Search NASA⌕ Search

SEARCH · Search NASA

Results for “scaling methods”

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 19 records

Fractional occupation numbers and self-interaction correction-scaling methods with the Fermi-Löwdin orbital self-interaction correction approach

In this work, we present a new assessment of the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) approach with an emphasis on its performance for predicting energies as a function of fractional occupation numbers (FONs) for various multielectron systems. Our approach is implemented in the massively parallelized NWChem quantum chemistry software package and has been benchmarked on the prediction of total energies, atomization energies, and ionization potentials of small molecules and relatively large aromatic systems. Within our study, we also derive an alternate expression for the FLO-SIC energy gradient expressed in terms of gradients of the Fermi-orbital eigenvalues and revisit how the FLO-SIC methodology can be seen as a constrained unitary transformation of the canonical Kohn–Sham orbitals. Finally, we conclude with calculations of energies as a function of FONs using various SIC-scaling methods to test the limits of the FLO-SIC formalism on a variety of multielectron systems. We find that these relatively simple scaling methods do improve the prediction of total energies of atomic systems as well as enhance the accuracy of energies as a function of FONs for other multielectron chemical species.

fractional occupation number↗

Further evaluation of traditional icing scaling methods

This report provides additional evaluations of two methods to scale icing test conditions; it also describes a hybrid technique for use when scaled conditions are outside the operating envelope of the test facility. The first evaluation is of the Olsen method which can be used to scale the liquid-water content in icing tests, and the second is the AEDC (Ruff) method which is used when the test model is less than full size. Equations for both scaling methods are presented in the paper, and the methods were evaluated by performing icing tests in the NASA Lewis Icing Research Tunnel (IRT). The Olsen method was tested using 53 cm diameter NACA 0012 airfoils. Tests covered liquid-water-contents which varied by as much as a factor of 1.8. The Olsen method was generally effective in giving scale ice shapes which matched the reference shapes for these tests. The AEDC method was tested with NACA 0012 airfoils with chords from 18 cm to 53 cm. The 53 cm chord airfoils were used in reference tests, and 1/2 and 1/3 scale tests were made at conditions determined by applying the AEDC scaling method. The scale and reference airspeeds were matched in these tests. The AEDC method was found to provide fairly effective scaling for 1/2 size tests, but for 1/3 size models, scaling was generally less effective. In addition to these two scaling methods, a hybrid approach was also tested in which the Olsen method was used to adjust the LWC after size was scaled using the constant Weber number method. This approach was found to be an effective way to test when scaled conditions would otherwise be outside the capability of the test facility.

Anderson, David N.↗

Evaluation of Alternative Altitude Scaling Methods for Thermal Ice Protection System in NASA Icing Research Tunnel

A test was conducted at NASA Icing Research Tunnel to evaluate altitude scaling methods for thermal ice protection system. Two new scaling methods based on Weber number were compared against a method based on Reynolds number. The results generally agreed with the previous set of tests conducted in NRCC Altitude Icing Wind Tunnel where the three methods of scaling were also tested and compared along with reference (altitude) icing conditions. In those tests, the Weber number-based scaling methods yielded results much closer to those observed at the reference icing conditions than the Reynolds number-based icing conditions. The test in the NASA IRT used a much larger, asymmetric airfoil with an ice protection system that more closely resembled designs used in commercial aircraft. Following the trends observed during the AIWT tests, the Weber number based scaling methods resulted in smaller runback ice than the Reynolds number based scaling, and the ice formed farther upstream. The results show that the new Weber number based scaling methods, particularly the Weber number with water loading scaling, continue to show promise for ice protection system development and evaluation in atmospheric icing tunnels.

upwind schemes↗

The nonlinear Galerkin method: A multi-scale method applied to the simulation of homogeneous turbulent flows

Using results of Direct Numerical Simulation (DNS) in the case of two-dimensional homogeneous isotropic flows, the behavior of the small and large scales of Kolmogorov like flows at moderate Reynolds numbers are first analyzed in detail. Several estimates on the time variations of the small eddies and the nonlinear interaction terms were derived; those terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, a multilevel scheme which treats differently the small and the large eddies was proposed. Using mathematical developments, estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptive procedure were derived. Finally, realistic simulations of (Kolmorov like) flows over several eddy-turnover times were performed. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.

