Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical error”

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 613 records · Page 34

A wave-envelope of sound propagation in nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave, thereby reducing the computation time and the round-off error encountered in purely numerical techniques. The solution recovers the solution based on the method of multiple scales for slowly varying duct geometry. A computer program was developed based on the wave-envelope analysis for general mean flows. Results are presented for the reflection and transmission coefficients as well as the acoustic pressure distributions for a number of conditions: both straight and variable area ducts with and without liners and mean flows from very low to high subsonic speeds are considered.

Nayfeh, A. H.↗

Transmission of sound through nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite hard-walled or lined circular duct carrying compressible, sheared mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave, thereby reducing the computation time and the round-off error encountered in purely numerical techniques. A number of test cases that demonstrate the flexibility of the program are included. Convergence of the transmission coefficients and the acoustic pressure profiles with an increasing number of modes is illustrated.

Nayfeh, A. H.↗

Daylight imagery of ocean surface waves for wave spectra

A simple second-order model is developed to describe the transformation between surface wave slope and radiance incident on an optical sensor. The model includes azimuth as well as elevation variations in the sky-radiance distribution and their effects on the imaging of wave slopes approaching the sensor azimuth from various directions. The model also includes upwelling radiance. Comparison between the exact transformation from wave slope to radiance and the second-order model suggests that they yield quantitatively similar results. The model is used in physical interpretations of how wave slopes are imaged and in indicating a way of optimizing the linearity and contrast of the transfer function relating wave slope to radiance for various sensor geometries, thereby minimizing sources of error. One-dimensional numerical simulations of the imaging of an analytically generated wave-slope profile demonstrate the utility of this technique in obtaining slope spectra.

Monaldo, F. M.↗

Evaluation of pulsed RFI effects on digital satellite repeaters

This paper presents an analytical approach for assessing the effect of pulsed RFI on the error probability of a coherent phase-shift keyed signal through a nonlinear satellite repeater. The RFI is assumed to affect the uplink channel and to consist of CW pulses with random power levels and arriving randomly in time with a Poisson distribution. A model to approximate the effect of intermodulation products is introduced and the error probability conditioned on the output of the satellite repeater is computed. The classical moment technique is then used as an efficient method of averaging the conditional error probability over the numerous random parameters associated with the uplink signal.

Huang, T. C.↗

Modeling and equalization of nonlinear bandlimited satellite channels

The problem of modeling and equalization of a nonlinear satellite channel is considered. The channel is assumed to be bandlimited and exhibits both amplitude and phase nonlinearities. A discrete time satellite link is modeled under both uplink and downlink white Gaussian noise. Under conditions of practical interest, a simple and computationally efficient design technique for the minimum mean square error linear equalizer is presented. The bit error probability and some numerical results for a binary phase shift keyed (BPSK) system demonstrate that the proposed equalization technique outperforms standard linear receiver structures.

Konstantinides, K.↗

Finite difference solution for transient cooling of a radiating-conducting semitransparent layer

Transient solutions were obtained for cooling a semitransparent material by radiation and conduction. The layer is in a vacuum environment so the only means for heat dissipation is by radiation from within the medium leaving through the boundaries. Heat conduction serves only to partially equalize temperatures across the layer. As the optical thickness is increased, steep temperature gradients exist near the boundaries when conduction is relatively small. A solution procedure is required that will provide accurate temperature distributions adjacent to the boundaries, or radiative heat losses will be in error. The approach utilized numerical Gaussian integration to obtain the local radiative source term, and a finite difference procedure with variable space and time increments to solve the transient energy equation.

Siegel, Robert↗

Accurate computation and continuation of homoclinic and heteroclinic orbits for singular perturbation problems

In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.

