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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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity

A simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems is presented. The analysis is formulated on the basis of conservation laws of elasticity and of fundamental relationships in fracture mechanics. The problem is reduced to the determination of mixed-mode stress-intensity factor solutions in terms of conservation integrals involving known auxiliary solutions. One of the salient features of the present analysis is that the stress-intensity solutions can be determined directly by using information extracted in the far field. Several examples with solutions available in the literature are solved to examine the accuracy and other characteristics of the current approach. This method is demonstrated to be superior in its numerical simplicity and computational efficiency to other approaches. Solutions of more complicated and practical engineering fracture problems dealing with the crack emanating from a circular hole are presented also to illustrate the capacity of this method

Yau, J. F.↗
NASA NTRS1972

Multipath propagation study for L-band, over-ocean, satellite-aircraft communication link

The results are presented of a study of multipath propagation between an aeronautical relay satellite in synchronous earth orbit and an aircraft flying over the ocean. An analytical model for the reflected power is developed and the results of a computer solution are compared with an approximate solution obtained through integration by the method of steepest descent. The computer solution is shown to differ considerably from the approximate solution. Both methods are compared with the limited experimental results available.

Deal, J. H.↗
NASA NTRS1980

Generation of C-type cascade grids for viscous flow computation

A rapid procedure for generating C-type cascade grids suitable for viscous flow computations in turbomachinery blade rows is presented. The resulting mesh is periodic from one blade passage to the next, nearly orthogonal, and continuous across the wake downstream of a blade. The procedure employs a pair of conformal mappings that take the exterior of the cascade into the interior of an infinite strip with curved boundaries. The final transformation to a rectangular computational domain is accomplished numerically. The boundary values are obtained from a panel solution of an integral equation and the interior values by a rapid ADI solution of Laplace's equation. Examples of C-type grids are presented for both compressor and turbine blades and the extension of the procedure to three dimensions is briefly outlined.

Sockol, P. M.↗
NASA NTRS1971

FORMAC integration program: A special applications package used in developing techniques of orbital decay and long term ephemeris prediction for satellites in earth orbit

The symbolic manipulation capabilities of the FORMAC (Formula Manipulation Compiler) language are employed to expand and analytically evaluate integrals. The program integration is effected by expanding the integral(s) into a series of subintegrals and then substituting a pre-derived and pre-coded solution for that particular subintegral. Derivation of the integral solutions necessary for precoding is included, as is a discussion of the FORMAC system limitations encountered in the programming effort.

Rowe, C. K.↗
NASA NTRS1994

A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

Hu, Fang Q.↗
NASA NTRS2011

Combined Weekly Coordinate Solutions from SLR and DORIS

In International Terrestrial Reference Frame (ITRF) 2005 and ITRF2008, the approach for the construction of solutions by the IERS has been for individual analysis centers of each technique to process geodetic tracking data, and for each technique to develop a solution (or contribution) that is integrated into the final ITRF solution by careful combination of the technique solutions. The connections between the geodetic networks are realized by the application of local ties. In an alternate approach, we may assure processing homogeneity by creating normal equations for different techniques with the same orbit determination software, using identically derived algorithms. Another derivative of this approach is to realize the ties between the techniques using satellites tracked with multiple techniques; in effect tieing the networks together using satellite dynamics. In this solution, we develop a time series and a set of cumulative solutions from Satellite Laser Ranging (SLR) & Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) based on homogeneous processing with the NASA GEODYN precise orbit determination suite of programs, where we jointly combine weekly the SLR data to Lageos1, Lageos2, Starlette, and Stella with the DORIS data from SPOT2-SPOT5, as well as satellites that utilize both techniques (TOPEX/Poseidon, Envisat, Jason-2). We discuss the modeling that is applied including upgrades implemented since the submission of the GSC ITRF2008 contributions for IDS. Firstly, we compare the SLR-only solutions comprising four geodetic satellites with the standard approach of utilizing only Lageos1 & Lageos2. Secondly, we evaluate the impact on the DORIS coordinates of the joint analysis with the SLR data.

