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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 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Flight flutter testing technology at Grumman

Analysis techniques used in the automated telemetry station (ATS) for on line data reduction are encompassed in a broad range of software programs. Concepts that form the basis for the algorithms used are mathematically described. The control the user has in interfacing with various on line programs is discussed. The various programs are applied to an analysis of flight data which includes unimodal and bimodal response signals excited via a swept frequency shaker and/or random aerodynamic forces. A nonlinear response error modeling analysis approach is described. Preliminary results in the analysis of a hard spring nonlinear resonant system are also included.

Perangelo, H. J.↗
NASA NTRS1977

Calculation of sheath and wake structure about a pillbox-shaped spacecraft in a flowing plasma

A computer program was used for studies of the disturbed zones around bodies in flowing plasmas, particularly spacecraft and their associated sheaths and wakes. The program solved a coupled Poisson-Vlasov system of nonlinear partial differential integral equations to obtain distributions of electric potential and ion and electron density about a finite length cylinder in a plasma flow at arbitrary ion Mach numbers. The approach was applicable to a larger range of parameters than other available approaches. In sample calculations, bodies up to 100 Debye lengths in radius were treated, that is, larger than any previously treated realistically. Applications were made to in-situ satellite experiments.

Parker, L. W.↗
NASA NTRS1979

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

Agapov, A. V.↗
NASA NTRS1978

An extension of MacCormack's method for flows with higher-order equations and in different configurations

The numerical scheme for the computation of a shock discontinuity developed by MacCormack has been extended to solve a number of differential equations, including cases explicitly containing higher-order derivatives: (1) Korteweg-de Vries equation with a term of third-order derivative, (2) a system of nonlinear equations governing nonsteady one-dimensional plasma flow in cylindrical coordinate, (3) equations of solar wind. Comparisons with previous results are made, if available, to illustrate the advantages of the present method. The question of convergence of the numerical calculation is discussed.

Ying, S. J.↗
NASA NTRS1980

Direct integration of transient rotor dynamics

An implicit method was developed for integrating the equations of motion for a lumped mass model of a rotor dynamics system. As an aside, a closed form solution to the short bearing theory was also developed for a damper with arbitrary motion. The major conclusions are that the method is numerically stable and that the computation time is proportional to the number of elements in the rotor dynamics model rather than to the cube of the number. This computer code allowed the simulation of a complex rotor bearing system experiencing nonlinear transient motion and displayed the vast amount of results in an easily understood motion picture format - a 10 minute, 16 millimeter, color, sound motion picture supplement. An example problem with 19 mass elements in the rotor dynamics model took 0.7 second of central processing unit time per time step on an IBM 360-67 computer in a time sharing mode.

Kascak, A. F.↗
NASA NTRS1979

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Jezewski, D. J.↗
NASA NTRS1980

Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Vezewski, D. J.↗
NASA NTRS1980

Numerical solution of the Navier-Stokes equations for high Reynolds number incompressible turbulent flow

The full Navier-Stokes equations for incompressible turbulent flow must be solved to accurately represent all flow phenomena which occur in a high Reynolds number incompressible flow. A two layer algebraic eddy viscosity turbulence model is used to represent the Reynolds stress in the primitive variable formulation. The development of the boundary-fitted coordinate systems makes the numerical solution of these equations feasible for arbitrarily shaped bodies. The nondimensional time averaged Navier-Stokes equations, including the turbulence mode, are represented by finite difference approximations in the transformed plane. The resulting coupled system of nonlinear algebraic equations is solved using a point successive over relaxation iteration. The test case considered was a NACA 64A010 airfoil section at an angle of attack of two degrees and a Reynolds number of 2,000,000.

Thompson, D. S.↗
NASA NTRS1979

Application of the method of integral relations to unsteady fluid flow problems with shocks

A mixed method using both the method of integral relations and the finite difference technique is developed for the solution of unsteady flow problems. The integral relations method is based upon a chosen interpolating function dependent only on the time domain. The resulting local semidiscrete finite element equations obtained are assembled into a global form. The spatial derivatives at the nodes are replaced by finite difference operators and the discretized nonlinear algebraic system is solved by an iterative scheme. Solutions are obtained for the one-dimensional gasdynamics equation, the one-dimensional wave equation and Burger's model of turbulence. Agreement with other numerical and analytical solutions is excellent for the gasdynamics problem and satisfactory for the Burger equation in cases of small viscous effects.

