SEARCH · Engineering Papers
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
The convergence properties of numerical schemes for partial differential equations are studied by examining the eigensystem of the discrete operator. This method of analysis is very general, and allows the effects of boundary conditions and grid nonuniformities to be examined directly. Algorithms for the Laplace equation and a two equation model hyperbolic system are examined.
Error analysis for extraterrestrial convergent photogrammetric mapping system
A quantitative analysis of coupling between systems of equations is introduced. This analysis is then applied to problems in multidisciplinary analysis, sensitivity, and optimization. For the sensitivity and optimization problems both multidisciplinary and single discipline feasibility schemes are considered. In all these cases a "convergence factor" is estimated in terms of the Jacobians and Hessians of the system, thus it can also be approximated by existing disciplinary analysis and optimization codes. The convergence factor is identified with the measure for the "coupling" between the disciplines in the system. Applications to algorithm development are discussed. Demonstration of the convergence estimates and numerical results are given for a system composed of two non-linear algebraic equations, and for a system composed of two PDEs modeling aeroelasticity.
The convergence properties of three modal methods for solving structural transient response (STR) problems are examined by comparing the accuracy of the total number of modes used to represent the responses. The goal is to identify a method which involves as few degrees of freedom as possible. Two mode superposition methods, the mode displacement method (MDM) and the mode acceleration method (MAM), are fitted with equivalent expressions for damped response. An error norm is employed to compare the accuracies of the methods in calculating displacements, moments, and shear forces for a viscously-damped cantilevered beam experiencing several dynamic loading conditions and levels of damping. The MAM converges quicker and uses fewer dof, mainly because it has a pseudo-static response term which accounts for some of the flexibility of higher modes. A third method, which integrates the convolution integral iteratively over time, generates a higher order approximation to the STR with a reduced number of modes. It converges fastest among the three, but requires definition of an appropriate forcing function. Finally, the MAM and MDM models are applied to study the effects of the forcing frequency and the initial conditions.
Coordinate transformation improves convergence pattern analysis of elliptical-aperture antennas. Modified version of Jacobi-Bessel expansion for vector diffraction analysis of reflector antennas uses coordinate transformation to improve convergence with elliptical apertures. Expansion converges rapidly for antennas with circular apertures, but less rapidly for elliptical apertures. Difference in convergence behavior between circular and elliptical Jacobi-Bessel algorithms indicated by highest values of indices m, n, and p required to achieve same accuracy in computed radiation pattern of offset paraboloidal antenna with elliptical aperture.
Due to production time constraints, most reanalyses are produced in multiple parallel streams instead of a single continuous one. These streams cover separate segments of the reanalysis time period with short overlaps to allow reconstruction of the official record. A fundamental assumption justifying this approach is that the streams will be assimilating the same observations during the periods where they overlap, and so will eventually converge to a similar atmospheric state, making discontinuities at stream junctions negligible. This assumption is revisited in this work by examining the impact of analysis error on the differences between MERRA-2 overlapping streams in three historical periods. Comparison results are shown in terms of standard deviations of stream differences as well as the spectral decomposition of the variance of their differences. Residual differences were found at the end of each year of overlap, with larger values observed in the earlier segments of the presatellite era. By drawing parallels with analysis error statistics estimated from the GMAO OSSE system, these differences are shown to reflect the varying constraint of data with the varying observing network, and to further carry the imprint of errors that the data assimilation process is not able to mitigate. As such, they are unlikely to be reduced by longer spinup periods. The ability of data assimilation to ensure continuity in the parallel streams is put into question when the observing system coverage is inadequate or simply when the data assimilation system as a whole is suboptimal.
A combined analytical-computational solution based on Hirs' lubrication equations (1970) is developed for tapered high-pressure annular seals typical of neck-ring and interstage seals employed in multistage centrifugal pumps. The results obtained coincide with earlier straight seal results at taper angles approaching zero and, under comparable assumptions, agree with Fleming's (1977) predictions for the direct stiffness coefficients. An optimal taper angle is shown to exist with respect to direct stiffness and the ratio of direct stiffness to leakage. Stiffness increases of about 85% are predicted.
