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At least 1,315 records · Page 73
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Acceleration of convergence by shifting the spectrum of implicit finite difference operators associated with the equations of gas dynamics

Eigensystem analysis techniques are applied to finite difference formulations of the Navier-Stokes equations in one dimension. Spectra of the resulting implicit difference operators are computed. The largest eigenvalues are calculated by using a combination of the Frechet derivative of the operators and Arnoldi's method. The accuracy of Arnoldi's method is tested by comparing the rate of convergence of the iterative method with the dominant eigenvalue of the original iteration matrix. On the basis of the pattern of eigenvalue distributions for various flow configurations, a shifting of the implicit operators in question is devised. This procedure has improved the rates of convergence of CFD codes by 20 - 50 percent.

Cheer, A.↗
NASA NTRS1995

Electromagnetic scattering analysis of a three-dimensional-cavity-backed aperture in an infinite ground plane using a combined finite element method/method of moments approach

A combined finite element method/method of moments (FEM/MoM) approach is used to analyze the electromagnetic scattering properties of a three-dimensional-cavity-backed aperture in an infinite ground plane. The FEM is used to formulate the fields inside the cavity, and the MoM (with subdomain bases) in both spectral and spatial domains is used to formulate the fields above the ground plane. Fields in the aperture and the cavity are solved using a system of equations resulting from the combination of the FEM and the MoM. By virtue of the FEM, this combined approach is applicable to all arbitrarily shaped cavities with inhomogeneous material fillings, and because of the subdomain bases used in the MoM, the apertures can be of any arbitrary shape. This approach leads to a partly sparse and partly full symmetric matrix, which is efficiently solved using a biconjugate gradient algorithm. Numerical results are presented to validate the analysis.

Reddy, C. J.↗
NASA NTRS1997

Relative Navigation In Elliptical Orbits Using An Iterative Nonlinear Filter

The two step filter is applied to process intersatellite radar measurements to determine the motion of one satellite relative to another in close elliptical orbits. This filter breaks a nonlinear estimation problem into two state vectors. The 'first step' state is chosen so as to have a linear measurement equation. This is nonlinearly related to the 'second step' state which describes the dynamics. Two different forms are used. In one, the first step state is the second step state vector augmented by the measurement equation. In the other, the first step and second step state vectors are of equal dimension. The two step filter is compared against an iterated extended Kalman filter and a Kalman filter using a change of variables. Analytical differences between the two step estimator and these conventional filters are highlighted. Special concerns for initializing the first step state covariance matrix and handling the possibility of numerically rank deficient covariance matrices are addressed. Numerical simulations are performed which show that the Two Step estimator produces a lower estimation bias under two circumstances; large apriori initial error; and small dimension observation vectors which require a longer arc of measurements to generate observability of the state.

Garrison, James L.↗
NASA NTRS1984

Investigation of the three-dimensional flow field within a transonic fan rotor: Experiment and analysis

An experimental investigation of the three dimensional flow field through a low aspect ratio, transonic, axial flow fan rotor has been conducted using an advanced laser anemometer (LA) system. Laser velocimeter measurements of the rotor flow field at the design operating speed and over a range of through flow conditions are compared to analytical solutions. The numerical technique used herein yields the solution to the full, three dimensional, unsteady Euler equations using an explicit time marching, finite volume approach. The numerical analysis, when coupled with a simplified boundary layer calculation, generally yields good agreement with the experimental data. The test rotor has an aspect ratio of 1.56, a design total pressure ratio of 1.629 and a tip relative Mach number of 1.38. The high spatial resolution of the LA data matrix (9 radial by 30 axial by 50 blade to blade) permits details of the transonic flow field such as shock location, turning distribution and blade loading levels to be investigated and compared to analytical results.

