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At least 1,117 records · Page 62
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

An efficient method for solving the steady Euler equations

An efficient numerical procedure for solving a set of nonlinear partial differential equations, the steady Euler equations, using Newton's linearization procedure is presented. A theorem indicating quadratic convergence for the case of differential equations is demonstrated. A condition for the domain of quadratic convergence Omega(2) is obtained which indicates that whether an approximation lies in Omega(2) depends on the rate of change and the smoothness of the flow vectors, and hence is problem-dependent. The choice of spatial differencing, of particular importance for the present method, is discussed. The treatment of boundary conditions is addressed, and the system of equations resulting from the foregoing analysis is summarized and solution strategies are discussed. The convergence of calculated solutions is demonstrated by comparing them with exact solutions to one and two-dimensional problems.

Liou, M.-S.↗
NASA NTRS1992

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

This research should lead to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle-of-attack aircraft such as the F18 (HARV). The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis and simulation is performed in some detail as well. Various models under investigation for different purposes are summarized in tabular form. Models and simulation for the longitudinal dynamics have been developed for all types except the nonlinear ordinary differential equation model. Briefly, studies completed indicate that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in alpha. The transient responses are compared where the desired alpha varies from 5 degrees to 60 degrees to 30 degrees and back to 5 degrees in all about 16 sec. Here, the horizontal stabilator is the only control used with an assumed first-order linear actuator with a 1/30 sec time constant.

Mohler, R. R.↗
NASA NTRS1985

Minimal norm constrained interpolation

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Irvine, L. D.↗
NASA NTRS1979

Non-linear dynamic response of a wind turbine blade

The paper outlines the nonlinear dynamic analysis of an isolated three-degree flap-lag-feather wind turbine blade under a gravity field and with shear flow. Lagrangian equations are used to derive the nonlinear equations of motion of blade for arbitrarily large angular deflections. The limit cycle analysis for forced oscillations and the determination of the principal parametric resonance of the blade due to periodic forces from the gravity field and wind shear are performed using the harmonic balance method. Results are obtained first for a two-degree flap-lag blade, then the effect of the third degree of freedom (feather) is studied. The self-excited flutter solutions are obtained for a uniform wind and with gravity forces neglected. The effects of several parameters on the blade stability are examined, including coning angle, structural damping, Lock number, and feather frequency. The limit cycle flutter solution of a typical configuration shows a substantial nonlinear softening spring behavior.

Chopra, I.↗
NASA NTRS1971

Similarity analysis of differential equations by Lie group.

Methods for transforming partial differential equations into forms more suitable for analysis and solution are investigated. The idea of Lie's infinitesimal contact transformation group is introduced to develop a systematic method which involves mostly algebraic manipulations. A thorough presentation of the application of this general method to the problem of similarity analysis in a broader sense - namely, the similarity between partial and ordinary differential equations, boundary value and initial value problems, and nonlinear and linear equations - is given with new and very general methods evolved for deriving the possible groups of transformations.

Na, T. Y.↗
NASA NTRS1984

Numerical simulation of boundary-layer transition

The transition to turbulence in boundary layers was investigated by direct numerical solution of the nonlinear, three-dimensional, incompressible Navier-Stokes equations in the half-infinite domain over a flat plate. Periodicity was imposed in the streamwise and spanwise directions. A body force was applied to approximate the effect of a nonparallel mean flow. The numerical method was spectra, based on Fourier series and Jacobi polynomials, and used divergence-free basis functions. Extremely rapid convergence was obtained when solving the linear Orr-Sommerfeld equation. The early nonlinear and three-dimensional stages of transition, in a boundary layer disturbed by a vibrating ribbon, were successfully simulated. Excellent qualitative agreement was observed with either experiments or weakly nonlinear theories. In particular, the breakdown pattern was staggered or nonstaggered depending on the disturbance amplitude.

Spalart, P. R.↗
NASA NTRS1986

Blade loss transient dynamics analysis, volume 1. Task 2: TETRA 2 theoretical development

The theoretical development of the forced steady state analysis of the structural dynamic response of a turbine engine having nonlinear connecting elements is discussed. Based on modal synthesis, and the principle of harmonic balance, the governing relations are the compatibility of displacements at the nonlinear connecting elements. There are four displacement compatibility equations at each nonlinear connection, which are solved by iteration for the principle harmonic of the excitation frequency. The resulting computer program, TETRA 2, combines the original TETRA transient analysis (with flexible bladed disk) with the steady state capability. A more versatile nonlinear rub or bearing element which contains a hardening (or softening) spring, with or without deadband, is also incorporated.

Gallardo, Vincente C.↗
NASA NTRS1991

A Variational Assimilation Method for Satellite and Conventional Data: Development of Basic Model for Diagnosis of Cyclone Systems

A summary is presented of the progress toward the completion of a comprehensive diagnostic objective analysis system based upon the calculus of variations. The approach was to first develop the objective analysis subject to the constraints that the final product satisfies the five basic primitive equations for a dry inviscid atmosphere: the two nonlinear horizontal momentum equations, the continuity equation, the hydrostatic equation, and the thermodynamic equation. Then, having derived the basic model, there would be added to it the equations for moist atmospheric processes and the radiative transfer equation.