Wadia, A. R.↗
NASA NTRS1981

A new method of Curie depth evaluation from magnetic data: Theory

An approach to estimating the Curie point isotherm uses the classical Gauss method inverting a system of nonlinear equations. The method, slightly modified by a differential correction technique, directly inverts filtered Magsat data to calculate the crustal structure above the Curie depth, which is modeled as a magnetized layer of varying thickness and susceptibility. Since the depth below the layer is assumed to be nonmagnetic, the bottom of the layer is interpreted as the Curie depth. The method, once fully developed, tested, and compared with previous work by others, is to be applied to a portion of the eastern U.S. when sufficient Magsat data are accumulated for the region.

Won, I. J.↗
NASA NTRS1981

Stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations

Implicit, noniterative, finite difference schemes were recently developed by several authors for multidimensional systems of nonlinear hyperbolic partial differential equations. When applied to linear model equations with periodic boundary conditions those schemes are unconditionally stable (A-stable). As applied in practice the algorithms often face a severe time step restriction. A major source of the difficulty is the treatment of the numerical boundary conditions. One conjecture was that unconditional stability requires implicit numerical boundary conditions. An apparent counter example was the space time extrapolation considered by Gustafsson, Kreiss, and Sunstrom. Spatial (implicit) and space time (explicit) extrapolation using normal mode analysis for a finite and infinite number of spatial mesh intervals are examined. The results indicate that for unconditional stability with a finite number of spatial mesh intervals, the numerical boundary conditions must be implicit.

Beam, R. M.↗
NASA NTRS1981

Fixed-trim re-entry guidance analysis

The terminal guidance problem for a fixed-trim re-entry body is formulated with the objective of synthesizing a closed-loop steering law. A transformation of variables and subsequent linearization of the motion, with the sight-line to the target as a reference, reduces the order of the state system for the guidance problem. The reduced order system, although nonlinear and time-varying, is simple enough to lend itself to synthesis of a class of guidance laws. A generalization of the feedforward device of classical control theory is successfully employed for compensation of roll autopilot lags. The proposed steering law exhibits superior miss-distance performance in a computational comparison with existing fixed-trim guidance laws.

Gracey, C.↗
NASA NTRS1982

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Sharma, A.↗
NASA NTRS1983

Joint state and parameter estimation

Recent results are described concerning the problem of state reconstruction for a class of nonlinear distributed systems. The methods are then applied to the problem of joint state and parameter estimation. An example with the wave equation is presented.

Carmichael, N.↗
NASA NTRS1984

Numerical modeling of D-mappings with applications to chemical kinetics

Numerical modeling of D-mappings was studied and applied to solving nonlinear stiff systems. These mappings were locally linearized for convergence analysis, and some applications were made to chemical kinetics. The technique avoids using multistep implicit codes that require inversion of Jacobian matrices, but depends on the Jacobians for its convergence analysis.

Dey, S. K.↗
NASA NTRS1984

Relative motion characteristics of 2 near-Earth Satellites

The stability of the nonlinear dynamical system of two GRAVSAT - type satellites was investigated by performing several numerical experiments which provide the simulations of the relative motion characteristics between the two satellites for various specified time intervals. The simulations included the relative range, range-rate, and relative acceleration magnitude. These simulations were generated with respect to appropriate initial orbital elements which were obtained such that the instantaneous separation distance between the two satellites has small fluctuations from a specified constant separation distance. The simulation results indicate that the behavior of the relative motions is very sensitive to the initial orbital elements of the satellites and that for a specified time interval of interest. A stable behavior is possible only with the use of an appropriate set of initial orbital elements compatible with the gravity field used to derive them.

Schutz, B. E.↗
NASA NTRS1985

New results on the PLL false lock phenomenon

Conditions, based on the multipliers of a linear differential equation with periodic coefficients, for the occurrence of false lock in a phase lock loop (PLL) are presented. Two new and powerful algorithms are presented for computing the frequency difference between the reference and voltage controlled oscillator when the loop is false locked. The first algorithm expresses omega f sup -1 as a power series in the closed loop gain. The second algorithm expresses omega sup -1 as part of a solution to a nonlinear algebraic system of equations which can be solved by numerical methods. The power of both algorithms is illustrated by application and comparison.

Stensby, J. L.↗
NASA NTRS1984

Electron precipitation in solar flares - Collisionless effects

A large fraction of the electrons which are accelerated during the impulsive phase of solar flares stream towards the chromosphere and are unstable to the growth of plasma waves. The linear and nonlinear evolution of plasma waves as a function of time is analyzed with a set of rate equations that follows, in time, the nonlinearly coupled system of plasma waves-ion fluctuations. As an outcome of the fast transfer of wave energy from the beam to the ambient plasma, nonthermal electron tails are formed which can stabilize the anomalous Doppler resonance instability responsible for the pitch angle scattering of the beam electrons. The non-collisional losses of the precipitating electrons are estimated, and the observational implication of these results are discussed.

Vlahos, L.↗