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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Modeling supersonic combustion using a fully-implicit numerical method

A fully-implicit finite-volume algorithm for two-dimensional axisymmetric flows has been coupled to a detailed hydrogen-air reaction mechanism (13 species and 33 reactions) so that supersonic combustion phenomena may be investigated. Numerical computations are compared with ballistic-range shadowgraphs of Lehr (1972) that exhibit two discontinuities caused by a blunt body as it passes through a premixed stoichiometric hydrogen-air mixture. The suitability of the numerical procedure for simulating these double-front flows is shown. The requirements for the physical formulation and the numerical modeling of these flowfields are discussed. Finally, the sensitivity of these external flowfields to changes in certain key reaction rate constants is examined.

Maccormack, Robert W.↗
NASA NTRS1989

Parallel multi-time step integration on a transputer system

An algorithm which allows different nodes of the finite element mesh to be integrated with different time steps is presented for second order finite element systems. The implementation of this algorithm on a system of transputer processors is discussed and a numerical example is used to evaluate the efficiency of the algorithm.

Smolinski, P.↗
NASA NTRS1976

A technique for pole-zero placement for dual-input control systems

A technique is presented for determining state variable feedback gains that will place both the poles and zeros of a selected transfer function of a dual-input control system at pre-determined locations in the s-plane. Leverrier's algorithm is used to determine the numerator and denominator coefficients of the closed-loop transfer function as functions of the feedback gains. The values of gain that match these coefficients to those of a pre-selected model are found by solving two systems of linear simultaneous equations. The algorithm has been used in a computer simulation of the CH-47 helicopter to control longitudinal dynamics.

Reid, G. F.↗
NASA NTRS1973

A parallel variable metric optimization algorithm

An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.

Straeter, T. A.↗
NASA NTRS1997

Steady-State and Transient Boundary Element Methods for Coupled Heat Conduction

Boundary element algorithms for the solution of steady-state and transient heat conduction are presented. The algorithms are designed for efficient coupling with computational fluid dynamic discretizations and feature piecewise linear elements with offset nodal points. The steady-state algorithm employs the fundamental solution approach; the integration kernels are computed analytically based on linear shape functions, linear elements, and variably offset nodal points. The analytic expressions for both singular and nonsingular integrands are presented. The transient algorithm employs the transient fundamental solution; the temporal integration is performed analytically and the nonsingular spatial integration is performed numerically using Gaussian quadrature. A series solution to the integration is derived for the instance of a singular integrand. The boundary-only character of the algorithm is maintained by integrating the influence coefficients from initial time. Numerical results are compared to analytical solutions to verify the current boundary element algorithms. The steady-state and transient algorithms are numerically shown to be second-order accurate in space and time, respectively.

Kontinos, Dean A.↗
NASA NTRS1989

Recursive linearization of multibody dynamics equations of motion

The equations of motion of a multibody system are nonlinear in nature, and thus pose a difficult problem in linear control design. One approach is to have a first-order approximation through the numerical perturbations at a given configuration, and to design a control law based on the linearized model. Here, a linearized model is generated analytically by following the footsteps of the recursive derivation of the equations of motion. The equations of motion are first written in a Newton-Euler form, which is systematic and easy to construct; then, they are transformed into a relative coordinate representation, which is more efficient in computation. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient because of its recursive nature. It has also turned out to be more accurate because of the fact that analytical perturbation circumvents numerical differentiation and other associated numerical operations that may accumulate computational error, thus requiring only analytical operations of matrices and vectors. The power of the proposed linearization algorithm is demonstrated, in comparison to a numerical perturbation method, with a two-link manipulator and a seven degrees of freedom robotic manipulator. Its application to control design is also demonstrated.

Lin, Tsung-Chieh↗
NASA NTRS1992

A generalized reusable guidance algorithm for optimal aerobraking

A practical real-time guidance algorithm was developed for guiding aerobraking vehicles in such a way that the maximum heating rate, the maximum structural loads, and the post-aeropass delta-V requirements (for post-aeropass orbit insertion) are all minimized. The algorithm is general and reusable in the sense that a minimum of assumptions are made, thus minimizing the number of gains and mission-dependent parameters that must be laboriously determined prior to a particular mission. A particularly interesting feature is that inplane guidance performance is tuned by simply adjusting one mission-dependent parameter, the bank margin; similarly, the out-of-plane guidance performance is turned by simply adjusting a plane controller time constant. Other objectives in the algorithm development are simplicity, efficiency, and ease of use. The algorithm is developed for, but not necessarily restricted to, a single pass mission and a trimmed vehicle with a bank angle modulation as the method of trajectory control. Guidance performance is demonstrated via results obtained using this algorithm integrated into an aerobraking test-bed program. Comparisons are made with numerical results from a version of the aerobraking guidance algorithm that was to be flown onboard NASA's aeroassist flight experiment (AFE) vehicle. Promising results are obtained with a minimum of development effort.

