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NASA NTRS1985

Buckling of simply supported plate assemblies subject to shear loading

An analysis is presented of the shear buckling load of an arbitrary simply-supported prismatic plate assembly or stiffened panel configuration. The method utilizes stiffness matrices developed by Wittrick (1968). For the restraint of simple support along edges perpendicular to the longitudinal direction, various wavelengths of response are combined using an energy method that involves only a boundary integral. Numerical results for plate and panel configurations show the accuracy and convergence of the method.

Anderson, M. S.↗
NASA NTRS2005

On the Hilbert-Huang Transform Theoretical Developments

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable Array (FPGA) computational resources, enhanced HHT synthesis, and broaden the scope of HHT applications for signal processing.

Kizhner, Semion↗
NASA NTRS2006

On Certain Theoretical Developments Underlying the Hilbert-Huang Transform

One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA) computational resources,

Kizhner, Semion↗
NASA NTRS2006

ALPS: The Age-Layered Population Structure for Reducing the Problem of Premature Convergence

To reduce the problem of premature convergence we define a new attribute of an individual, its age, and propose the Age-Layered Population Structure (ALPS), in which age is used to restrict competition and breeding between members of the population. ALPS differs from a typical EA by segregating individuals into different age-layers by their age - a measure of how long the genetic material has been in the population - and by regularly replacing all individuals in the bottom layer with randomly generated ones. The introduction of new, randomly generated individuals at regular intervals results in an EA that is never completely converged and is always looking at new parts of the fitness landscape. By using age to restrict competition and breeding search is able to develop promising young individuals without them being dominated by older ones. We demonstrate the effectiveness of the ALPS algorithm on an antenna design problem in which evolution with ALPS produces antennas more than twice as good as does evolution with two other types of EAs. Further analysis shows that the ALPS model does allow the offspring of newly generated individuals to move the population out of mediocre local-optima to better parts of the fitness landscape.

Hornby, Gregory S.↗
NASA NTRS2008

The Impact of High-Resolution Sea Surface Temperatures on the Simulated Nocturnal Florida Marine Boundary Layer

High- and low-resolution sea surface temperature (SST) analysis products are used to initialize the Weather Research and Forecasting (WRF) Model for May 2004 for short-term forecasts over Florida and surrounding waters. Initial and boundary conditions for the simulations were provided by a combination of observations, large-scale model output, and analysis products. The impact of using a 1-km Moderate Resolution Imaging Spectroradiometer (MODIS) SST composite on subsequent evolution of the marine atmospheric boundary layer (MABL) is assessed through simulation comparisons and limited validation. Model results are presented for individual simulations, as well as for aggregates of easterly- and westerly-dominated low-level flows. The simulation comparisons show that the use of MODIS SST composites results in enhanced convergence zones. earlier and more intense horizontal convective rolls. and an increase in precipitation as well as a change in precipitation location. Validation of 10-m winds with buoys shows a slight improvement in wind speed. The most significant results of this study are that 1) vertical wind stress divergence and pressure gradient accelerations across the Florida Current region vary in importance as a function of flow direction and stability and 2) the warmer Florida Current in the MODIS product transports heat vertically and downwind of this heat source, modifying the thermal structure and the MABL wind field primarily through pressure gradient adjustments.