Lemoine, F.↗
NASA NTRS2008

High Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

Taylor series integration is implemented in a spacecraft trajectory analysis code-the Spacecraft N-body Analysis Program (SNAP) - and compared with the code s existing eighth-order Runge-Kutta Fehlberg time integration scheme. Nine trajectory problems, including near Earth, lunar, Mars and Europa missions, are analyzed. Head-to-head comparison at five different error tolerances shows that, on average, Taylor series is faster than Runge-Kutta Fehlberg by a factor of 15.8. Results further show that Taylor series has superior convergence properties. Taylor series integration proves that it can provide rapid, highly accurate solutions to spacecraft trajectory problems.

Scott, James R.↗
NASA NTRS2001

Coarse Grid Modeling of Turbine Film Cooling Flows Using Volumetric Source Terms

The recent trend in numerical modeling of turbine film cooling flows has been toward higher fidelity grids and more complex geometries. This trend has been enabled by the rapid increase in computing power available to researchers. However, the turbine design community requires fast turnaround time in its design computations, rendering these comprehensive simulations ineffective in the design cycle. The present study describes a methodology for implementing a volumetric source term distribution in a coarse grid calculation that can model the small-scale and three-dimensional effects present in turbine film cooling flows. This model could be implemented in turbine design codes or in multistage turbomachinery codes such as APNASA, where the computational grid size may be larger than the film hole size. Detailed computations of a single row of 35 deg round holes on a flat plate have been obtained for blowing ratios of 0.5, 0.8, and 1.0, and density ratios of 1.0 and 2.0 using a multiblock grid system to resolve the flows on both sides of the plate as well as inside the hole itself. These detailed flow fields were spatially averaged to generate a field of volumetric source terms for each conservative flow variable. Solutions were also obtained using three coarse grids having streamwise and spanwise grid spacings of 3d, 1d, and d/3. These coarse grid solutions used the integrated hole exit mass, momentum, energy, and turbulence quantities from the detailed solutions as volumetric source terms. It is shown that a uniform source term addition over a distance from the wall on the order of the hole diameter is able to predict adiabatic film effectiveness better than a near-wall source term model, while strictly enforcing correct values of integrated boundary layer quantities.

Heidmann, James D.↗
NASA NTRS1973

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 1: Technical discussion

Previously published asymptotic solutions for lunar and interplanetary trajectories have been modified and combined to formulate a general analytical solution to the problem on N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The derivation of the second-order solution is summarized by showing the essential steps, some in functional form. The general asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-earth, and interplanetary solutions. The results show that the accuracies of the asymptotic solutions range from an order of magnitude better than conic approximations to that of numerical integration itself. Also, since no iterations are required, the asymptotic boundary value solutions are obtained in a fraction of the time required for comparable numerically integrated solutions. The subject of minimizing the second-order error is discussed, and recommendations made for further work directed toward achieving a uniform accuracy in all applications.

Lancaster, J. E.↗
NASA NTRS1971

Computational investigations of low-discrepancy point sets

The quasi-Monte Carlo method of integration offers an attractive solution to the problem of evaluating integrals in a large number of dimensions; however, the associated error bounds are difficult to obtain theoretically. Since these bounds are associated with the L2 discrepancy of the set of points used in the integration. Numerical calculations of the L2 discrepancy for several types of quasi-Monte Carlo formulae are presented.

Warnock, T. T.↗
NASA NTRS1971

Interactive program for analysis and design problems in advanced composites technology

During the past year an experimental program in the fracture of advanced fiber composites has been completed. The experimental program has given direction to additional experimental and theoretical work. A synthesis program for designing low weight multifastener joints in composites is proposed, based on extensive analytical background. A number of failed joints have been thoroughly analyzed to evaluate the failure hypothesis used in the synthesis procedure. Finally, a new solution is reported for isotropic and anisotropic laminates using the boundary-integral method. The solution method offers significant savings of computer core and time for important problems.

