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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 433 records · Page 24

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NASA NTRS1975

Finite-element solution for a combined radiative-conductive analysis with mixed diffuse-specular surface characteristics

The finite-element method has been applied to solve a combined radiative-conductive heat transfer problem for a large space telescope similar to those used in orbiting satellites. The derivation of the underlying matrices and associated solution algorithm for a 2-D triangular element is presented in detail. The resulting expressions for this triangular element typify such an analysis, which yields constitutive matrices when the heat equation is cast in the matrix form. The relevant matrices include those pertaining to thermal conductance, internal heat generation, radiative exchanges, and all possible external thermal loadings. Emphasis is placed on the treatment of non-linear radiative interchange between surfaces in an enclosure having mixed diffuse-specular surface characteristics. Essential differences in governing equations describing these distinctive surface characteristics are identified. Concluding remarks are drawn from an example simulating a Cassegrainian space telescope.

Lee, H.-P.↗

NASA NTRS1975

Inviscid to turbulent transition of trailing vortices

The plateau region in which trailing vortices initially exhibit slow decay of maximum tangential speed is demonstrated with the aid of constant and variable eddy viscosity models. The existence of the plateau is explained by the presence of the viscous core and by the necessity for transition of the initial, nearly inviscid profile to similarity far downstream. Span loading is shown to affect the initial maximum tangential speed as well as the duration of the plateau region. Triangular span loading is shown to present less hazard to trailing aircraft, at least in the near field, than elliptic loading because the inviscid profile for triangular loading exhibits a finite tangential speed at the vortex centerline and a large inviscid core.

Iversen, J. D.↗

NASA NTRS1976

Multivariate normal integration

Monte Carlo program evaluates integrals over rectangular regions for dimensions less than six and over elliptical regions in bivariate case. Program gives positive definite symmetric variance/covariance matrix factorization and calculates reciprocal of lower triangular matrix and product of diagonal elements of triangular matrix.

Falls, L. W.↗

NASA NTRS1975

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Cooke, C. H.↗

NASA NTRS1975

Gram-Schmidt algorithms for covariance propagation

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Thornton, C. L.↗

NASA NTRS1977

Gram-Schmidt algorithms for covariance propagation

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UD(transpose of U), where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increase mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Thornton, C. L.↗

NASA NTRS1977

Application of the TRPLT1 element to large amplitude free vibrations of plates

A finite element formulation is developed for analyzing large amplitude free flexural vibrations of thin plates in NASTRAN. Stress distributions in the plate, in addition to deflection shapes and nonlinear frequencies are determined. Linearized equations of motion governing large amplitude oscillations of plates and a linearized geometrical stiffness matrix are presented. The solution procedure and convergence characteristics are discussed. The quasi-linear geometrical stiffness matrix for an eighteen degree-of-freedom higher order triangular plate element is evaluated by using a seven-point numerical integration. Nonlinear frequencies for square, rectangular, rhombic, and isosceles triangular plates, with edges simply supported or clamped, are compared with earlier solutions. The present formulation is found to give results entirely adequate for engineering purposes.

Mei, C.↗

NASA NTRS1979

Wave propagation in ducts using the finite element method

The paper outlines a comparative study designed to assess and compare the accuracy of the finite element method (FEM) for linear and quadratic elements as applied to problems in duct acoustics. The acoustic disturbances are assumed to be irrotational and isentropic so that the problem can be formulated in terms of the acoustic velocity potential. It is shown that for the case of plane wave propagation in a hard-walled annular cylinder, the accuracy of the FEM solution can be increased at higher frequencies by using quadratic triangular elements instead of linear triangular elements. Evidence is presented to enhance the confidence in applying the developed FEM by comparing results with those obtained by other independently developed numerical approaches such as an integral equation technique and a finite difference method.

Majjigi, R. K.↗

NASA NTRS1979

Beam builder for space fabrication

Construction of a beam builder for producing triangular truss aluminum beams for use on large space structures is described. The machine will fabricate 0.04 cm thick 2024-T3 aluminum alloy into beams weighing 1.265 kg-m with side braces spot-welded to end caps to fabricate a triangular truss configuration up to 305 m long. The design characteristics, the electrical subsystems, the power requirements of the spot welding equipment, and the computer system for coordinating the motion of the Yoder rolling mills for forming caps from aluminum coils are described. Spot welding was compared with ultrasonic welding, stapling, wire stitching, riveting, grommets, stamp-lok, and pierce and fold joining methods with respect to ease of operation, safety, practicality, and ease of energy consumption. The beam builder will be evaluated to identify design requirements which can be utilized for the space flight version of its concept.

