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At least 1,063 records · Page 59

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NASA NTRS1987

Ice growth in supercooled solutions of antifreeze glycoproteins

The effects of different degrees of supercooling on the habit and rates of growth of ice crystals from solutions of antifreeze glycoproteins are reported. To isolate the influence of different solutions and supercooling alone, a system was devised that nucleated crystals in the middle of a uniformly supercooled sample. Alternatively, single crystals of selected orientation were inserted into free liquid surface. A crystallization rate up to five times greater than that in pure water was found. A mechanism explaining these results is suggested.

Harrison, K.↗

NASA NTRS1987

A general solution to the silhouette problem

In displaying computer-generated graphics, it is advantageous to have the facility to render any subset of polygons as a silhouette with respect to itself. While the silhouette problem has been addressed before, there has been no completely general solution. In this report, the silhouette problem for calligraphic drawings is solved for the most general case. This solution offers all possible combinations of silhouette and non-silhouette specifications for an arbitrary solid. It allows the flexibility to enhance the clarity of any three-dimensional scene presented in two dimensions.

Hedgley, David R., Jr.↗

NASA NTRS1986

Numerical solutions of three-dimensional Navier-Stokes equations for closed-bluff bodies

Methods of grid adaption are reviewed and a method is developed with the capability of adaption to several flow variables. This method is based on a variational approach and is an algebraic method which does not require the solution of partial differential equations. The method has also been formulated in such a way that there is no need for any matrix inversion. The method is used in conjunction with the calculation of hypersonic flow over a blunt nose. The equations of motion are the compressible Navier-Stokes equations where all viscous terms are retained. They are solved by the MacCormack time-splitting method and a movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption. The results are compared with the experimental and other numerical results.

Abolhassani, Jamshid S.↗

NASA NTRS1987

Effect of element size on the solution accuracies of finite-element heat transfer and thermal stress analyses of space shuttle orbiter

The effect of element size on the solution accuracies of finite-element heat transfer and thermal stress analyses of space shuttle orbiter was investigated. Several structural performance and resizing (SPAR) thermal models and NASA structural analysis (NASTRAN) structural models were set up for the orbiter wing midspan bay 3. The thermal model was found to be the one that determines the limit of finite-element fineness because of the limitation of computational core space required for the radiation view factor calculations. The thermal stresses were found to be extremely sensitive to a slight variation of structural temperature distributions. The minimum degree of element fineness required for the thermal model to yield reasonably accurate solutions was established. The radiation view factor computation time was found to be insignificant compared with the total computer time required for the SPAR transient heat transfer analysis.

Ko, William L.↗

NASA NTRS1988

Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes

A method for accurately solving inviscid compressible flow in the subcritical and supercritical regimes about complex configurations is presented. The method is based on the use of unstructured triangular meshes in two dimensions, and special emphasis is placed on the accuracy and efficiency of the solutions. High accuracy is achieved by careful scaling of the artificial dissipation terms, and by reformulating the inner and outer boundary conditions for both the convective and dissipative operators. An adaptive grid refinement strategy is presented which enhances the solution accuracy for complex flows. When coupled with an unstructured multigrid algorithm, this method is shown to produce an efficient solver for flows about arbitrary configurations.

Mavriplis, Dimitri J.↗

NASA NTRS1987

Stochasticity in numerical solutions of the nonlinear Schroedinger equation

The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Liapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.

Shen, Mei-Mei↗

NASA NTRS1987

Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems

Fundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties.

Streett, C. L.↗

NASA NTRS1988

Accelerating the computation of steady state solutions for non-equilibrium, chemically reacting flow fields

The objective of the study is to develop a technique for accelerating the computation of steady state solutions for nonequilibrium chemically reacting flow fields using the time marching method. To achieve this, a better initial condition is introduced for the time marching scheme to achieve a faster convergence to the steady state solution. This is done by replacing the source terms of the original system of equations, which are responsible for the sitffness, by approximate source terms. It is shown that the saving in computation time increases in direct proportion to the stiffness of the flow model, with a factor of 10 increase in convergence rate observed for the models tested in this study.

Krispin, Jacob↗

NASA NTRS1987

Inverse solution of Kepler's equation for hyperbolic orbits

An algorithm is presented for efficient inverse solution of Kepler's equation for hyperbolic orbits. It is shown that an expansion of Barker's equation into a bicubic polynomial provides a good approximation to obtain accurate starting values for rapid numerical solution of Kepler's equation. In the approximate equation a cubic in normalized elapsed flight time from pericenter is set equal to a cubic in a function S of eccentricity and true anomaly. The initial estimate of S to use in an iteration formula is obtained by evaluating the cubic in normalized flight time and finding in most cases the single real root of the other cubic. This initial estimate has an accuracy corresponding to values of true anomaly in error by less than 0.5 degrees generally.

Boltz, Frederick W.↗

NASA NTRS1988

Evidence for a scaling solution in cosmic-string evolution

Numerical simulations are used to study the most fundamental issue of cosmic-string evolution: the existence of a scaling solution. Strong evidence is found that a scaling solution does indeed exist. This justifies the main assumption on which the cosmic-string theories of galaxy formation is based. The main conclusion coincides with that of Albrecht and Turok (1985) but the results are not consistent with theirs. In fact, the results indicate that the details of string evolution are very different from the standard dogma.