Cruse, T. A.↗
NASA NTRS1981

A solution for two-dimensional Fredholm integral equations of the second kind with periodic, semiperiodic, or nonperiodic kernels

A numerical scheme for solving two dimensional Fredholm integral equations of the second kind is developed. The proof of the convergence of the numerical scheme is shown for three cases: the case of periodic kernels, the case of semiperiodic kernels, and the case of nonperiodic kernels. Applications to the incompressible, stationary Navier-Stokes problem are of primary interest.

Gabrielsen, R. E.↗
NASA NTRS1984

Random equations in aerodynamics

Literature was reviewed to identify aerodynamic models which might be treated by probablistic methods. The numerical solution of some integral equations that arise in aerodynamical problems were investigated. On the basis of the numerical studies a qualitative theory of random integral equations was developed to provide information on the behavior of the solutions of these equations (in particular, boundary and asymptotic behavior, and stability) and their statistical properties without actually obtaining explicit solutions of the equations.

Bharucha-Reid, A. T.↗
NASA NTRS1985

A procedure for obtaining explicit solutions to a class of Fredholm integral equations

A Fredholm integral equation is solved in closed form by reducing it to a standard boundary value problem for a sectionally analytic function. The procedure maybe extended to more general classes of functions whose Fourier transforms only exist along certain lines in the complex k-plane. Examples are used to illustrate the results.

Goldstein, M. E.↗
NASA NTRS1984

Overcoming time-integration errors in SINDA's FWDBCK solution routine

The FWDBCK time step, which is usually chosen intuitively to achieve adequate accuracy at reasonable computational costs, can in fact lead to large errors. NASA observed such errors in solving cryogenic problems on the COBE spacecraft, but a similar error is also demonstrated for a single node radiating to space. An algorithm has been developed for selecting the time step during the course of the simulation. The error incurred when the time derivative is replaced by the FWDBCK time difference can be estimated from the Taylor-Series expression for the temperature. The algorithm selects the time step to keep this error small. The efficacy of the method is demonstrated on the COBE and single-node problems.

Skladany, J. T.↗
NASA NTRS1987

A finite-difference outer layer and integral inner layer method for the solution of the turbulent boundary layer equations

A new turbulent boundary-layer method is developed which models the inner region with the law of the wall while the outer region uses Clauser's eddy viscosity in Matsuno's finite-difference method. The match point between the inner and outer regions as well as the wall shear stress are determined at each marching step during the computation. Results obtained for incompressible, two-dimensional flow over flat plates and ellipses are compared with solutions from a baseline method which uses a finite-difference method for the entire boundary layer. Since the present method used the finite-difference method in the outer region only, the number of grid points required was about half that needed for the baseline method. Accurate displacement and momentum thicknesses were predicted for all cases. Skin friction was predicted well for the flat plate, but the accuracy decreased significantly for the ellipses. Adding a wake functions to the law of the wall allows some of the pressure gradient effect to be taken into account thereby increasing the accuracy of the method.

Barnwell, R. W.↗
NASA NTRS1989

Solution of multi-center molecular integrals of Slater-type orbitals

The troublesome multi-center molecular integrals of Slater-type orbitals (STO) in molecular physics calculations can be evaluated by using the Fourier transform and proper coupling of the two center exchange integrals. A numerical integration procedure is then readily rendered to the final expression in which the integrand consists of well known special functions of arguments containing the geometrical arrangement of the nuclear centers and the exponents of the atomic orbitals. A practical procedure was devised for the calculation of a general multi-center molecular integrals coupling arbitrary Slater-type orbitals. Symmetry relations and asymptotic conditions are discussed. Explicit expressions of three-center one-electron nuclear-attraction integrals and four-center two-electron repulsion integrals for STO of principal quantum number n=2 are listed. A few numerical results are given for the purpose of comparison.

Tai, H.↗