LaCasse, Katherine M.↗
NASA NTRS2022

Low-Level Jets and the Convergence of Mars Data Assimilation Algorithms

Data assimilation is an increasingly popular technique in Mars atmospheric science, but its effect on the mean states of the underlying atmosphere models has not been thoroughly examined. The robustness of results to the choice of model and assimilation algorithm also warrants further study. We investigate these issues using two Mars general circulation models (MGCMs), with particular emphasis on zonal wind and temperature fields. When temperature retrievals from the Mars Global Surveyor Thermal Emission Spectrometer (TES) are assimilated into the U.K.-Laboratoire de M ́et ́eorologie Dynamique (UK-LMD) MGCM to create the Mars Analysis Correction Data Assimilation (MACDA) reanalysis, low-level zonal jets in the winter northern hemisphere shift equatorward and weaken relative to a free-running control simulation from the same MGCM. The Ensemble Mars Atmosphere Reanalysis System (EMARS) reanalysis, which is also based on TES temperature retrievals, also shows jet weakening (but less if any shifting) relative to a control simulation performed with the underlying Geophysical Fluid Dynamics Laboratory (GFDL) MGCM. Examining higher levels of the atmosphere, monthly mean three-dimensional temperature and zonal wind fields are in generally better agreement between the two reanalyses than between the two control simulations. In conjunction with information about the MGCMs’ physical parametrizations, intercomparisons between the various reanalyses and control simulations suggest that overall the EMARS control run is plausibly less biased (relative to the true state of the Martian atmosphere) than the MACDA control run. Implications for future observational studies are discussed. Plain Language Summary An increasingly popular way to study Martian weather and climate is to combine atmospheric temperature observations with a computer model (specifically, a global climate model). The process of combining model and observations is called “data assimilation”, and the resulting merged data set is called a “reanalysis”. One advantage of reanalyses is that they include variables (such as wind) that are not directly observed. For scientific and practical applications we want these variables to be reasonably accurate— however, it is not clear how well data assimilation algorithms compute them. Our study investigates this issue using two Mars reanalyses and two model simulations that do not assimilate temperature data. We focus on slowly-varying atmospheric phenomena (timescales from 10 Mars days to a season). Assimilating temperature data into two different global climate models changes the strength and/or spatial pattern of east-west winds at low altitudes. Furthermore, monthly mean three-dimensional temperature and east-west wind fields agree better between reanalyses than between non-assimilating model simulations. This suggests that the data assimilation process is basically successful. One non-assimilating model simulation has less realistic representations of atmospheric physical processes than the other—we argue that this plausibly gives it larger biases relative to the true state of the atmosphere.

Todd A Mooring↗
DOE OSTI2022

Clustering of inertial particles in turbulent flow through a porous unit cell

We report direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centred cubic porous unit cell on the transport, clustering and deposition of fine particles at different Stokes numbers (St = 0.01, 0.1, 0.5, 1, 2) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and the collision of particles with pore walls is modelled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geometry of the pore walls. The pattern and dynamics of clustering are investigated using the volume change of Voronoi tesselation in time to analyse the divergence and convergence of the particles. Similar to the case of homogeneous, isotropic turbulence, the cluster formation is present at large volumes, while cluster destruction is prominent at small volumes and these effects are amplified with the Stokes number. However, unlike homogeneous, isotropic turbulence, the formation of a large number of very small volumes was observed at all Stokes numbers and attributed to the collision of particles with the pore wall. Multiscale wavelet analysis of the particle number density indicates that the peak of the energy density spectrum, representative of enhanced particle clustering, shifts towards larger scales with an increase in the Stokes number. Scale-dependent skewness and flatness quantify the intermittent void and cluster distribution, with cluster formation observed at small scales for all Stokes numbers, and void regions at large scales for large Stokes numbers.

42 ENGINEERING↗
DOE OSTI2026

Atacama Cosmology Telescope: B-mode delensing with DR6 data and external tracers of large-scale structure

Large-scale -mode polarization of the cosmic microwave background (CMB) is a prime target for current and future experiments in search of primordial gravitational waves. With increasingly sensitive instruments being deployed, secondary -modes induced by the weak gravitational lensing of CMB photons are becoming an important limitation and need to be removed, a process known as delensing. In this work, we combine internally reconstructed CMB lensing maps from the Atacama Cosmology Telescope (ACT) data release 6 (DR6) with galaxy samples from unWISE and a map of the cosmic infrared background (CIB) fluctuations from Planck to produce a well-correlated tracer of the CMB lensing field. Our coadded tracer, shown to be 55%–85% correlated with the true lensing convergence at multipoles , is then convolved with ACT DR6 -mode polarization to yield a template of the lensing -modes. We assess its performance on a wide range of scales by using it to delens ACT DR6 and Planck -modes over 23% of the sky, removing around 39% of the lensing power at and 47% at , respectively. Our template achieves the highest delensing efficiency to date and will be useful for the analysis of early polarization maps from the Simons Observatory. We finally outline prospects for further improvements by including additional large-scale structure tracers from upcoming cosmological surveys.