Bennett, David P.↗

NASA NTRS1988

I-BIEM, an iterative boundary integral equation method for computer solutions of current distribution problems with complex boundaries: A new algorithm. I - Theoretical

A new algorithm for an iterative computation of solutions of Laplace's or Poisson's equations in two dimensions, using Green's second identity, is presented. This algorithm converges strongly and geometrically and can be applied to curved, irregular, or moving boundaries with nonlinear and/or discontinuous boundary conditions. It has been implemented in Pascal on a number of micro- and minicomputers and applied to several geometries. Cases with known analytic solutions have been tested. Convergence to within 0.1 percent to 0.01 percent of the theoretical values are obtained in a few minutes on a microcomputer.

Cahan, B. D.↗

NASA NTRS1987

Evaluation of Navier-Stokes and Euler solutions for leading-edge separation vortices

Extensive study on the numerical simulation of the vortical flow over a double delta wing is carried out using the thin layer Navier-Stokes and Euler equations. Two important flow characteristics, vortex interaction and vortex breakdown, are successfully simulated. Grid resolution is one of the most important factors associated with the vortex problem. Computations were performed on a series of grids with various levels of refinement, coarse, medium, and fine. Computations using either the coarse or medium grids fail to capture the proper physical phenomena. The computed result using a fine grid shows flow unsteadiness once the vortex breakdown takes place. The C sub L - alpha characteristics are well predicted up to the breakdown angle of attack for all the grid distributions. The Euler solutions show fairly good agreement with the experiment on the C sub L - alpha characteristics. However, other aspects of the solution at each angle of attack, such as the locus of the leading edge separation vortex, are not consistent with the experiment. Even for the fine grid Navier-Stokes computations, further grid resolution is required to obtain good quantitative agreement with the experiment.

Fujii, K.↗

NASA NTRS1988

Developing fluid flow in a curved duct of square cross-section and its fully developed dual solutions

Developing fluid flow in a curved duct of square cross-section is studied numerically by a factored ADI finite-difference method on a staggered grid. A central-difference scheme with primitive variables is used inside the computational domain to reduce numerical diffusion. Two Reynolds numbers, 574 and 790, based upon a bulk velocity and hydraulic diameter are chosen for curvature ratios of 1/6.45 and 1/2.3, respectively. It is found that the secondary flow is far more complicated than expected, with the appearance of at least two pairs of vortices. Main-flow separation is also observed for the higher curvature ratio. Furthermore, it is observed that the flow develops into two quite different states downstream, depending upon the inlet conditions. Solutions of the fully developed Navier-Stokes equations is shown to be not unique beyond a certain critical Reynolds number. Developing flow seems to evolve into the fully developed state along a particular branch into which the fully developed solution bifurcates.

Soh, W. Y.↗

NASA NTRS1988

Solution of structural analysis problems on a parallel computer

The problems of a blade-stiffened panel with a hole subjected to compression, and a deployable space mast subjected to tip loads, are treated through the application of FEM to model generation followed by the solution of a linear system of equations. Direct and iterative approaches to the solution of the linear systems are solved in turn; for the panel problems using varying numbers of processors, the incomplete Cholesky-conjugate gradient method was the fastest iterative method on all but two instances in which the number of processors was large.

Storaasli, Olaf↗

NASA NTRS1988

Direct finite element solution on an optical laboratory matrix-vector processor

The first optical laboratory system results employing a direct LU decomposition solution of a system of linear algebraic equations are presented for a finite element problem solution. This also represents the first laboratory demonstration of the use of sign-magnitude negative number representation as well as new bit partitioning techniques to increase the accuracy of an optical encoded processor beyond the number of bit channels available.

Casasent, David↗

NASA NTRS1988

Error indicators and accuracy improvements of finite element solutions

Practical and reliable estimators of the discretization errors in engineering problems are developed. Error indicators for identifying the regions or elements of the solution domain which are likely to have the largest discretization errors are presented, and a simple computational procedure for improving the accuracy of the finite element solutions for shell problems is given. The similarities between the proposed procedure and a preconditioned conjugate gradient (PCG) technique are identified and exploited to generate pointwise error indicators from the PCG technique. Numerical examples in the linear static analysis of shells are presented.

Noor, Ahmed K.↗

NASA NTRS1988

Enthalpies of formation of CaAl4O7 and CaAl12O19 (hibonite) by high temperature, alkali borate solution calorimetry

Enthalpies of formation were determined for two calcium aluminate phases, CaAl4O7 and CaAl12O19, using high-temperature alkali borate solution calorimetry. The aluminates were synthesized by multiple-cycle heating and grinding stoichiometric mixtures of CaCO3 and Al2O3, and the products were characteized by X-ray diffraction and SEM microbeam analysis. The data on impurities (CaAl4O7 was found to be about 89.00 percent pure by weight and the CaAl12O19 samples about 91.48 percent pure) were used to correct the heat of solution values of the synthetic products. The enthalpies of formation, at 1063 K, from oxides, were found to be equal to -(25.6 + or - 4.7) kJ/g.f.w. for CaAl4O7 and -(33.0 + or - 9.7) kJ/g.f.w. for CaAl12O19; the respective standard enthalpies of formation from elements, at 298 K, were estimated to be -4007 + or - 5.2 kJ/g.f.w. and -10,722 + or - 12 kJ/g.f.w.

Geiger, C. A.↗