SEARCH · Engineering Papers

Results for “linear equation systems”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,171 records · Page 65

All sources NASA NTRS DOE OSTI

NASA NTRS1987

Navier-Stokes analysis of two- and three-dimensional flow field in solid rocket motors with segment joints

A multidimensional implicit Navier-Stokes analysis which uses numerical solution of ensemble-averaged Navier-Stokes equations in a nonorthogonal bodyfitted cylindrical-polar coordinate system has been applied to simulation of the internal flow field in solid-propellant rocket motor chambers with segment joints. The calculation procedure incorporates a two-equation (k-epsilon) turbulence model and utilizes a consistently split, linearized block-implicit algorithm for numerical solution of the governing equations. Computations performed to simulate the axisymmetric flow field in the vicinity of the aft field joint in the Space Shuttle SRB using 14,725 grid points show the presence of a region of reversed axial flow near the downstream edge of the slot. Calculations were also performed for two cases involving asymmetric three-dimensional flow in the vicinity of the aft field joint in the SRB using 721,525 grid points to estimate circumferential velocities and pressure gradients at the joint.

Sabnis, J. S.↗

NASA NTRS1990

Galerkin approximations for dissipative magnetohydrodynamics

A Galerkin approximation scheme is proposed for voltage-driven, dissipative magnetohydrodynamics. The trial functions are exact eigenfunctions of the linearized continuum equations and represent helical deformations of the axisymmetric, zero-flow, driven steady state. The lowest nontrivial truncation is explored: one axisymmetric trial function and one helical trial function each for the magnetic and velocity fields. The system resembles the Lorenz approximation to Benard convection, but in the region of believed applicability, its dynamical behavior is rather different, including relaxation to a helically deformed state similar to those that have emerged in the much higher resolution computations of Dahlburg et al.

Chen, Hudong↗

NASA NTRS1993

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Vaughan, William W.↗

NASA NTRS1993

An automatic multigrid method for the solution of sparse linear systems

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

Shapira, Yair↗

NASA NTRS1993

Control of nonlinear systems represented in quasilinear form

Methods to synthesize controllers for nonlinear systems are developed by exploiting the fact that under mild differentiability conditions, systems of the form: x-dot = f(x) + G(x)u can be represented in quasilinear form, viz: x-dot = A(x)x + B(x)u. Two classes of control methods are investigated. The first is zero-look-ahead control, where the control input depends only on the current values of A(x) and B(x). For this case the control input is computed by continuously solving a matrix Riccati equation as the system progresses along a trajectory. The second is controllers with look-ahead, where the control input depends on the future behavior of A(x) and B(x). These controllers use the similarity between quasilinear systems and linear time varying systems to find approximate solutions to optimal control type problems. The methods that are developed are not guaranteed to be globally stable. However in simulation studies they were found to be useful alternatives for synthesizing control laws for a general class of nonlinear systems.

Coetsee, Josef A.↗

NASA NTRS1998

Symbolic Computational Approach to the Marangoni Convection Problem With Soret Diffusion

A recently reported solution for stationary stability of a thermosolutal system with Soret diffusion is re-derived and examined using a symbolic computational package. Symbolic computational languages are well suited for such an analysis and facilitate a pragmatic approach that is adaptable to similar problems. Linearization of the equations, normal mode analysis, and extraction of the final solution are performed in a Mathematica notebook format. An exact solution is obtained for stationary stability in the limit of zero gravity. A closed form expression is also obtained for the location of asymptotes in relevant parameter, (Sm(sub c), Mac(sub c)), space. The stationary stability behavior is conveniently examined within the symbolic language environment. An abbreviated version of the Mathematica notebook is given in the Appendix.

Skarda, J. Raymond↗

NASA NTRS2013

Uncertainties in Atomic Data and Their Propagation Through Spectral Models. I.