Ehl, J. H.↗

NASA NTRS1981

Low thermal conductance rigidizer for reducing torsional oscillations in cryogenic Dewars

A rigidizer, which provides greater rigidity against torsional oscillations, is highly resistant to radial motions, and has low thermal conductivity, has been developed to decrease vibrational levels affecting infrared detectors operated in cryostats (e.g., HD-3L Dewar) in aircraft such as NASA's Kuiper Airborne Observatory. The rigidizer is composed of two triangular elements and an intermediate support structure which joins them at the centers of their sides. The reentrant design provides a long heat path, while the triangular truss structure provides high rigidity in the horizontal plane. The structure is relatively compliant in the vertical direction, a desirable feature since the internal structure of the Dewar contracts as it cools. Rigidity in the vertical direction is provided by the neck tube. The support structure is quite compact. Several variants of the rigidizer have been fabricated, using flat sheets of G-10 fiberglass epoxy in thicknesses between 0.75-1.5 mm for the upper and lower truss assemblies, and either G-10 or stainless steel for the intermediate structure.

Harper, D. A.↗

NASA NTRS1982

Stacbeam - An efficient, low-mass, sequentially deployable structure

Design features of the stacking triangular articulated compact beam (Stacbeam) as a candidate truss structure for GEOS spacecraft solar power arrays are explored. Solar arrays of increasing size require folding, noninterfering structures, minimal thermal effects, slow and controlled deployment, and a high aspect ratio. The Stacbeam consists of a triangular batten frame perpendicular to the beam axis, three longerons attached at the corners of the batten frame and mounted parallel to the beam axis, and three diagonals to provide shear and torsional stiffness. Locking hinges are installed at the midpoint and ends of each longeron and at the midpoint and ends of each diagonal. The material is graphite/epoxy composite with a 120 GPa modulus and a 1500 kg/sq m density. Successful vertical deployment on the ground has been effected with a prototype deployer, together with horizontal cantilever in a fully deployed configuration.

Adams, L. R.↗

NASA NTRS1984

Algorithms for solving large sparse systems of simultaneous linear equations on vector processors

Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.

David, R. E.↗

NASA NTRS1985

The application of some lifting-body reentry concepts to missile design

The aerodynamic characteristics of some lifting-body concepts are examined with a view to the applicability of such concepts to the design of missiles. A considerable amount of research has been done in past years with vehicle concepts suitable for manned atmospheric-entry and atmospheric flight. Some of the concepts appear to offer some novel design approaches for missiles for a variety of missions and flight profiles, including long-range orbital/reentry with transatmospheric operation for strategic penetration, low altitude penetration, and battlefield tactical. The concepts considered include right triangular pyramidal configurations, a lenticular configuration, and various 75-degree triangular planform configurations with variations in body camber and control systems. The aerodynamic features are emphasized but some observations are also made relative to other factors such as heat transfer, structures, carriage, observability, propulsion, and volumetric efficiency.

Spearman, M. L.↗

NASA NTRS1985

Distribution and Properties of Large Symmetric Knobs on Mars

Knobby terrain on Mars exists in a variety of forms from small closely spaced hills to widely separated large massifs. Fractional areal distributions of knobby terrain range from over 49% of the sampled area in regions of chaotic terrain to less than 5% along the cratered highland boundary in Amenthes and Aeolis. All symmetric knobs with long dimensions greater than or equal to 10 km were identified, mapped, and classified by shape. The spatial and dimensional distributions and shape characteristics of these features are discussed. The most common shape is elliptical: 79% of the knobs fall into this category, 11% were circular or round, 6% were triangular or wedge-shaped and the remaining 4% other shapes. All types show a roughly similar trend of rapidly decreasing number with increasing size, such that overall less than 10% of the knobs are larger than 20 km in long dimension. Circular knobs show the steepest fall-off in numbers with increasing diameter. Triangular knobs have a broader maximum with more than 65% falling in the 10 to 14 km range.

Frey, H.↗

NASA NTRS1985

The application of some lifting-body reentry concepts to missile design

Spearman, M. L.↗

NASA NTRS1985

Application of High Order Acoustic Finite Elements to Transmission Losses and Enclosure Problems

A family of acoustic finite elements was developed based on C continuity (acoustic pressure being the nodal variable) and the no-flow condition. The family include triangular, quadrilateral and hexahedral isoparametric elements with linear quadratic and cubic variation in modelling and distortion. Of greatest use in problems with irregular boundaries are the cubic isoparametric elements: the 32 node hexahedral element for three-dimensional systems; and the twelve node quadrilateral and ten node triangular elements for two-dimensional/axisymmetric applications. These elements were applied to problems involving cavity resonances, transmission loss in silencers and the study of end effects, using a Floating Point Systems 164 attached array processor accessed through an Amdahl 5860 mainframe. The elements are presently being used to study the end effects associated with duct terminations within finite enclosures. The transmission losses with various silencers and sidebranches in ducts is also being studied using the same elements.

Craggs, A.↗

NASA NTRS1983

Transformation matrices between non-linear and linear differential equations

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

Sartain, R. L.↗

NASA NTRS1986

Solution of the symmetric eigenproblem AX=lambda BX by delayed division

Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity.

Thurston, G. A.↗