Vaughan, William W.↗

Application of the Space-Time Conservation Element and Solution Element Method to One-Dimensional Advection-Diffusion Problems

Test problems are used to examine the performance of several one-dimensional numerical schemes based on the space-time conservation and solution element (CE/SE) method. Investigated in this paper are the CE/SE schemes constructed previously for solving the linear unsteady advection-diffusion equation and the schemes derived here for solving the nonlinear viscous and inviscid Burgers equations. In comparison with the numerical solutions obtained using several traditional finite-difference schemes with similar accuracy, the CE/SE solutions display much lower numerical dissipation and dispersion errors.

Wang, Xiao-Yen↗

Moisture Forecast Bias Correction in GEOS DAS

Data assimilation methods rely on numerous assumptions about the errors involved in measuring and forecasting atmospheric fields. One of the more disturbing of these is that short-term model forecasts are assumed to be unbiased. In case of atmospheric moisture, for example, observational evidence shows that the systematic component of errors in forecasts and analyses is often of the same order of magnitude as the random component. we have implemented a sequential algorithm for estimating forecast moisture bias from rawinsonde data in the Goddard Earth Observing System Data Assimilation System (GEOS DAS). The algorithm is designed to remove the systematic component of analysis errors and can be easily incorporated in an existing statistical data assimilation system. We will present results of initial experiments that show a significant reduction of bias in the GEOS DAS moisture analyses.

Dee, D.↗

Aeroacoustic Simulations of Tandem Cylinders with Subcritical Spacing

Tandem cylinders are being studied because they model a variety of component level interactions of landing gear. The present effort is directed at the case of two identical cylinders with their centroids separated in the streamwise direction by 1.435 diameters. Experiments in the Basic Aerodynamic Research Tunnel and Quiet Flow Facility at NASA Langley Research Center have provided an extensive experimental database of the nearfield flow and radiated noise. The measurements were conducted at a Mach number of 0.1285 and Reynolds number of 1.66x10(exp 5) based on the cylinder diameter. A trip was used on the upstream cylinder to insure a fully turbulent flow separation and, hence, to simulate a major aspect of high Reynolds number flow. The parallel computational effort uses the three-dimensional Navier-Stokes solver CFL3D with a hybrid, zonal turbulence model that turns off the turbulence production term everywhere except in a narrow ring surrounding solid surfaces. The experiments exhibited an asymmetry in the surface pressure that was persistent despite attempts to eliminate it through small changes in the configuration. To model the asymmetry, the simulations were run with the cylinder configuration at a nonzero but small angle of attack. The computed results and experiments are in general agreement that vortex shedding for the spacing studied herein is weak relative to that observed at supercritical spacings. Although the shedding was subdued in the simulations, it was still more prominent than in the experiments. Overall, the simulation comparisons with measured near-field data and the radiated acoustics are reasonable, especially if one is concerned with capturing the trends relative to larger cylinder spacings. However, the flow details of the 1.435 diameter spacing have not been captured in full even though very fine grid computations have been performed. Some of the discrepancy may be associated with the simulation s inexact representation of the experimental configuration, but numerical and flow modeling errors are also likely contributors to the observed differences.

Lockard, David P.↗

A Process for Assessing NASA's Capability in Aircraft Noise Prediction Technology

An acoustic assessment is being conducted by NASA that has been designed to assess the current state of the art in NASA s capability to predict aircraft related noise and to establish baselines for gauging future progress in the field. The process for determining NASA s current capabilities includes quantifying the differences between noise predictions and measurements of noise from experimental tests. The computed noise predictions are being obtained from semi-empirical, analytical, statistical, and numerical codes. In addition, errors and uncertainties are being identified and quantified both in the predictions and in the measured data to further enhance the credibility of the assessment. The content of this paper contains preliminary results, since the assessment project has not been fully completed, based on the contributions of many researchers and shows a select sample of the types of results obtained regarding the prediction of aircraft noise at both the system and component levels. The system level results are for engines and aircraft. The component level results are for fan broadband noise, for jet noise from a variety of nozzles, and for airframe noise from flaps and landing gear parts. There are also sample results for sound attenuation in lined ducts with flow and the behavior of acoustic lining in ducts.