We present a method for computing uncertainties in spectral models, i.e., level populations, line emissivities, and emission line ratios, based upon the propagation of uncertainties originating from atomic data.We provide analytic expressions, in the form of linear sets of algebraic equations, for the coupled uncertainties among all levels. These equations can be solved efficiently for any set of physical conditions and uncertainties in the atomic data. We illustrate our method applied to spectral models of Oiii and Fe ii and discuss the impact of the uncertainties on atomic systems under different physical conditions. As to intrinsic uncertainties in theoretical atomic data, we propose that these uncertainties can be estimated from the dispersion in the results from various independent calculations. This technique provides excellent results for the uncertainties in A-values of forbidden transitions in [Fe ii]. Key words: atomic data - atomic processes - line: formation - methods: data analysis - molecular data - molecular processes - techniques: spectroscopic

linear sets↗

NASA NTRS1972

Characteristics of hingeless rotors with hub moment feedback controls including experimental rotor frequency response, Volume 1

Wind tunnel tests to determine the dynamic characteristics of hingeless rotors with hub moment feedback controls and to acquire experimental hingeless rotor transfer functions are discussed. Rotor transfer functions were calculated from data acquired during open loop frequency response tests. The transfer functions are linear and present the rotor longitudinal and lateral frequency responses to collective pitch, longitudinal cyclic pitch, and lateral cyclic pitch. The theoretical analysis was based on the rigid blade flapping model coupled with appropriate control system and cyclic pitch actuator equations of motion.

Kuczynski, W. A.↗

NASA NTRS1974

Attitude dynamics simulation subroutines for systems of hinge-connected rigid bodies

Several computer subroutines are designed to provide the solution to minimum-dimension sets of discrete-coordinate equations of motion for systems consisting of an arbitrary number of hinge-connected rigid bodies assembled in a tree topology. In particular, these routines may be applied to: (1) the case of completely unrestricted hinge rotations, (2) the totally linearized case (all system rotations are small), and (3) the mixed, or partially linearized, case. The use of the programs in each case is demonstrated using a five-body spacecraft and attitude control system configuration. The ability of the subroutines to accommodate prescribed motions of system bodies is also demonstrated. Complete listings and user instructions are included for these routines (written in FORTRAN V) which are intended as multi- and general-purpose tools in the simulation of spacecraft and other complex electromechanical systems.

Fleischer, G. E.↗

NASA NTRS1975

Control optimization, stabilization and computer algorithms for aircraft applications

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Source record↗

NASA NTRS1982

Microwave remote sensing of soil moisture, volume 1

Multifrequency sensor data from NASA's C-130 aircraft were used to determine which of the all weather microwave sensors demonstrated the highest correlation to surface soil moisture over optimal bare soil conditions, and to develop and test techniques which use visible/infrared sensors to compensate for the vegetation effect in this sensor's response to soil moisture. The L-band passive microwave radiometer was found to be the most suitable single sensor system to estimate soil moisture over bare fields. The perpendicular vegetation index (PVI) as determined from the visible/infrared sensors was useful as a measure of the vegetation effect on the L-band radiometer response to soil moisture. A linear equation was developed to estimate percent field capacity as a function of L-band emissivity and the vegetation index. The prediction algorithm improves the estimation of moisture significantly over predictions from L-band emissivity alone.

Mcfarland, M. J.↗

NASA NTRS1985

A Factored Implicit Scheme for Numerical Weather Prediction with Small Factorization Error

Numerical results show that, for large time steps, the factorization error can be significant, even for the slowly propagating Rossby modes. A new scheme is formulated based on a more accurate factorization of the equations. By grouping separately the terms of the equations which give rise to the fast and slow motion, the equations are factored more accurately. The fast-slow factorization eliminated the factorization error. If each of the fast and slow factors are factored again according to spatial components, the resulting scheme only involves the solution of one dimensional linear systems, and computational efficient. It is shown that the factorization error for the slow made component is negligible for this new scheme.

Augenbaum, J. M.↗

NASA NTRS1987

Mean-square error bounds for reduced-error linear state estimators

The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Lyapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.

Baram, Y.↗

NASA NTRS1987

Mean-square-error bounds for reduced-order linear state estimators

The mean-square error of reduced-order linear state estimators for continuous-time linear systems is investigated. Lower and upper bounds on the minimal mean-square error are presented. The bounds are readily computable at each time-point and at steady state from the solutions to the Ricatti and the Liapunov equations. The usefulness of the error bounds for the analysis and design of reduced-order estimators is illustrated by a practical numerical example.

