied with the aid of a specific example involving a particular stiffened shell of revolution.
Thornton, W. A.↗
The computation of optimal control programmes using a modified successive sweep method.
A second-order method for numerically solving control optimization problems has been developed. The method, referred to as the modified sweep method (MSM), differs from the successive sweep method (SSM) proposed by McReynolds and Bryson (1965) in that the conditions for local control optimality are used to determine the control as an explicit function of the state variables and time. The control is eliminated from the problem and the solution to the resulting two-point boundary value problem can be obtained by linear perturbation methods. The modified sweep method proposed here uncouples the perturbation equations for the state variables and the Lagrange multipliers by using a generalized matrix-Riccati transformation of variables. The resulting algorithm for the numerical iteration process is concerned with determining the initial values of a set of Lagrange multipliers rather than correcting a numerical control programme over the entire time interval of interest.
Colunga, D.↗
Molecular collisions. V.
Transport coefficient expressions for collisions between rigid diatomic molecules, using perturbation method
TRANSPORT COEFFICIENT↗
Control theory based airfoil design using the Euler equations
This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.
Jameson, Antony↗
A numerical assessment of rough surface scattering theories. I - Horizontal polarization. II - Vertical polarization
A numerical evaluation is presented of the regime of validity for various rough surface scattering theories against numerical results obtained by employing the method of moments. The contribution of each theory is considered up to second order in the perturbation expansion for the surface current. Considering both vertical and horizontal polarizations, the unified perturbation method provides best results among all theories weighed.
Rodriguez, Ernesto↗
Aerodynamic shape optimization using control theory
Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.
Reuther, James↗
Asymptotic methods for internal transonic flows
For many internal transonic flows of practical interest, some of the relevant nondimensional parameters typically are small enough that a perturbation scheme can be expected to give a useful level of numerical accuracy. A variety of steady and unsteady transonic channel and cascade flows is studied with the help of systematic perturbation methods which take advantage of this fact. Asymptotic representations are constructed for small changes in channel cross-section area, small flow deflection angles, small differences between the flow velocity and the sound speed, small amplitudes of imposed oscillations, and small reduced frequencies. Inside a channel the flow is nearly one-dimensional except in thin regions immediately downstream of a shock wave, at the channel entrance and exit, and near the channel throat. A study of two-dimensional cascade flow is extended to include a description of three-dimensional compressor-rotor flow which leads to analytical results except in thin edge regions which require numerical solution. For unsteady flow the qualitative nature of the shock-wave motion in a channel depends strongly on the orders of magnitude of the frequency and amplitude of impressed wall oscillations or fluctuations in back pressure. One example of supersonic flow is considered, for a channel with length large compared to its width, including the effect of separation bubbles and the possibility of self-sustained oscillations. The effect of viscosity on a weak shock wave in a channel is discussed.
Adamson, T. C., Jr.↗
Studies using IMP, Voyager and Pioneer cosmic ray data to determine the size of the heliosphere
The purpose of this project was to use the cosmic ray data from the IMP, Voyager and Pioneer spacecraft in the heliosphere out to approximately 65 AU to estimate the size of the heliosphere. We used several techniques to develop a consistent picture of the size of the heliosphere. The first method used a response function approach which determined the intensity as a function of time by scaling the modulation effect as they move outward and eventually reach the boundary of the heliosphere. In this model the effects of transient cosmic ray disturbances is included. A second approach using the perturbation method in which drifts are considered as a perturbation to the standard diffusion-convection modulation models was not fully developed. In a third approach the location of the modulation boundary beyond the termination shock was estimated using observations of the intensity and radial gradients between Voyager 2 and Pioneer 10 along with new estimates of the interstellar intensity of more than 70 MeV galactic cosmic rays. Using this method we found that for 7 years, from 1983 to 1990, the modulation boundary remained constant at 83 +/- 5 AU. We infer from these studies that a modulation boundary can be estimated only by extrapolating the observed radial gradients when the solar magnetic field polarity is such that cosmic-ray particles are drifting in the heliosphere inward toward the Earth along the neutral sheet. The boundary distance is larger than the estimates of the location of the termination shock at 67 +/- 5 AU using the same method. Two other studies partially supported by this grant are attached. The first deals with the recovery period of the greater than 70 MeV cosmic rays in the outer heliosphere from 1992-1995. In the second paper we compare the rigidity dependence of the 11-year cosmic ray variation at the Earth in two cycles of opposite solar magnetic field polarity.