A combined analytical-computational method has been developed to calculate the pressure field and dynamic coefficients for tapered high-pressure annular seals. Completely developed turbulent flow is assumed in both the circumferential and axial directions, according to Hirs' (1973) bulk-flow turbulent-lubrication equations. In a numerical experiment with the method, a short bearing approximation is used to derive an analytical expression for the first-order (dynamic) pressure gradient. This expression is integrated numerically to define dynamic coefficients of the seal. Numerical results of the integration are compared with previous results for straight and tapered seals. It is found that direct stiffness and leakage coefficients increase in the present seal, while the remaining coefficients decrease. An optimal taper angle is shown to exist with respect to: (1) the direct stiffness and (2) the ratio of direct stiffness to leakage. On the basis of the optimal taper angle calculations, stiffness increases on the order of 40 to 50 percent are predicted. Experimental results for three taper angles are presented, and are found to be in good agreement with the theoretical predictions.
Material presented at a NASA-sponsored workshop on risk models for exposure conditions relevant to prolonged space flight are described in this paper. Analyses used mortality data from experiments conducted at Argonne National Laboratory on the long-term effects of external whole-body irradiation on B6CF1 mice by 60Co gamma rays and fission neutrons delivered as a single exposure or protracted over either 24 or 60 once-weekly exposures. The maximum dose considered was restricted to 1 Gy for neutrons and 10 Gy for gamma rays. Proportional hazard models were used to investigate the shape of the dose response at these lower doses for deaths caused by solid-tissue tumors and tumors of either connective or epithelial tissue origin. For protracted exposures, a significant mortality effect was detected at a neutron dose of 14 cGy and a gamma-ray dose of 3 Gy. For single exposures, radiation-induced mortality for neutrons also occurred within the range of 10-20 cGy, but dropped to 86 cGy for gamma rays. Plots of risk relative to control estimated for each observed dose gave a visual impression of nonlinearity for both neutrons and gamma rays. At least for solid-tissue tumors, male and female mortality was nearly identical for gamma-ray exposures, but mortality risks for females were higher than for males for neutron exposures. As expected, protracting the gamma-ray dose reduced mortality risks. Although curvature consistent with that observed visually could be detected by a model parameterized to detect curvature, a relative risk term containing only a simple term for total dose was usually sufficient to describe the dose response. Although detectable mortality for the three pathology end points considered typically occurred at the same level of dose, the highest risks were almost always associated with deaths caused by tumors of epithelial tissue origin.
Explore the source record for details and available documents.
For special model problems, Fourier analysis gives exact convergence rates for the two-grid multigrid cycle and, for more general problems, provides estimates of the two-grid convergence rates via local mode analysis. A method is presented for obtaining mutigrid convergence rate estimates for cycles involving more than two grids (using essentially the same analysis as for the two-grid cycle). For the simple cast of the V-cycle used as a fast Laplace solver on the unit square, the k-grid convergence rate bounds obtained by this method are sharper than the bounds predicted by the variational theory. Both theoretical justification and experimental evidence are presented.
NASTRAN flat plate finite element convergence properties for stress analysis of cylindrical and conical shells
The question of convergence of three finite element algorithms for the modelling of acoustic transmission in ducts carrying a nonuniform mean flow is addressed. The details of each algorithm are stated and example calculations in uniform and nonuniform ducts are made and assessed for accuracy and convergence. The algorithm based on the assumption of irrotationality is found to be highly convergent. This algorithm is the one used in current turbo-fan inlet acoustic radiation codes. A theoretical analysis indicating convergence is supported by example calculations. Two additional algorithms which do not require irrotationality are found to be less convergent, and perhaps not convergent at all for certain severely sheared velocity profiles. No theoretical convergence criteria can presently be established for these algorithms and convergence difficulties are shown here by example. Included in this class of algorithms is the duct analysis program ADAM which is known to display apparently nonconvergent solutions in certain cases.