Dukeman, G. A.↗
NASA NTRS1987

Stability and transition in supersonic boundary layers

The full three-dimensional time-dependent compressible Navier-Stokes equations are numerically solved by a Fourier-Chebyshev collocation algorithm to study the stability of supersonic flows over a flat plate. Several non-linear numerical experiments suggest the existence of a secondary instability which might provide a possible route to transition. The interaction of the modes involved in this secondary instability is possibly amenable to a Floquet theory. Pertinent differences between this instability and the more common incompressible K-type instabilities are pointed out.

Erlebacher, Gordon↗
NASA NTRS1992

The cool-star spectral catalog: A uniform collection of IUE SWP-LOs

Over the past decade and a half of its operations, the International Ultraviolet Explorer has recorded low-dispersion spectrograms in the 1150-2000 A interval of more than 800 stars of late spectral type (F-M). The sub-2000 A region contains a number of emission lines that are key diagnostics of physical conditions in the high-excitation chromospheres and subcoronal 'transition zones' of such stars. Many of the sources have been observed a number of times, and the available collection of SWP-LO exposures in the IUE Archives exceeds 4,000. With support from the Astrophysics Data Program, we have assembled the archival material into a catalog of IUE far-UV fluxes of late-type stars. In order to ensure uniform processing of the spectra, we: (1) photometrically corrected the raw vidicon images with a custom version of the 1985 SWP ITF; (2) identified and eliminated, sharp cosmic-ray 'hits' by means of a spatial filter; (3) extracted the spectral traces with the 'optimal' (weighted-slit) strategy; and (4) calibrated them against a well-characterized reference source, the DA white dwarf G191-B2B. Our approach is similar to that adopted by the IUE Project for its 'Final Archive', but our implementation is specialized to the case of chromospheric emission-line sources. We measured the resulting SWP-LO spectra using a semi-autonomous algorithm that establishes a smooth continuum by numerical filtering, and then fits the significant emissions (or absorptions) by means of a constrained Bevington-type multiple-Gaussian procedure. The algorithm assigns errors to the fitted fluxes - or upper limits in the absence of a significant detection - according to a model based on careful measurements of the noise properties of the IUE's intensified SEC cameras. Here, we describe the 'visualization' strategies we adopted to ensure human-review of the semi-autonomous processing and measuring algorithms; the derivation of the noise model and the assignment of errors; and the structure of the final catalog as delivered to the Astrophysics Data System.

Ayres, T.↗
NASA NTRSDate not supplied

Numerical Predictor-Corrector Based Guidance Scheme For Aero-Gravity Assist at Titan For Enceladus Missions

Aero-gravity assist is a spacecraft maneuver than can enable a vehicle to insert into an orbit of one planetary body using the atmosphere and gravity field of a secondary body, reducing the required propellant mass relative to a fully-propulsive orbit insertion. The Fully Numerical Predictor-Corrector Aerocapture Guidance algorithm was modified to work with a direct force control blunt body vehicle, executing an aero-gravity assist at Titan to enter a Saturnian orbit and conduct fly-by at Enceladus. Additionally, a proportional-integral-derivative controller was implemented to command sideslip angles for control of the orbital inclination. Numerical simulation showed the developed guidance scheme was capable of minimizing the energy and inclination error at atmospheric exit, allowing Saturnian moon tour trajectories and Enceladus exploration at a small delta-V cost, on the order of 100 m/s, in the nominal case.

Daniel Louis Engel↗
NASA NTRSDate not supplied

Numerical Predictor-Corrector Based Guidance Scheme For Aero-Gravity Assist at Titan For Enceladus Missions

Aero-gravity assist is a spacecraft maneuver than can enable a vehicle to insert into an orbit of one planetary body using the atmosphere and gravity field of a secondary body, reducing the required propellant mass relative to a fully-propulsive orbit insertion. The Fully Numerical Predictor-Corrector Aerocapture Guidance algorithm was modified to work with a direct force control blunt body vehicle, executing an aero-gravity assist at Titan to enter a Saturnian orbit and conduct fly-by at Enceladus. Additionally, a proportional-integral-derivative controller was implemented to command sideslip angles for control of the orbital inclination. Numerical simulation showed the developed guidance scheme was capable of minimizing the energy and inclination error at atmospheric exit, allowing Saturnian moon tour trajectories and Enceladus exploration at a small delta-V cost, on the order of 100 m/s, in the nominal case.