Debussche, A.↗

Evaluation of Alternative Altitude Scaling Methods for Thermal Ice Protection System in NASA Icing Research Tunnel

A test was conducted at NASA Icing Research Tunnel to evaluate altitude scaling methods for thermal ice protection system. Two scaling methods based on Weber number were compared against a method based on the Reynolds number. The results generally agreed with the previous set of tests conducted in NRCC Altitude Icing Wind Tunnel. The Weber number based scaling methods resulted in smaller runback ice mass than the Reynolds number based scaling method. The ice accretions from the Weber number based scaling method also formed farther upstream. However there were large differences in the accreted ice mass between the two Weber number based scaling methods. The difference became greater when the speed was increased. This indicated that there may be some Reynolds number effects that isnt fully accounted for and warrants further study.

thermal scaling↗

Manual of Scaling Methods

This manual reviews the derivation of the similitude relationships believed to be important to ice accretion and examines ice-accretion data to evaluate their importance. Both size scaling and test-condition scaling methods employing the resulting similarity parameters are described, and experimental icing tests performed to evaluate scaling methods are reviewed with results. The material included applies primarily to unprotected, unswept geometries, but some discussion of how to approach other situations is included as well. The studies given here and scaling methods considered are applicable only to Appendix-C icing conditions. Nearly all of the experimental results presented have been obtained in sea-level tunnels. Recommendations are given regarding which scaling methods to use for both size scaling and test-condition scaling, and icing test results are described to support those recommendations. Facility limitations and size-scaling restrictions are discussed. Finally, appendices summarize the air, water and ice properties used in NASA scaling studies, give expressions for each of the similarity parameters used and provide sample calculations for the size-scaling and test-condition scaling methods advocated.

Bond, Thomas H.↗

Improved Pyrotechnic Shock Scaling Method Based on Shock Response Spectrum and Statistical Energy Analysis

It has been more than forty years since the pyrotechnic shock scaling method was introduced. The scaling method estimates the attenuation of the Shock Response Spectrum (SRS) based on the distance from the source, structural configurations, types of structural joints and interfaces, and intervening structure [1]. The method has been successfully used in the spacecraft community countless times and still is frequently used to develop pyrotechnic shock requirements at various levels of assembly of a spacecraft. However, since the method was derived empirically from a limited set of shock test data [2], the aerospace community has been looking for an alternative approach. In this paper, a computational scaling method based on Statistical Energy Analysis (SEA) is re-visited. SEA is traditionally used as a method for investigating the diffusion of acoustic and vibratory energies of a system at steady-state [3]. Previously, an approach using the SRS as an acceleration constraint condition to the SEA model was introduced to estimate the attenuation from a shock source [4,5]. In the current investigation, additional examples are provided to further validate the approach. In addition, responses in the time domain are produced by the Local Modal Phase Reconstruction (LMPR) approach which was recently introduced to the community [6].

Fernandez, Juan P.↗

Updating and Evaluating Anthropogenic Emissions for NOAA’s Global Ensemble Forecast Systems for Aerosols (GEFS-Aerosols): Application of an SO 2 Bias-Scaling Method

We updated the anthropogenic emissions inventory in NOAA’s operational Global Ensemble Forecast for Aerosols (GEFS-Aerosols) to improve the model’s prediction of aerosol optical depth (AOD). We used a methodology to quickly update the pivotal global anthropogenic sulfur dioxide (SO 2 ) emissions using a speciated AOD bias-scaling method. The AOD bias-scaling method is based on the latest model predictions compared to NASA’s Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA2). The model bias was subsequently applied to the CEDS 2019 SO 2 emissions for adjustment. The monthly mean GEFS-Aerosols AOD predictions were evaluated against a suite of satellite observations (e.g., MISR, VIIRS, and MODIS), ground-based AERONET observations, and the International Cooperative for Aerosol Prediction (ICAP) ensemble results. The results show that transitioning from CEDS 2014 to CEDS 2019 emissions data led to a significant improvement in the operational GEFS-Aerosols model performance, and applying the bias-scaled SO 2 emissions could further improve global AOD distributions. The biases of the simulated AODs against the observed AODs varied with observation type and seasons by a factor of 3~13 and 2~10, respectively. The global AOD distributions showed that the differences in the simulations against ICAP, MISR, VIIRS, and MODIS were the largest in March–May (MAM) and the smallest in December–February (DJF). When evaluating against the ground-truth AERONET data, the bias-scaling methods improved the global seasonal correlation (r), Index of Agreement (IOA), and mean biases, except for the MAM season, when the negative regional biases were exacerbated compared to the positive regional biases. The effect of bias-scaling had the most beneficial impact on model performance in the regions dominated by anthropogenic emissions, such as East Asia. However, it showed less improvement in other areas impacted by the greater relative transport of natural emissions sources, such as India. The accuracies of the reference observation or assimilation data for the adjusted inputs and the model physics for outputs, and the selection of regions with less seasonal emissions of natural aerosols determine the success of the bias-scaling methods. A companion study on emission scaling of anthropogenic absorbing aerosols needs further improved aerosol prediction.