Dahl, Milo D.↗

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

Shaykhian, Gholam Ali↗

Comment on “Advanced Testing of Low, Medium, and High ECS CMIP6 GCM Simulations Versus ERA5-T2m” by N. Scafetta (2022)

Scafetta (2022, https://doi.org/10.1029/2022gl097716) purports to test Coupled Model Intercomparison Project Phase 6 (CMIP6) climate models through a comparison of temperature changes over three decades. Unfortunately, the paper contains numerous conceptual and statistical errors that undermine all of the conclusions. First, no uncertainty is given for the observational temperature difference, making it impossible to assess compatibility with any model result. Second, the CMIP6 data are the ensemble means for each model, but the metric being tested is sensitive to the internal variability and so the full ensemble for each model must be used. When this is corrected, the conclusion that “all models with ECS > 3.0°C overestimate the observed global surface warming” is not sustained. Third, the statistical test in Section 2 would reject all models even in a perfect model setup given sufficient ensemble members, thus the second conclusion “that spatial t-statistics rejects the data-model agreement” is also not sustainable.

CMIP6↗

Integrated fiducial sample mount and software for correlated microscopy

A novel design sample mount with integrated fiducials and software for assisting operators in easily and efficiently locating points of interest established in previous analytical sessions is described. The sample holder and software were evaluated with experiments to demonstrate the utility and ease of finding the same points of interest in two different microscopy instruments. Also, numerical analysis of expected errors in determining the same position with errors unbiased by a human operator was performed. Based on the results, issues related to acquiring reproducibility and best practices for using the sample mount and software were identified. Overall, the sample mount methodology allows data to be efficiently and easily collected on different instruments for the same sample location.

36 MATERIALS SCIENCE↗

An Online Dynamic Amplitude-Correcting Gradient Estimation Technique to Align X-ray Focusing Optics

High-brightness X-ray pulses, as generated at synchrotrons and X-ray free electron lasers (XFELs), are used in a variety of scientific experiments. At these facilities, measurements often require optical equipment, e.g Compound Refractive Lenses (CRLs) to be precisely aligned and focused. The lateral alignment of CRLs to a beamline requires precise positioning along four axes: two translational, and the two rotational. At a synchrotron, alignment is often accomplished manually. However, XFEL beamlines present a beam brightness that fluctuates stochastically, making manual alignment a time-consuming endeavor. Automation using simplex or classic stochastic descent often fails, given the errant gradient estimates. Herein we present a dynamic-amplitude correction to the usual gradient based on the combination of a generalized finite difference stencil and a time-dependent sampling pattern. Intensity is recorded periodically, then used to normalize numerical derivatives against fluctuations. Error expectation is analyzed, and efficacy is demonstrated on classic benchmarks. We provide a proof of concept by laterally aligning optics on a simulated XFEL beamline using data recorded at both synchrotron and XFEL facilities.

97 MATHEMATICS AND COMPUTING↗

P{sub N} source expansion nodal method in MPACT for boiling water reactors

This paper describes the one-node P{sub N}-Source Expansion Nodal Method (SENM) axial solver for the 2D/1D method recently implemented in MPACT to support Boiling Water Reactors (BWR) analysis. Since the BWR has a more complicated design and strong burnable absorber, the existing PN-Nodal Expansion Method (NEM) axial solver in MPACT may not be sufficient to accurately represent the intranodal flux and source profiles for BWRs. The one-node P{sub N}-SENM has been implemented in this work to reduce the axial spatial discretization error for BWRs. From numerical results, we verify that the P{sub N}-SENM can improve the accuracy of the pin power prediction, and confirm that P{sub N}-SENM can use more than a 1.5 times larger axial mesh size than P{sub N}-NEM to have similar accuracy for the BWR GE14 3D assembly problem. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