Hertig, Emilie↗
NASA NTRS1979

Oceanic geoid and tides derived from GEOS 3 satellite data in the Northwestern Atlantic Ocean

Two sets of GEOS 3 altimeter data which fall within about a 2.5-deg width are analyzed for ocean geoid and tides. One set covers a path from Newfoundland to Cuba, and the other a path from Puerto Rico to the North Carolina coast. Forty different analyses using various parameters are performed in order to investigate convergence. Profiles of the geoid and four tides, M2, O1, S2, and K1, are derived along the two strips. While the analyses produced convergent solutions for all 40 cases, the uncertainty caused by the linear orbital bias error of the satellite is too large to claim that the solutions represent the true ocean tides in the area. A spot check of the result with the Mode deep-sea tide gauge data shows poor agreement. A positive conclusion of this study is that despite the uncertain orbital error the oceanic geoid obtained through this analysis can improve significantly the short-wavelength structure over existing spherical harmonic geoid models.

Won, I. J.↗
NASA NTRS1984

Analysis of airfoil transitional separation bubbles

A previously developed local inviscid-viscous interaction technique for the analysis of airfoil transitional separation bubbles, ALESEP (Airfoil Leading Edge Separation), has been modified to utilize a more accurate windward finite difference procedure in the reversed flow region, and a natural transition turbulence model has been incorporated for the prediction of transition within the separation bubble. Numerous calculations and experimental comparisons are presented to demonstrate the effects of the windward differencing scheme and the natural transition turbulence model. Grid sensitivity and convergence capabilities of this inviscid-viscous interaction technique are briefly addressed. A major conclusion of this paper is that a second, counter-rotating eddy has been found to exist in the wall layer of the primary separation bubble with the use of windward differencing.

Davis, R. L.↗
NASA NTRS1988

Propulsive-jet flow field analysis using the three-dimensional Navier-Stokes equations

A three-dimensional Navier-Stokes code has been applied to the analysis of flow fields containing propulsive jets. Specifically, the application was made to a flow field containing a supersonic jet injected at an angle of 90 degrees to a subsonic free stream. Although wind tunnel data were available, the computational results were not readily comparable to the experimental data because of significant differences between the two plume trajectories. Reasons for the differences are suggested in the report and include: (1) incomplete convergence, (2) inadequate grid resolution in the high gradient regions, and (3) use of a low-order turbulence closure model.

Reed, C. L.↗
NASA NTRS1989

The cloud and surface contributions to the net radiation balance during the 1982-83 El Nino

This paper investigates the interannual fluctuations in cloud and surface forcing associated with the unusually intense ENSO event of 1982-1983. The analysis was performed over a six-year period for which global radiation budget and cloudiness measurements from the Nimbus-7 experiments were available simultaneously. It is shown that major anomalies in cloudiness, due mostly to shifts of a major convective center in the Pacific Ocean associated with inactive or active ENSO phase, are most notable over the equatorial central Pacific, the maritime continent over the western Pacific, the South Pacific convergence zone, and the Indian Ocean.

Sohn, Byung-Ju↗
NASA NTRS1991

Modal truncation, Ritz vectors, and derivatives of closed-loop damping ratios

The effect of modal truncation on the damping ratio and their derivatives with respect to an added mass is investigated for a simply supported, multispan beam with a linear quadratic Gaussian control system. It is found that both the damping ratios and derivatives converge slowly, but the derivatives converge more slowly than the damping ratios. However, it is shown that when Ritz vectors corresponding to static displacements due to actuator forces are added to the reduced model, the convergence of both the damping ratios and their derivatives is accelerated. It is also shown that the accuracy of the damping ratio predicted by a reduced-model control design can be improved significantly if the Ritz vectors are included in the design of the control system. Thus, it appears that Ritz vectors added to the reduced model of flexible structures can improve greatly the accuracy of both the design and analysis of the control system.

Sandridge, Chris A.↗
NASA NTRS1993

Applications of computer algebra to distributed parameter systems

In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

Storch, Joel A.↗
NASA NTRS2000

First-Order Model Management With Variable-Fidelity Physics Applied to Multi-Element Airfoil Optimization

First-order approximation and model management is a methodology for a systematic use of variable-fidelity models or approximations in optimization. The intent of model management is to attain convergence to high-fidelity solutions with minimal expense in high-fidelity computations. The savings in terms of computationally intensive evaluations depends on the ability of the available lower-fidelity model or a suite of models to predict the improvement trends for the high-fidelity problem, Variable-fidelity models can be represented by data-fitting approximations, variable-resolution models. variable-convergence models. or variable physical fidelity models. The present work considers the use of variable-fidelity physics models. We demonstrate the performance of model management on an aerodynamic optimization of a multi-element airfoil designed to operate in the transonic regime. Reynolds-averaged Navier-Stokes equations represent the high-fidelity model, while the Euler equations represent the low-fidelity model. An unstructured mesh-based analysis code FUN2D evaluates functions and sensitivity derivatives for both models. Model management for the present demonstration problem yields fivefold savings in terms of high-fidelity evaluations compared to optimization done with high-fidelity computations alone.