54 ENVIRONMENTAL SCIENCES↗

Scaling Methods for Simulating Aircraft In-Flight Icing Encounters

This paper discusses scaling methods which permit the use of subscale models in icing wind tunnels to simulate natural flight in icing. Natural icing conditions exist when air temperatures are below freezing but cloud water droplets are super-cooled liquid. Aircraft flying through such clouds are susceptible to the accretion of ice on the leading edges of unprotected components such as wings, tailplane and engine inlets. To establish the aerodynamic penalties of such ice accretion and to determine what parts need to be protected from ice accretion (by heating, for example), extensive flight and wind-tunnel testing is necessary for new aircraft and components. Testing in icing tunnels is less expensive than flight testing, is safer, and permits better control of the test conditions. However, because of limitations on both model size and operating conditions in wind tunnels, it is often necessary to perform tests with either size or test conditions scaled. This paper describes the theoretical background to the development of icing scaling methods, discusses four methods, and presents results of tests to validate them.

Anderson, David N.↗

Evaluation of Scaling Methods for Rotorcraft Icing

This paper reports result of an experimental study in the NASA Glenn Icing Research Tunnel (IRT) to evaluate how well the current recommended scaling methods developed for fixed-wing unprotected surface icing applications might apply to representative rotor blades at finite angle of attack. Unlike the fixed-wing case, there is no single scaling method that has been systematically developed and evaluated for rotorcraft icing applications. In the present study, scaling was based on the modified Ruff method with scale velocity determined by maintaining constant Weber number. Models were unswept NACA 0012 wing sections. The reference model had a chord of 91.4 cm and scale model had a chord of 35.6 cm. Reference tests were conducted with velocities of 76 and 100 kt (39 and 52 m/s), droplet MVDs of 150 and 195 fun, and with stagnation-point freezing fractions of 0.3 and 0.5 at angle of attack of 0deg and 5deg. It was shown that good ice shape scaling was achieved for NACA 0012 airfoils with angle of attack lip to 5deg.

Tsao, Jen-Ching↗

Further Evaluation of Scaling Methods for Rotorcraft Icing

The paper will present experimental results from two recent icing tests in the NASA Glenn Icing Research Tunnel (IRT). The first test, conducted in February 2009, was to evaluate the current recommended scaling methods for fixed wing on representative rotor airfoils at fixed angle of attack. For this test, scaling was based on the modified Ruff method with scale velocity determined by constant Weber number and water film Weber number. Models were un-swept NACA 0012 wing sections. The reference model had a chord of 91.4 cm and scale model had a chord of 35.6 cm. Reference tests were conducted with velocity of 100 kt (52 m/s), droplet medium volume diameter (MVD) 195 m, and stagnation-point freezing fractions of 0.3 and 0.5 at angle of attack of 5deg and 7deg . It was shown that good ice shape scaling was achieved with constant Weber number for NACA 0012 airfoils with angle of attack up to 7deg . The second test, completed in May 2010, was primarily focused on obtaining transient and steady-state iced aerodynamics, ice accretion and shedding, and thermal icing validation data from an oscillating airfoil section over some selected ranges of icing conditions and blade assembly operational configurations. The model used was a 38.1-cm chord Sikorsky SC2110 airfoil section installed on an airfoil test apparatus with oscillating capability in the IRT. For two test conditions, size and condition scaling were performed. It was shown that good ice shape scaling was achieved for SC2110 airfoil at dynamic pitching motion. The data obtained will be applicable for future main rotor blade and tail rotor blade applications.

Tsao, Jen-Ching↗

Acoustic Treatment Design Scaling Methods: Overview, Results, and Recommendations - Volume 1

Scale model fan rigs that simulate new generation ultra-high-bypass engines at about 1/5-scale are achieving increased importance as development vehicles for the design of low-noise aircraft engines. Testing at small scale allows the tests to be performed in existing anechoic wind tunnels, which provides an accurate simulation of the important effects of aircraft forward motion on the noise generation. The ability to design, build, and test miniaturized acoustic treatment panels on scale model fan rigs representative of the fullscale engine provides not only a cost-savings, but an opportunity to optimize the treatment by allowing tests of different designs. The primary objective of this study was to develop methods that will allow scale model fan rigs to be successfully used as acoustic treatment design tools. The study focuses on finding methods to extend the upper limit of the frequency range of impedance prediction models and acoustic impedance measurement methods for subscale treatment liner designs, and confirm the predictions by correlation with measured data. This phase of the program had as a goal doubling the upper limit of impedance measurement from 6 kHz to 12 kHz. The program utilizes combined analytical and experimental methods to achieve the objectives.