Pierzga, M. J.↗
NASA NTRS1992

A non-linearly stable implicit finite element algorithm for hypersonic aerodynamics

A generalized curvilinear coordinate Taylor weak statement implicit finite element algorithm is developed for the two-dimensional and axisymmetric compressible Navier-Stokes equations for ideal and reacting gases. For accurate hypersonic simulation, air is modeled as a mixture of five perfect gases, i.e., molecular and atomic oxygen and nitrogen as well as nitric oxide. The associated pressure is then determined via Newton solution of the classical chemical equilibrium equation system. The directional semidiscretization is achieved using an optimal metric data Galerkin finite element weak statement, on a developed 'companion conservation law system', permitting classical test and trial space definitions. Utilizing an implicit Runge-Kutta scheme, the terminal algorithm is then nonlinearly stable, and second-order accurate in space and time on arbitrary curvilinear coordinates. Subsequently, a matrix tensor product factorization procedure permits an efficient numerical linear algebra handling for large Courant numbers. For ideal- and real-gas hypersonic flows, the algorithm generates essentially nonoscillatory numerical solutions in the presence of strong detached shocks and boundary layer-inviscid flow interactions.

Iannelli, G. S.↗
NASA NTRS1998

Design of Constant Gain Dissipative Controllers for Eigensystem Assignment in Passive Systems

Partial eigensystem assignment with output feedback can lead to an unstable closed-loop system. However, output feedback with passive linear time-invariant systems, such as flexible space structures, is guaranteed to be stable if the controller is dissipative. This paper presents a novel approach for synthesis of dissipative output feedback gain matrices for assigning a selected number of closed-loop poles. Dissipativity of a gain matrix is known to be equivalent to positive semidefiniteness of the symmetric part of the matrix. A sequential procedure is presented to assign one self-conjugate pair of closed-loop eigenvalues at each step using dissipative output feedback gain matrices, while ensuring that the eigenvalues assigned in the previous steps are not disturbed. The problem of assigning one closed-loop pair is reduced to a constrained solution of a system of quadratic equations, and necessary and sufficient conditions for the existence of a solution are presented. A minimax approach is presented for determining parameters which satisfy these conditions. This method can assign as many closed-loop system poles as the number of control inputs. A numerical example of damping enhancement for a flexible structure is presented to demonstrate the approach.

Maghami, Peiman G.↗
NASA NTRS2017

X-Ray Spectro-Polarimetry with Photoelectric Polarimeters

We derive a generalization of forward fitting for X-ray spectroscopy to include linear polarization of X-ray sources, appropriate for the anticipated next generation of space-based photoelectric polarimeters. We show that the inclusion of polarization sensitivity requires joint fitting to three observed spectra, one for each of the Stokes parameters, I(E), U(E), and Q(E). The equations for StokesI (E) (the total intensity spectrum) are identical to the familiar case with no polarization sensitivity, and for which the model-predicted spectrum is obtained by a convolution of the source spectrum, F (E), with the familiar energy response function,(E) R(E,E), where (E) and R(E,E) are the effective area and energy redistribution matrix, respectively. In addition to the energy spectrum, the two new relations for U(E) and Q(E) include the source polarization fraction and position angle versus energy, a(E), and 0(E), respectively, and the model-predicted spectra for these relations are obtained by a convolution with the modulated energy response function, (E)(E) R(E,E), where(E) is the energy-dependent modulation fraction that quantifies a polarimeters angular response to 100 polarized radiation. We present results of simulations with response parameters appropriate for the proposed PRAXyS Small Explorer observatory to illustrate the procedures and methods, and we discuss some aspects of photoelectric polarimeters with relevance to understanding their calibration and operation.

polarization↗
NASA NTRS2017

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗
NASA NTRS1994

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Coutsias, Evangelos A.↗
NASA NTRS1984

Investigation of the three-dimensional flow field within a transonic fan rotor - Experiment and analysis