Alexandrov, N. M.↗
NASA NTRS2003

Tropospheric Ozone Over a Tropical Atlantic Station in the Northern Hemisphere: Paramaribo, Surinam (6 deg N, 55 deg W)

We present an analysis of 2.5 years of weekly ozone soundings conducted at a new monitoring station in Paramaribo, Surinam (6 deg N,55 deg W). This is currently one of only three ozone sounding stations in the northern hemisphere (NH) tropics, and the only one in the equatorial Atlantic region. Paramaribo is part of the Southern Hemisphere ADditional Ozone Sounding program (SHADOZ). Due to its position close to the equator, the Inter Tropical Convergence Zone (ITCZ) passes over Paramaribo twice per year, which results in a semi-annual seasonality of many parameters including relative humidity and ozone. The dataset from Paramaribo is used to: (1) evaluate ozone variability relative to precipitation, atmospheric circulation patterns and biomass burning; (2) contrast ozone at the NH equatorial Atlantic with that at nearby southern hemisphere (SH) stations Natal (6 deg S,35 deg W) and Ascension (8 deg S,14 deg W); (3) compare the seasonality of tropospheric ozone with a satellite-derived ozone product: Tropical Tropospheric Ozone Columns from the Modified Residual method (MR-TTOC). We find that Paramaribo is a distinctly Atlantic station. Despite its position north of the equator, it resembles nearby SH stations during most of the year. Transport patterns in the lower and middle troposphere during February and March differ from SH stations, which leads to a seasonality of ozone with two maxima. MR-TTOC over Paramaribo does not match the observed seasonality of ozone due to the use of a SH ozone sonde climatology in the MR method. The Paramaribo ozone record is used to suggest an improvement for northern hemisphere MR-TTOC retrievals. We conclude that station Paramaribo shows unique features in the region, and clearly adds new information to the existing SHADOZ record.

Peters, W.↗
NASA NTRS2001

Coupled-Flow Simulation of HP-LP Turbines Has Resulted in Significant Fuel Savings

Our objective was to create a high-fidelity Navier-Stokes computer simulation of the flow through the turbines of a modern high-bypass-ratio turbofan engine. The simulation would have to capture the aerodynamic interactions between closely coupled high- and low-pressure turbines. A computer simulation of the flow in the GE90 turbofan engine's high-pressure (HP) and low-pressure (LP) turbines was created at GE Aircraft Engines under contract with the NASA Glenn Research Center. The three-dimensional steady-state computer simulation was performed using Glenn's average-passage approach named APNASA. The areas upstream and downstream of each blade row mutually interact with each other during engine operation. The embedded blade row operating conditions are modeled since the average passage equations in APNASA actively include the effects of the adjacent blade rows. The turbine airfoils, platforms, and casing are actively cooled by compressor bleed air. Hot gas leaks around the tips of rotors through labyrinth seals. The flow exiting the high work HP turbines is partially transonic and, therefore, has a strong shock system in the transition region. The simulation was done using 121 processors of a Silicon Graphics Origin 2000 (NAS 02K) cluster at the NASA Ames Research Center, with a parallel efficiency of 87 percent in 15 hr. The typical average-passage analysis mesh size per blade row was 280 by 45 by 55, or approx.700,000 grid points. The total number of blade rows was 18 for a combined HP and LP turbine system including the struts in the transition duct and exit guide vane, which contain 12.6 million grid points. Design cycle turnaround time requirements ran typically from 24 to 48 hr of wall clock time. The number of iterations for convergence was 10,000 at 8.03x10(exp -5) sec/iteration/grid point (NAS O2K). Parallel processing by up to 40 processors is required to meet the design cycle time constraints. This is the first-ever flow simulation of an HP and LP turbine. In addition, it includes the struts in the transition duct and exit guide vanes.

Veres, Joseph P.↗
NASA NTRS1997

Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis

A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.

Swanson, R. C.↗