Kraft, R. E.↗

Poincare-Lighthill and linear-time-scales methods for linear perturbation problems.

For a class of multidimensional linear perturbation problems of considerable significance in applications, the Poincare-Lighthill technique is shown to give first-order expansion terms which grow unbounded relative to the leading term (secular behavior), while the method of linear time scales leads to well-behaved expansion terms. A solvable example is introduced for comparison with the exact solution.

Klimas, A.↗

Performance of the spin-component-scaled methods for energy bands

The performance of various spin-component-scaled parameterisations is examined for the second-order many-body Green's-function [MBGF(2)] calculations of valence energy bands, taking three of the experimentally well-characterised polymers as examples: polyethylene, polytetrafluoroethylene, and polyacetylene. The parameterisations considered are Grimme's original SCS parameter set, Jung et al.'s original SOS set (retaining the opposite-spin component only), Śmiga et al.'s SCS(IP) set (calibrated specifically for ionization energies), and Śmiga et al.'s SOS(IP) set (calibrated for ionization energies with the opposite-spin component only; implicit in the os-D2 model of Opoku et al.). The SCS(IP) and SOS(IP) parameterisations are found to shift both outer and inner valence bands by up to a few electronvolts away from the experimental data. The original SCS and SOS parameter sets do not improve upon, but largely maintain the accuracy of the unscaled MBGF(2) methods. Given that the SOS-MBGF(2) method can be implemented in a quartic-scaling algorithm (for all roots), it is most promising for solid-state applications. Furthermore this observation is consistent with the success of the quartic-scaling GW methods without the vertex correction based on a density-functional theory reference.

Green’s-function theory↗

Acoustic Treatment Design Scaling Methods

The ability to design, build and test miniaturized acoustic treatment panels on scale model fan rigs representative of full scale engines provides not only cost-savings, but also an opportunity to optimize the treatment by allowing multiple tests. To use scale model treatment as a design tool, the impedance of the sub-scale liner must be known with confidence. This study was aimed at developing impedance measurement methods for high frequencies. A normal incidence impedance tube method that extends the upper frequency range to 25,000 Hz. without grazing flow effects was evaluated. The free field method was investigated as a potential high frequency technique. The potential of the two-microphone in-situ impedance measurement method was evaluated in the presence of grazing flow. Difficulties in achieving the high frequency goals were encountered in all methods. Results of developing a time-domain finite difference resonator impedance model indicated that a re-interpretation of the empirical fluid mechanical models used in the frequency domain model for nonlinear resistance and mass reactance may be required. A scale model treatment design that could be tested on the Universal Propulsion Simulator vehicle was proposed.

Clark, L.↗

Acoustic Treatment Design Scaling Methods: Test Plans, Hardware, Results, and Evaluation - Volume 3

The ability to design, build, and test miniaturized acoustic treatment panels on scale-model fan rigs representative of the full-scale engine provides not only a cost-savings, but an opportunity to optimize the treatment by allowing tests of different designs. To be able to use scale model treatment as a full-scale design tool, it is necessary that the designer be able to reliably translate the scale model design and performance to an equivalent full-scale design. The primary objective of the study presented in this volume of the final report was to conduct laboratory tests to evaluate liner acoustic properties and validate advanced treatment impedance models. These laboratory tests include DC flow resistance measurements, normal incidence impedance measurements, DC flow and impedance measurements in the presence of grazing flow, and in-duct liner attenuation as well as modal measurements. Test panels were fabricated at three different scale factors (i.e., full-scale, half-scale, and one-fifth scale) to support laboratory acoustic testing. The panel configurations include single-degree-of-freedom (SDOF) perforated sandwich panels, SDOF linear (wire mesh) liners, and double-degree-of-freedom (DDOF) linear acoustic panels.

Yu, J.↗

Linear regulator design for stochastic systems by a multiple time scales method

A hierarchically-structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems is considered. The controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short period modes of the longitudinal dynamics of the F-8 aircraft.

Teneketzis, D.↗