Daniel L. Engel↗
NASA NTRS1995

A case study of view-factor rectification procedures for diffuse-gray radiation enclosure computations

The view factors which are used in diffuse-gray radiation enclosure calculations are often computed by approximate numerical integrations. These approximately calculated view factors will usually not satisfy the important physical constraints of reciprocity and closure. In this paper several view-factor rectification algorithms are reviewed and a rectification algorithm based on a least-squares numerical filtering scheme is proposed with both weighted and unweighted classes. A Monte-Carlo investigation is undertaken to study the propagation of view-factor and surface-area uncertainties into the heat transfer results of the diffuse-gray enclosure calculations. It is found that the weighted least-squares algorithm is vastly superior to the other rectification schemes for the reduction of the heat-flux sensitivities to view-factor uncertainties. In a sample problem, which has proven to be very sensitive to uncertainties in view factor, the heat transfer calculations with weighted least-squares rectified view factors are very good with an original view-factor matrix computed to only one-digit accuracy. All of the algorithms had roughly equivalent effects on the reduction in sensitivity to area uncertainty in this case study.

Taylor, Robert P.↗
NASA NTRS1982

A general algorithm for solving the algebraic Riccati equation

The generalized eigenvalue problem provides a suitable framework for reliable solutions of many system theoretic, control, and estimation problems. A general algorithm for solving the matrix algebraic Riccati equation (ARE) which utilizes a pencil structure is described here. This algorithm avoids unnecessary inversion of cost or transition matrices, making it a numerically sound way to solve for the gains and/or ARE with singular quadratic costs, for cases satisfying detectability and stabilizability conditions. Examples are solution with discrete dead-beat control, noiseless measurements in Kalman filters and time-delays in discrete-time systems, which cause difficulties in the Hamiltonian standard eigenvalue problem formulation. The ARE algorithm implementatiton and numerical examples are shown.

Walker, R. A.↗
NASA NTRS1992

On the distribution of pitch angles in external galactic spirals NGC 1232 and NGC 5457

A numerical method, originally developed to analyze the morphology of global and local structure in prototype galaxies, is modified for analyzing observed disk-shape galaxies. Two digitized spiral galaxies NGC 1232 and NGC 5457 with varying degrees of contrast between arm and interarm regions are analyzed. A synergism of partitioning methods and a geometric mean least-squares regression algorithm serves to isolate local arm segments, spurs, feathers, and secondary features and to measure their pitch angles and lengths. The global arms are actually highly disjointed, with arm segments frequently revealing pitch angles between 30 and 50 deg, certainly greater than those of the parent arms. Prominent spurs tend to exhibit a much greater pitch angle. The automated mathematical algorithm is shown to have negligible numerical biasing and could be applied to any number of spiral galaxies manifesting flocculent structure, either prototype or observed, and could possibly be used as a tool for classification of multiple-armed-type galaxies.

Russell, William S.↗
NASA NTRSDate not supplied

Control Effector Unsaturation Modification to the Cascading Generalized Inverse Control Allocation Algorithm

Control allocation has sufficiently progressed such that it is used in front-line fighter aircraft such as the F-18Superhornet and the F-35 Joint Strike Fighter. Published literature shows the F-35 utilizes Nonlinear Dynamic Inversion in conjunction with an Effector Blender that incorporates the Cascading Generalized Inverse control allocation algorithm. While the Cascading Generalized Inverse algorithm is one of the premier generalized inverse methods, it does suffer from three deficiencies. In particular, it suffers from an inability to achieve some desired outcomes, it intermittently provides non-optimal solutions and generally fails to preserve moment direction near maximal achievable moments. An effector unsaturation method based on a Scalar Difference Quadratic was first introduced and implemented on the iterative Prediction Method control allocation algorithm which was shown to consistently achieve optimal (weighted) control allocation solutions throughout the entire Attainable Moment Set while preserving desired moment direction. In this paper, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the baseline algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Numerical case studies demonstrate that the Modified Cascading Generalized Inverse algorithm resolves the aforementioned deficiencies.

Michael J Acheson↗
NASA NTRS1991

Comparison of polynomial approximations and artificial neural nets for response surfaces in engineering optimization

Engineering optimization problems involve minimizing some function subject to constraints. In areas such as aircraft optimization, the constraint equations may be from numerous disciplines such as transfer of information between these disciplines and the optimization algorithm. They are also suited to problems which may require numerous re-optimizations such as in multi-objective function optimization or to problems where the design space contains numerous local minima, thus requiring repeated optimizations from different initial designs. Their use has been limited, however, by the fact that development of response surfaces randomly selected or preselected points in the design space. Thus, they have been thought to be inefficient compared to algorithms to the optimum solution. A development has taken place in the last several years which may effect the desirability of using response surfaces. It may be possible that artificial neural nets are more efficient in developing response surfaces than polynomial approximations which have been used in the past. This development is the concern of the work.

Carpenter, William C.↗
NASA NTRS1988

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS1988

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Baritzhack, Itzhack Y.↗