Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “convergence analysis”

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.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

The role of analysis error in the convergence of reanalysis production streams in MERRA-2

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.

Amal El Akkraoui↗
DOE OSTI2021

Comparing Global Spray Combustion Characteristics and Local Shot-to-Shot Variations in a Reacting n -Heptane Spray

In support of efforts to develop improved models of turbulent spray behavior and combustion in diesel engines, experimental data and analysis must be obtained for guidance and validation. For Reynolds-averaged Navier–Stokes (RANS)-based Computational fluid dynamics (CFD) modeling approaches, representative ensemble average experimental results are important. For high-fidelity models such as large eddy simulations (LES)-based CFD, precise individual experimental results are desirable. However, making comparisons between a given experiment and LES is a challenge since local parameters cannot be directly compared. In this work, an optically accessible constant pressure flow rig (CPFR) is utilized to acquire diesel-like fuel injection and reaction behavior simultaneously with three optical diagnostic techniques: rainbow Schlieren deflectometry (RSD), OH* chemiluminescence (OH*), and two-color pyrometry (2CP). The CPFR allows a large number of repeated injection experiments to be performed for statistical analysis and convergence using ensemble-averaging techniques, while maintaining highly repeatable test conditions. Even for stable test conditions, variations in local turbulent fuel–air mixing introduce variability, which manifests as significant differences in OH* and 2CP results. Experimental measurements of characteristic parameters including liquid and vapor jet penetration, liftoff length, soot temperature and concentration, and turbulent flame speed, along with the shot-to-shot variability of each dataset, are presented and discussed. Finally, a statistical method is utilized to analyze the extent of this variability, and to identify superlative injections within the dataset for discussion and analysis of shot-to-shot variations.

42 ENGINEERING↗
NASA NTRS1981

Convergent-tapered annular seals - Analysis for rotordynamic coefficients

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.

Childs, D. W.↗
NASA NTRS1984

Convergent-tapered annular seals - Analysis and testing for rotordynamic coefficients

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.

Childs, D. W.↗
NASA NTRS2001

Risk analysis: divergent models and convergent interpretations

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.

Non-NASA Center↗
NASA NTRS1988

A simplified analysis of the multigrid V-cycle as a fast elliptic solver

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.

Decker, Naomi H.↗
DOE OSTI2020

The arbitrary‐order virtual element method for linear elastodynamics models: convergence, stability and dispersion‐dissipation analysis

Abstract We design the conforming virtual element method for the numerical approximation of the two‐dimensional elastodynamics problem. We prove stability and convergence of the semidiscrete approximation and derive optimal error estimates under h ‐ and p ‐refinement in both the energy and the L 2 norms. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including nonconvex cells up to order four in the h ‐refinement setting. Exponential convergence is also experimentally observed under p ‐refinement. Finally, we present a dispersion‐dissipation analysis for both the semidiscrete and fully discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion‐dissipation properties.

Antonietti, Paola F.↗
NASA NTRS1986

Fundamental investigations of the finite element solutions for acoustic propagation in ducts

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.

Walkington, N. J.↗
NASA NTRS1978

Interpolation and extrapolation of creep rupture data by the Minimum Commitment Method. I - Focal-point convergence. II - Oblique translation. III - Analysis of multiheats

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.

Manson, S. S.↗
NASA NTRS1993

On waveform multigrid method

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.

Taasan, Shlomo↗
NASA NTRS1992

Dynamic analysis of pretwisted elastically-coupled rotor blades

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.

Nixon, Mark W.↗
NASA NTRS1994

Dynamic analysis of pretwisted elastically-coupled rotor blades

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.

Nixon, Mark W.↗
NASA NTRS2007

Influences of Local Sea-Surface Temperatures and Large-scale Dynamics on Monthly Precipitation Inferred from Two 10-year GCM-Simulations

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.

Sud, Y. C.↗
DOE OSTI2021

IMEX Runge-Kutta Parareal for Non-diffusive Equations

Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on non-diffusive equations. This paper analyzes linear stability and convergence for IMEX Runge-Kutta Parareal methods on non-diffusive equations. By combining standard linear stability analysis with a simple convergence analysis, we find that certain Parareal configurations can achieve parallel speedup on non-diffusive equations. These stable configurations all posses low iteration counts, large block sizes, and a large number of processors. Numerical examples using the nonlinear Schrodinger equation demonstrate the analytical conclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Chemical timescale effects on detonation convergence

Numerical simulations of detonation-containing flows have emerged as crucial tools for designing next- generation power and propulsion devices. As these tools mature, it is important for the combustion community to properly understand and isolate grid resolution effects when simulating detonations. To this end, the objective of this work is to provide a comprehensive analysis of the numerical convergence of unsteady detonation simulations, with focus on isolating the impacts of chemical timescale modifications on convergence characteristics in the context of operator splitting. With the aid of an AMReX-based adaptive mesh refinement flow solver-which enables resolutions up to ($\mathcal{O}$ (1000) cells-per-induction length-the convergence analysis is conducted using two kinetics configurations: (1) the simplified three-step Arrhenius-based model mechanism of Short and Quirk (1997), where chemical timescales in the detonation are modified by adjusting activation energies in the initiation and branching reactions, and (2) a detailed hydrogen- air mechanism, where the chemical timescales are adjusted by varying the ambient pressure. The convergence of unsteady self-sustained detonations in one-dimensional channels is then analyzed with reference to steady-state theoretical baseline solutions using these mechanisms. The goal of the analysis is to provide a detailed comparison of the effects of grid resolution on both macroscopic (peak pressures and wave speeds) and microscopic (wave structure) quantities of interest, drawing connections between the deviations from steady-state baselines and minimum chemical timescales. In particular, chemical timescale reductions were found to have minimal impact on the convergence of macroscopic properties. Furthermore, analyses of microscopic convergence trends, particularly in the reaction front location, revealed a key insight: maintaining the induction time while eliminating prohibitive chemical timescales through mechanism simplifications and combustion modeling can significantly enhance detonation convergence properties. Ultimately, this work uncovers resolution-dependent unsteady detonation convergence regimes and highlights the important role played by not only the chemical timescales, but also the ratio between the chemical timescale and induction time on the numerical convergence of the detonation wave structure.

Adaptive mesh refinement↗