Baram, Y.↗

NASA NTRS1990

Attitude control/momentum management of the Space Station Freedom for large angle torque-equilibrium-attitude configurations

An attitude-control and momentum-management (ACMM) system for the Space Station in a large-angle torque-equilibrium-attitude (TEA) configuration is developed analytically and demonstrated by means of numerical simulations. The equations of motion for a rigid-body Space Station model are outlined; linearized equations for an arbitrary TEA (resulting from misalignment of control and body axes) are derived; the general requirements for an ACMM are summarized; and a pole-placement linear-quadratic regulator solution based on scheduled gains is proposed. Results are presented in graphs for (1) simulations based on configuration MB3 (showing the importance of accounting for the cross-inertia terms in the TEA estimate) and (2) simulations of a stepwise change from configuration MB3 to the 'assembly complete' stage over 130 orbits (indicating that the present ACCM scheme maintains sufficient control over slowly varying Space Station dynamics).

Parlos, Alexander G.↗

NASA NTRS1993

A comparison of viscoelastic damping models

Modern finite element methods (FEM's) enable the precise modeling of mass and stiffness properties in what were in the past overwhelmingly large and complex structures. These models allow the accurate determination of natural frequencies and mode shapes. However, adequate methods for modeling highly damped and high frequency dependent structures did not exist until recently. The most commonly used method, Modal Strain Energy, does not correctly predict complex mode shapes since it is based on the assumption that the mode shapes of a structure are real. Recently, many techniques have been developed which allow the modeling of frequency dependent damping properties of materials in a finite element compatible form. Two of these methods, the Golla-Hughes-McTavish method and the Lesieutre-Mingori method, model the frequency dependent effects by adding coordinates to the existing system thus maintaining the linearity of the model. The third model, proposed by Bagley and Torvik, is based on the Fractional Calculus method and requires fewer empirical parameters to model the frequency dependence at the expense of linearity of the governing equations. This work examines the Modal Strain Energy, Golla-Hughes-McTavish and Bagley and Torvik models and compares them to determine the plausibility of using them for modeling viscoelastic damping in large structures.

Slater, Joseph C.↗

NASA NTRS1993

Global dynamic modeling of a transmission system

The work performed on global dynamic simulation and noise correlation of gear transmission systems at the University of Akron is outlined. The objective is to develop a comprehensive procedure to simulate the dynamics of the gear transmission system coupled with the effects of gear box vibrations. The developed numerical model is benchmarked with results from experimental tests at NASA Lewis Research Center. The modal synthesis approach is used to develop the global transient vibration analysis procedure used in the model. Modal dynamic characteristics of the rotor-gear-bearing system are calculated by the matrix transfer method while those of the gear box are evaluated by the finite element method (NASTRAN). A three-dimensional, axial-lateral coupled bearing model is used to couple the rotor vibrations with the gear box motion. The vibrations between the individual rotor systems are coupled through the nonlinear gear mesh interactions. The global equations of motion are solved in modal coordinates and the transient vibration of the system is evaluated by a variable time-stepping integration scheme. The relationship between housing vibration and resulting noise of the gear transmission system is generated by linear transfer functions using experimental data. A nonlinear relationship of the noise components to the fundamental mesh frequency is developed using the hypercoherence function. The numerically simulated vibrations and predicted noise of the gear transmission system are compared with the experimental results from the gear noise test rig at NASA Lewis Research Center. Results of the comparison indicate that the global dynamic model developed can accurately simulate the dynamics of a gear transmission system.

Choy, F. K.↗

NASA NTRS2006

Adjoint Method and Predictive Control for 1-D Flow in NASA Ames 11-Foot Transonic Wind Tunnel

This paper describes a modeling method and a new optimal control approach to investigate a Mach number control problem for the NASA Ames 11-Foot Transonic Wind Tunnel. The flow in the wind tunnel is modeled by the 1-D unsteady Euler equations whose boundary conditions prescribe a controlling action by a compressor. The boundary control inputs to the compressor are in turn controlled by a drive motor system and an inlet guide vane system whose dynamics are modeled by ordinary differential equations. The resulting Euler equations are thus coupled to the ordinary differential equations via the boundary conditions. Optimality conditions are established by an adjoint method and are used to develop a model predictive linear-quadratic optimal control for regulating the Mach number due to a test model disturbance during a continuous pitch

Nguyen, Nhan↗