Lockwood, John A.↗
Geomagnetic Euler potentials
Perturbation method to derive geomagnetic Euler potentials for magnetic field
PERTURBATION THEORY↗
Application of multivariable search techniques to the optimization of airfoils in a low speed nonlinear inviscid flow field
Multivariable search techniques are applied to a particular class of airfoil optimization problems. These are the maximization of lift and the minimization of disturbance pressure magnitude in an inviscid nonlinear flow field. A variety of multivariable search techniques contained in an existing nonlinear optimization code, AESOP, are applied to this design problem. These techniques include elementary single parameter perturbation methods, organized search such as steepest-descent, quadratic, and Davidon methods, randomized procedures, and a generalized search acceleration technique. Airfoil design variables are seven in number and define perturbations to the profile of an existing NACA airfoil. The relative efficiency of the techniques are compared. It is shown that elementary one parameter at a time and random techniques compare favorably with organized searches in the class of problems considered. It is also shown that significant reductions in disturbance pressure magnitude can be made while retaining reasonable lift coefficient values at low free stream Mach numbers.
Hague, D. S.↗
An Analytical Investigation of an Oscillating Wedge in a Supersonic Perfect Gas Flow
Several aspects of the oscillating wedge are investigated to evaluate both the resulting trends for the wedge and methods of analyzing unsteady flows. An existing hypersonic small disturbance theory for an oscillating thin wedge is extended and applied. A perturbation method involving linearization about the known flow is then derived and discussed. Subsequently, a finite difference technique for calculating the complete unsteady flow field of the wedge in motion is presented and discussed in conjunction with some calculated quasi-static nonlinear trends.
Bennett, R. M.↗
Cosmic-ray-modified stellar winds. II - A perturbation approach
A perturbation method is developed to describe the modification of a stellar wind flow with termination shock by the Galactic cosmic rays. The perturbation parameter epsilon used in the analysis is the ratio of the galactic cosmic-ray pressure to the thermal gas pressure at a large distance from the star. The positive galactic cosmic-ray pressure gradient serves to brake the outflowing stellar wind gas, particularly just upstream of the termination shock of the wind. A one-fluid polytropic model is used to describe the thermal stellar wind gas, with the coupling between the cosmic rays and the thermal gas being determined by an average hydrodynamical diffusion coefficient kappa describing the scattering of cosmic rays by magnetohydrodynamic waves traveling in the background flow. The analysis takes into account cosmic-ray modifications of the critical point of the wind, the thermal gas entropy constants on both sides of the shock, and the fluid velocity profile.
Ko, C. M.↗
Film stability in a vertical rotating tube with a core-gas flow.
The linear hydrodynamic stability of a thin-liquid layer flowing along the inside wall of a vertical tube rotating about its axis in the presence of a core-gas flow is examined. The stability problem is formulated under the conditions that the liquid film is thin, the density and viscosity ratios of gas to liquid are small and the relative (axial) pressure gradient in the gas is of the same order as gravity. The resulting eigenvalue problem is first solved by a perturbation method appropriate to axisymmetric long-wave disturbances. The damped nature (to within the thin-film and other approximations made) of the nonaxisymmetric and short-wave disturbances is noted. In view of the limitations on a truncated perturbation solution when the disturbance wavenumber is not small, an initial value method using digital computer is presented. Stability characteristics of neutral, growing, and damped modes are presented showing the influences of rotation, surface tension, and the core-gas flow. Energy balance in a neutral mode is also illustrated.
Sarma, G. S. R.↗