The framework in which minimum-commitment analyses of creep-rupture data can be implemented is outlined. The approach is termed the focal point convergence method (FPCM) because the basic parameter A, also known as stability factor, is geometrically the (imaginary) focal point of convergence of all isothermals when extended to the very long or very short times necessary for such convergence to occur. The method can be implemented either by manual-graphical analysis or by computer code. The method is illustrated in detail for the nickel-base alloy Astroloy, as well as for steels, other nickel-base alloys, and aluminum alloys. The minimum-commitment concept is extended to the analysis of creep-rupture data where each isothermal is generated by an oblique translation of the 'master curve' when plotted on log rupture time and log stress axes. The oblique translation method uses the same types of functions in the FPCM. Approaches for treating multiheats on the basis of the FPCM are discussed in detail.
Waveform multigrid method is an efficient method for solving certain classes of time dependent PDEs. This paper studies the relationship between this method and the analogous multigrid method for steady-state problems. Using a Fourier-Laplace analysis, practical convergence rate estimates of the waveform multigrid iterations are obtained. Experimental results show that the analysis yields accurate performance prediction.
This paper addresses the accuracy of using a one-dimensional analysis to predict frequencies of elastically-coupled highly-twisted rotor blades. Degrees of freedom associated with shear deformation are statically condensed from the formulation, so the analysis uses only those degrees of freedom associated with classical beam theory. The effects of cross section deformation (warping) are considered, and are shown to become significant for some types of elastic coupling. Improved results are demonstrated for highly-coupled blade structures through account of warping in a local cross section analysis, without explicit inclusion of these effects in the beam analysis. A convergence study is also provided which investigates the potential for improving efficiency of elastically-coupled beam analysis through implementation of a p-version beam finite element.
The accuracy of using a one-dimensional analysis to predict frequencies of elastically-coupled highly-twisted rotor blades is addressed. Degrees of freedom associated with shear deformation are statically condensed from the formulation, so the analysis uses only those degrees of freedom associated with classical beam theory. The effects of cross section deformation (warping) are considered, and are shown to become significant for some types of elastic coupling. Improved results are demonstrated for highly-coupled blade structures through account of warping in a local cross section analysis, without explicit inclusion of these effects in the beam analysis. A convergence study is also provided which investigates the potential for improving efficiency of elastically-coupled beam analysis through implementation of a p-version beam finite element.
Two parallel sets of 10-year long: January 1, 1982 to December 31, 1991, simulations were made with the finite volume General Circulation Model (fvGCM) in which the model integrations were forced with prescribed sea-surface temperature fields (SSTs) available as two separate SST-datasets. One dataset contained naturally varying monthly SSTs for the chosen period, and the oth& had the 12-monthly mean SSTs for the same period. Plots of evaporation, precipitation, and atmosphere-column moisture convergence, binned by l C SST intervals show that except for the tropics, the precipitation is more strongly constrained by large-scale dynamics as opposed to local SST. Binning data by SST naturally provided an ensemble average of data contributed from disparate locations with same SST; such averages could be expected to mitigate all location related influences. However, the plots revealed: i) evaporation, vertical velocity, and precipitation are very robust and remarkably similar for each of the two simulations and even for the data from 1987-ENSO-year simulation; ii) while the evaporation increased monotonically with SST up to about 27 C, the precipitation did not; iii) precipitation correlated much better with the column vertical velocity as opposed to SST suggesting that the influence of dynamical circulation including non-local SSTs is stronger than local-SSTs. The precipitation fields were doubly binned with respect to SST and boundary-layer mass and/or moisture convergence. The analysis discerned the rate of change of precipitation with local SST as a sum of partial derivative of precipitation with local SST plus partial derivative of precipitation with boundary layer moisture convergence multiplied by the rate of change of boundary-layer moisture convergence with SST (see Eqn. 3 of Section 4.5). This analysis is mathematically rigorous as well as provides a quantitative measure of the influence of local SST on the local precipitation. The results were recast to examine the dependence of local rainfall on local SSTs; it was discernible only in the tropics. Our methodology can be used for computing relationship between any forcing function and its effect(s) on a chosen field.