An experimental investigation of the three-dimensional flow field through a low aspect ratio, transonic, axial flow fan rotor has been conducted, using an advanced laser anemometer (LA) system. Laser velocimeter measurements of the rotor flow field at the design operating speed and over a range of throughflow conditions are compared to analytical solutions. The numerical technique used herein yields the solution to the full, three-dimensional, unsteady Euler equations using an explicit time-marching, finite volume approach. The numerical analysis, when coupled with a simplified boundary layer calculation, generally yields good agreement with the experimental data. The test rotor has an aspect ratio of 1.56, a design total pressure ratio of 1.629 and a tip relative Mach number of 1.38. The high spatial resolution of the LA data matrix (9 radial x 30 axial x 50 blade-to-blade) permits details of the transonic flow field such as shock location, turning distribution, and blade loading levels to be investigated and compared to analytical results.

Pierzga, M. J.↗
NASA NTRS1989

An efficient method for computation of the manipulator inertia matrix

An efficient method of computation of the manipulator inertia matrix is presented. Using spatial notations, the method leads to the definition of the composite rigid-body spatial inertia, which is a spatial representation of the notion of augmented body. The previously proposed methods, the physical interpretations leading to their derivation, and their redundancies are analyzed. The proposed method achieves a greater efficiency by eliminating the redundancy in the intrinsic equations as well as by a better choice of coordinate frame for their projection. In this case, removing the redundancy leads to greater efficiency of the computation in both serial and parallel senses.

Fijany, Amir↗
NASA NTRS2012

SAR Polarimetry

Radar Scattering includes: Surface Characteristics, Geometric Properties, Dielectric Properties, Rough Surface Scattering, Geometrical Optics and Small Perturbation Method Solutions, Integral Equation Method, Magellan Image of Pancake Domes on Venus, Dickinson Impact Crater on Venus (Magellan), Lakes on Titan (Cassini Radar, Longitudinal Dunes on Titan (Cassini Radar), Rough Surface Scattering: Effect of Dielectric Constant, Vegetation Scattering, Effect of Soil Moisture. Polarimetric Radar includes: Principles of Polarimetry: Field Descriptions, Wave Polarizations: Geometrical Representations, Definition of Ellipse Orientation Angles, Scatter as Polarization Transformer, Scattering Matrix, Coordinate Systems, Scattering Matrix, Covariance Matrix, Pauli Basis and Coherency Matrix, Polarization Synthesis, Polarimeter Implementation.

radar scattering↗
NASA NTRS1972

Study of effects of design details on structural response to acoustic excitation

The normal mode vibration characteristics of one-dimensional and two-dimensional panel arrays were investigated analytically and experimentally. The finite element displacement method was used to formulate the structural models. The structural models include a stiffness and consistent mass matrix for thin-walled open-section beams not previously reported, and a modification of a rectangular plate bending element to include a fundamental interior mode for the element as a generalized coordinate. Provision for adding lumped masses to represent accelerometers is also included. For the one-dimensional panel, the normal mode stress resultants are obtained by integrating the equilibrium equations directly. For the two-dimensional panel arrays, the solution for the stress resultants in the cover sheet was attempted by introducing stress functions dependent upon the displacement field of the plate element. This approach, although incomplete, is a natural extension of the one-dimensional analysis for plate elements. The exerimental program which was used to verify the analysis is described and experimental results are compared with the analysis.

Rudder, F. F., Jr.↗
NASA NTRS1977

NASTRAN hydroelastic modal studies. Volume 3: NASTRAN 3-D hydroelastic analysis and MESHGEN user's manuals

The method used to formulate the fluid/structure equations is described in the updates to the NASTRAN Theoretical Manual. The basis for defining the fluid are three dimensional finite elements connected to fluid grid points defining the Eulerian pressure at a point fixed in space. The use of a pressure single degree of freedom at each point rather than three displacements allows a finer mesh of elements with a reasonable matrix order. In the formulation of the fluid/structure system the interior fluid degrees of freedom are transformed and removed from the solution matrices. The eigenvalues of the combination are extracted from small, fully dense, symmetric mass and stiffness matrices, efficiently processed with the Givens method. The solution matrices are defined by the free surface displacements and the reduced structure coordinates.

