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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 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Efficient computer algebra algorithms for polynomial matrices in control design

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

Baras, J. S.↗
NASA NTRS1994

Sensitivity derivatives for three dimensional supersonic Euler code using incremental iterative strategy

In a recent work, an incremental strategy was proposed to iteratively solve the very large systems of linear equations that are required to obtain quasianalytical sensitivity derivatives from advanced computational fluid dynamics (CFD) codes. The technique was sucessfully demonstrated for two large two-dimensional problems: a subsonic and a transonic airfoil. The principal feature of this incremental iterative stategy is that it allows the use of the identical approximate coefficient matrix operator and algorithm to solve the nonlinear flow and the linear sensitivity equations; at convergence, the accuracy of the sensitivity derivatives is not compromised. This feature allows a comparatively straightforward extension of the methodology to three-dimensional problems; this extension is successfully demonstrated in the present study for a space-marching solution of the three-dimensional Euler equations over a Mach 2.4 blended wing-body configuration.

Korivi, Vamshi Mohan↗
NASA NTRS2007

Estimating the Inertia Matrix of a Spacecraft

A paper presents a method of utilizing some flight data, aboard a spacecraft that includes reaction wheels for attitude control, to estimate the inertia matrix of the spacecraft. The required data are digitized samples of (1) the spacecraft attitude in an inertial reference frame as measured, for example, by use of a star tracker and (2) speeds of rotation of the reaction wheels, the moments of inertia of which are deemed to be known. Starting from the classical equations for conservation of angular momentum of a rigid body, the inertia-matrix-estimation problem is formulated as a constrained least-squares minimization problem with explicit bounds on the inertia matrix incorporated as linear matrix inequalities. The explicit bounds reflect physical bounds on the inertia matrix and reduce the volume of data that must be processed to obtain a solution. The resulting minimization problem is a semidefinite optimization problem that can be solved efficiently, with guaranteed convergence to the global optimum, by use of readily available algorithms. In a test case involving a model attitude platform rotating on an air bearing, it is shown that, relative to a prior method, the present method produces better estimates from few data.

Acikmese, Behcet↗
NASA NTRS1994

Pseudomaster equation for the no-count process in a continuous photodetection

The detection of cavity radiation with the detector placed outside the cavity is studied. Each leaked photon has a certain probability of propagating away without being detected. It is viewed as a continuous quantum measurement in which the density matrix is continuously revised according to the readout of the detector. The concept of pseudomaster equation for the no-count process is introduced; its solution leads to the discovery of the superoperator for the same process. It has the potential to become the key equation for continuous measurement process.

Lee, Ching-Tsung↗
NASA NTRS1976

Electric dipole moment function of the X1 Sigma/+/ state of CO - Vibration-rotation matrix elements for transitions of gas laser and astrophysical interest

The electric dipole moment function of the ground electronic state of carbon monoxide has been determined by combining numerical solutions of the radial Schrodinger equation with absolute intensity data of vibration-rotation bands. The derived dipole moment function is used to calculate matrix elements of interest to stellar astronomy and of importance in the carbon monoxide laser.

Chackerian, C., Jr.↗
NASA NTRS1990

Development of a model of space station solar array

Space structures, such as the space station solar arrays, must be extremely lightweight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a control system. The tension preload in the blanket of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomena known as grounding, or false stiffening, of the stiffness matrix occurs during rigid body rotation. The grounding phenomena is examined in detail. Numerous stiffness matrices developed by others are examined for rigid body rotation capability, and found lacking. Various techniques are used for developing new stiffness matrices from the rigorous solutions of the differential equations, including the solution of the directed force problem. A new directed force stiffness matrix developed by the author provides all the rigid body capabilities for the beam in space.

Bosela, Paul A.↗
NASA NTRS1996

Optimization of Orifice Geometry for Cross-Flow Mixing in a Cylindrical Duct

Mixing of gaseous jets in a cross-flow has significant applications in engineering, one example of which is the dilution zone of a gas turbine combustor. Despite years of study, the design of the jet injection in combustors is largely based on practical experience. The emergence of NO(x) regulations for stationary gas turbines and the anticipation of aero-engine regulations requires an improved understanding of jet mixing as new combustor concepts are introduced. For example, the success of the staged combustor to reduce the emission of NO(x) is almost entirely dependent upon the rapid and complete dilution of the rich zone products within the mixing section. It is these mixing challenges to which the present study is directed. A series of experiments was undertaken to delineate the optimal mixer orifice geometry. A cross-flow to core-flow momentum-flux ratio of 40 and a mass flow ratio of 2.5 were selected as representative of a conventional design. An experimental test matrix was designed around three variables: the number of orifices, the orifice length-to- width ratio, and the orifice angle. A regression analysis was performed on the data to arrive at an interpolating equation that predicted the mixing performance of orifice geometry combinations within the range of the test matrix parameters. Results indicate that the best mixing orifice geometry tested involves eight orifices with a long-to-short side aspect ratio of 3.5 at a twenty-three degree inclination from the center-line of the mixing section.

Kroll, J. T.↗
NASA NTRS2017

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗
NASA NTRS1979

Gust alleviation - Criteria and control laws

The relationships between criteria specified for aircraft gust alleviation and the form of the control laws that result from the criteria are considered. Open-loop gust alleviation based on the linearized, small perturbation equations of aircraft motion is discussed, and an approximate solution of the open-loop control law is presented for the case in which the number of degrees of freedom of the aircraft exceeds the rank of the control effectiveness matrix. Excessive actuator lag is compensated for by taking into account actuator dynamics in the equations of motion, resulting in the specification of a general load network. Criteria for gust alleviation when output motions are gust alleviated and the closed-loop control law derived from them are examined and linear optimal control law is derived. Comparisons of the control laws reveal that the effectiveness of an open-loop control law is greatest at low aircraft frequencies but deteriorates as the natural frequency of the actuators is approached, while closed-loop methods are found to be more effective at higher frequencies.