Achtemeier, Gary L.↗
NASA NTRS2000

Nonlinear Transient Problems Using Structure Compatible Heat Transfer Code

The report documents the recent effort to enhance a transient linear heat transfer code so as to solve nonlinear problems. The linear heat transfer code was originally developed by Dr. Kim Bey of NASA Largely and called the Structure-Compatible Heat Transfer (SCHT) code. The report includes four parts. The first part outlines the formulation of the heat transfer problem of concern. The second and the third parts give detailed procedures to construct the nonlinear finite element equations and the required Jacobian matrices for the nonlinear iterative method, Newton-Raphson method. The final part summarizes the results of the numerical experiments on the newly enhanced SCHT code.

Hou, Gene↗
NASA NTRS2013

Very Large Eddy Simulations of a Jet-A Spray Reacting Flow in a Single Element LDI Injector With and Without Invoking an Eulerian Scalar DWFDF Method

This paper presents the very large eddy simulations (VLES) of a Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the Eulerian scalar DWFDF method, in which DWFDF is defined as the density weighted time filtered fine grained probability density function. The flow field is calculated by using the time filtered compressible Navier-Stokes equations (TFNS) with nonlinear subscale turbulence models, and when the Eulerian scalar DWFDF method is invoked, the energy and species mass fractions are calculated by solving the equation of DWFDF. A nonlinear subscale model for closing the convection term of the Eulerian scalar DWFDF equation is used and will be briefly described in this paper. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the Eulerian scalar DWFDF method in both improving the simulation quality and maintaining economic computing cost are observed.

Shih, Tsan-Hsing↗
NASA NTRS1985

Nonlinear Dynamic Analysis of Deploying Flexible Space Booms

A fundamental investigation of the planar deployment and lock-up of two flexible boom type appendages which have attached tip masses and are connected to a central rigid body through a rotational spring is presented. Nondimensional parameters are identified and it is shown that, in general, the solution depends only on two mass ratios and one nondimensional stiffness parameter. Results are presented for boom tip deflections, deployment time and root moments at lock-up. A threshold value of the nondimensional stiffness parameter is identified beyond which boom deflections become large. Also, a thorough examination of the effect of nonlinear terms in the equations governing the deployment phase is performed. Nonlinear terms in the deployment equations due to kinematics and structural deformation are required to predict more accurately boom deflections, but retention of an inconsistent set of nonlinear terms leads to erroneous results. In particular, retaining nonlinear kinematic terms while neglecting nonlinear structural terms can produce inaccurate results even below the threshold stiffness value.

Mcgowan, P. E.↗
NASA NTRS1980

Turbulent solution of the Navier-Stokes equations

To study the nonlinear physics of incompressible turbulent flow, the unaveraged Navier-Stokes equations are solved numerically. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used. No mean gradients are present. The three components of the mean-square velocity fluctuations are equal for the initial conditions chosen. The resulting solution shows characteristics of turbulence, such as the nonlinear excitation of small-scale fluctuations. For the higher Reynolds numbers the initially nonrandom flow develops into an apparently random turbulence.

Deissler, R. G.↗
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 NTRS1985

Quasiperiodically forced damped pendula and Schroedinger equations with quasiperiodic potentials - Implications of their equivalence

Certain first-order nonlinear ordinary differential equations exemplified by strongly damped, quasiperiodically driven pendula and Josephson junctions are isomorphic to Schroedinger equations with quasiperiodic potentials. The implications of this equivalence are discussed. In particular, it is shown that the transition to Anderson localization in the Schroedinger problem corresponds to the occurrence of a novel type of strange attractor in the pendulum problem. This transition should be experimentally observable in the frequency spectrum of the pendulum of Josephson junction.

Bondeson, A.↗
NASA NTRS1979

Stability analysis of a liquid fuel annular combustion chamber

The problems of combustion instability in an annular combustion chamber are investigated. A modified Galerkin method was used to produce a set of modal amplitude equations from the general nonlinear partial differential acoustic wave equation. From these modal amplitude equations, the two variable perturbation method was used to develop a set of approximate equations of a given order of magnitude. These equations were modeled to show the effects of velocity sensitive combustion instabilities by evaluating the effects of certain parameters in the given set of equations. By evaluating these effects, parameters which cause instabilities to occur in the combustion chamber can be ascertained. It is assumed that in the annular combustion chamber, the liquid propellants are injected uniformly across the injector face, the combustion processes are distributed throughout the combustion chamber, and that no time delay occurs in the combustion processes.

Mcdonald, G. H.↗
NASA NTRS1978

Stability analysis of a liquid fuel annular combustion chamber

High frequency combustion instability problems in a liquid fuel annular combustion chamber are examined. A modified Galerkin method was used to produce a set of modal amplitude equations from the general nonlinear partial differential acoustic wave equation in order to analyze the problem of instability. From these modal amplitude equations, the two variable perturbation method was used to develop a set of approximate equations of a given order of magnitude. These equations were modeled to show the effects of velocity sensitive combustion instabilities by evaluating the effects of certain parameters in the given set of equations.

Mcdonald, G. H.↗