Source record↗
NASA NTRS1981

Remarks on nonstandard least-squares problems

It is shown that after treating a least-squares problem in the standard fashion, the imposition of stochastic restrictions on certain parameters can be accomplished essentially by inverting a matrix of an order no larger than the total number of restricted parameters, and that generally there is an explicit term for correcting the unrestricted to the restricted solution. In addition, any known type of nonstandard least-squares adjustment problem can be reduced to an equivalent standard linear problem, that is, one in which there is exactly one observation per condition equation and in which the observations are not correlated.

Eichhorn, H.↗
NASA NTRS1997

Electron-H2 Collisions Studied Using the Finite Element Z-Matrix Method

We have applied the Z-matrix method, using a mixed basis of finite elements and Gaussians, to study e-H2 elastic and inelastic collisions. Special attention is paid to the quality of the basis set and the treatment of electron correlation. The calculated cross sections are invariant, to machine accuracy, with respect to the choice of parameters a, b, d, e as long as they satisfy Equation (3). However, the log derivative approach, i.e., the choice a = -e = 1, b = d = 0 appears to converge slightly faster than other choices. The cross sections agree well with previous theoretical results. Comparison will be made with available experimental data.

Huo, Winifred M.↗
NASA NTRS2021

Melt Infiltration Studies of 2D Tyranno SA3(R) Ceramic Matrix Composite Preforms with CrSi2 Intermetallic Alloy

The present paper reports the results of melt infiltrating 2D Tyranno SA3@ fiber woven preforms with molten CrSi2 between 1768 and 1896 K under a vacuum of 1.3 x 10-4 Pa (10-6 torr). The infiltration times varied between 1800 and 7200 s, which did not have any significant effect on the volume fraction of voids filled with the metal. Optical and scanning electron microscopy, back scattered electron imaging, energy dispersion spectroscopy and Raman spectroscopy were used to characterize the infiltrated preforms. A plot of the volume fraction of open voids infiltrated against the absolute melt infiltration temperature showed a sharp peak at 1773 K with almost complete infiltration of the voids at this temperature. The extent of silicide infiltration of the preforms dropped steeply above 1773 K with increasing melt infiltration temperature irrespective of the amount of infiltration time. Above 1805 K, the volume fraction of voids infiltrated with the melt was nearly 0%. It is demonstrated that CrSi2 did not show evidence of a reaction with the SiC fibers. The possibility that a resisting force due to contact angle hysteresis (CAH) may have influenced the diminishing amount of voids filled with increasing temperature above 1773 K was examined. The resistance force was estimated to be extremely small to be consequential. Another possibility that the CrSi2 may have decomposed into Cr(g) and Si(g) in the vacuum melt infiltration furnace appeared to be more plausible based on thermodynamic analyses. An empirical equation is proposed to calculate the amount of remaining charge left to infiltrate the preforms at the infiltration temperature. It is shown that an initial charge of 10 g would rationalize the present observations. While the decomposition of the CrSi2 appeared to mostly explain the present results, some discrepancies were observed, which were inconsistent with the decomposition model.

CrSi2, chromium silicide, ceramic matrix composite↗
NASA NTRS1983

Global transformations of nonlinear systems

Necessary and sufficient conditions for a nonlinear system of equations to be locally equivalent, in a neighborhood of the origin in the real number system, to a controllable linear system are combined with several versions of the global inverse function theorem to define sufficient conditions for transforming the nonlinear system into a linear system. Additionally, a technique is introduced for developing a transformation under the assumptions that the columns of a controllability matrix span an n-dimensional space. Finally, the n-l form of the controllability matrix columns is demonstrated to be involutive

Hunt, L. R.↗