Rynaski, E. G.↗
NASA NTRS2004

Associative Flow Rule Used to Include Hydrostatic Stress Effects in Analysis of Strain-Rate-Dependent Deformation of Polymer Matrix Composites

designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and the strain-rate dependence of the composite response are due primarily to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. By applying micromechanics techniques along with given fiber properties, one can also determine the effects of the hydrostatic stresses in the polymer on the overall composite deformation response. First efforts to account for the hydrostatic stress effects in the composite deformation applied purely empirical methods that relied on composite-level data. In later efforts, to allow polymer properties to be characterized solely on the basis of polymer data, researchers at the NASA Glenn Research Center developed equations to model the polymers that were based on a non-associative flow rule, and efforts to use these equations to simulate the deformation of representative polymer materials were reasonably successful. However, these equations were found to have difficulty in correctly analyzing the multiaxial stress states found in the polymer matrix constituent of a composite material. To correct these difficulties, and to allow for the accurate simulation of the nonlinear strain-rate-dependent deformation analysis of polymer matrix composites, in the efforts reported here Glenn researchers reformulated the polymer constitutive equations from basic principles using the concept of an associative flow rule. These revised equations were characterized and validated in an experimental program carried out through a university grant with the Ohio State University, wherein tensile and shear deformation data were obtained for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. Tensile deformation data also were obtained over a variety of strain rates and fiber orientation angles for a representative polymer matrix composite composed using the polymer.

Goldberg, Robert K.↗
DOE OSTI2026

Back-to-back dijet production in DIS at arbitrary Bjorken x: TMD gluon distributions to twist-3 accuracy

We derive the gluon transverse-momentum-dependent (TMD) operator structure of back-to-back\\\\r\\\\nquark–antiquark dijet production in deep inelastic scattering at arbitrary Bjorken-x to twist-3 ac\\\\r\\\\ncuracy. Working at leading order in the strong coupling and in the kinematic regime where the\\\\r\\\\ntransverse momentum imbalance of the jets is much smaller than their individual transverse mo\\\\r\\\\nmenta, we perform a systematic gradient expansion of the quark propagator in a background gluon\\\\r\\\\nfield. This expansion organizes multiple interactions with the target in terms of longitudinal Wilson\\\\r\\\\nlines and gauge-invariant field-strength insertions, yielding a TMD description valid beyond the\\\\r\\\\nstrict high-energy eikonal (x → 0) approximation. We obtain explicit cross sections for longitudi\\\\r\\\\nnally and transversely polarized virtual photons, identifying all contributing gluon TMD operators\\\\r\\\\nup to twist-3, including structures involving F+−, Fij, and three-gluon correlators. The full lon\\\\r\\\\ngitudinal phase eixP+z− associated with Bjorken-x is retained throughout. In the small-x limit,\\\\r\\\\nour results reproduce the known sub-eikonal expressions obtained in the Color Glass Condensate\\\\r\\\\nframework, establishing a direct connection between the general-x TMD expansion and high-energy\\\\r\\\\nfactorization. We further reduce the operator basis using equations of motion, minimizing the num\\\\r\\\\nber of independent nonperturbative matrix elements entering the cross section. This work provides\\\\r\\\\na systematic foundation for extending TMD analyses of dijet production beyond leading twist, es\\\\r\\\\ntablishing a unified operator framework valid at arbitrary Bjorken-x that smoothly interpolates\\\\r\\\\nbetween moderate- and small-x descriptions of gluon TMDs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Quarkonium polarization in medium from open quantum systems and chromomagnetic correlators

Here, by considering the Markovian condition and applying the Wigner transformation upon the diagonal spin components of the quarkonium density matrix with the semiclassical expansion, we systematically derive the Boltzmann transport equation for quarkonia with polarization dependence in the quantum optical limit. Unlike the spin-independent collision terms governed by certain chromoelectric field correlators, new gauge invariant correlators of chromomagnetic fields determine the recombination and dissociation terms with polarization dependence at the order we are working. We also derive a Lindblad equation describing the in-medium transitions between spin-singlet and spin-triplet heavy quark-antiquark pairs in the quantum Brownian motion limit. The Lindblad equation is governed by new transport coefficients defined in terms of the chromomagnetic field correlators. Our formalism is generic and valid for both weakly coupled and strongly coupled quark gluon plasmas. It can be further applied to study spin alignment of vector quarkonia in heavy ion collisions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1964

Three-dimension heat transfer program

An IBM 7094, three dimensional, heat transfer program for satellite application is discussed. The program may be applied to all phases of spacecraft life, from launch to orbital quasi-steady state. Launch phase heating includes inputs by radiation from the hot fairing and free molecule flow heating after nose cone ejection. Orbital heat fluxes are accounted for by direct sunlight, earth-reflected sunlight, and earth-emitted input to the satellite. Internal heat exchange by conduction and radiation is determined, provided the appropriate conductances, radiation view factors, and effective emittances are known. A simplified analysis of an active thermal controlled spacecraft is incorporated into the program. One or more surfaces may contain shutter systems which have optical properties specified as a function of shutter opening. The program evaluates the feasibility of any configuration based upon maintaining an internal component within its tolerable temperature limits. The program employs a matrix inversion subroutine (Gauss Elimination Method) to solve the heat balance equations.

COMPUTER PROGRAM↗
NASA NTRS1973

Interaction between a circular inclusion and an arbitrarily oriented crack

The plane interaction problem for a circular elastic inclusion imbedded into an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equation with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress intensity factors are given.

Erdogan, F.↗