Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “delta method”

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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Nonlinear structure formation in flat cosmological models

This paper describes the formation of nonlinear structure in flat (zero curvature) Friedmann cosmological models. We consider models with two components: the usual nonrelativistic component that evolves under gravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not clump under gravity, and whose energy density varies with the scale factor a(t) like a(t)(sup -n), where n is a free parameter. Each model is characterized by two parameters: the exponent n and the present density parameter Omega(sub 0) of the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n is greater than 3, and n is less than 3. The case n = 3 is relevant to model with massive neutrinos. The presence of the uniform component strongly reduces the growth of the perturbation compared with the Einstein-de Sitter model. We show that the Meszaros effect (suppression of growth at high redshift) holds not only for n = 4, radiation-dominated models, but for all models with n is greater than 3. This essentially rules out any such model. For the case n is less than 3, we numerically integrate the perturbation equations from the big bang to the present, for 620 different models with various values of Omega(sub 0) and n. Using these solutions, we show that the function f(Omega(sub 0), n) = (a/delta(sub +))d(delta)(sub +)/da, which enters in the relationship between the present density contrast delta(sub 0) and peculiar velocity field u(sub 0) is essentially independent of n. We derive approximate solutions for the second-order perturbation equations. These second-order solutions are tested against the exact solutions and the Zel'dovich approximation for spherically symmetric perturbations in the marginally nonlinear regime (the absolute value of delta is less than or approximately 1). The second-order and Zel'dovich solutions have comparable accuracy, significantly higher than the accuracy of the linear solutions. We then investigate the dependence of the delta(sub 0) - u(sub 0) relationship upon the value of n in the nonlinear regime using the second-order solutions for marginally nonlinear, general perturbations, and the exact solutions for strongly nonlinear, spherically symmetric perturbations. In both cases, we find that the delta(sub 0) - u(sub 0) relationship remains independent of n. We speculate that this result extends to strongly nonlinear, general perturbations as well. This eliminates any hope to determine the presence of the uniform component or the value of n using dynamical methods. Finally, we compute the nonlinear evolution of the skewness of the distribution of values of delta, assuming Gaussian initial conditions. We find that the skewness is not only independent of n, but also of Omega(sub 0). Thus the skewness cannot be used to discriminate among various models with Gaussian initial conditions. However, it can be used for testing the Gaussianity of the initial conditions themselves. We conclude that the uniform component leaves no observable signature in the present large-scale structure of the universe. To determine its presence and nature, we must investigate the relationship between the past and present universe, using redshift-dependent tests.

Martel, Hugo↗
NASA NTRS1997

Kinetics and Thermochemistry of the Br((sup 2)P3/2) + NO2 Association Reaction

A laser flash photolysis-resonance fluorescence technique has been employed to study the kinetics of the Br((sup 2)P3/2) + NO2 association reaction as a function of temperature (259-432 K) pressure (12.5 - 700 Torr), and buffer gas identity (He, Ar, H2, N2, CO2, CF4, SF6). The reaction is found to be in the falloff regime between third and second order over the entire range of conditions investigated. At temperatures below 350 K, the association reaction is found to be irreversible on the time scale of the experiment (approximately 30 ms). At higher temperatures reversible addition is observed, allowing equilibrium constants for BrNO2 formation and dissociation to be determined. Second- and third-law analyses of the equilibrium data are in only fair agreement and lead to the following thermochemical parameters for the association reaction: Delta-H(298) = 19.6 +/- 1.7 kcal/mol, Delta-H(0) = -18.6 +/- 2.0 kcal/mol, Delta-S(298) = 29.3 +/- 4.2 cal/mol/K, Delta-H(sub f)(sub 298)(BrNO2) = 17.0 +/-1.8 kcal/mol(uncertainties are 2 sigma estimates of absolute accuracy). The value for Delta-H(0) determined in this study has been employed to calculate k(sub 0)(sup SC), the low-pressure third-order rate coefficient in the strong collision limit, by using the method of Troe; calculated values of k(sub 0)(sup SC) are inconsistent with experimental results unless Delta-H(0) is assigned a value near the lower limit derived from analysis of the high-temperature approach to equilibrium data, i.e. delta-H(0) approximately equals -16.6 kcal/mol. A potential source of systematic error in the calculation of both k(sub 0)(sup SC) and the absolute entropy of BrNO2 results from the complete lack of knowledge of the energies and degeneracies of the electronic states of BrNO3. The procedure developed by Troe and co-workers has been employed to extrapolate experimental falloff curves to the low- and high-pressure limits. Derived values for k(sub 0)(M,298K) in units of 10(exp -31) cm(exp 6)/sq molecule/s range from 2.75 for M = He to 6.54 for M = CO2; 2 sigma uncertainties are estimated to be +/- 20%. Values for k(sub 0)(N2,T) in units of 10(exp -31) cm(exp 6)/sq molecule/s are 5.73 at 259 K, 4.61 at 298 K, and 3.21 at 346 K; the observed temperature dependence for k(sub 0)(N2,T) is consistent with the theoretical temperature dependence for Beta(sub c)k(sub 0)(sup SC). Values for k(sub infinity)(T) in units of 10(exp -11) cu cm/molecule/s are 2.86 at 259 K, 3.22 at 298 K, and 3.73 at 346 K; 2 sigma uncertainties are estimated to be a factor of 2. Approximate falloff parameters in a convenient format for atmospheric modeling are also derived.

Kreutter, K. D.↗
NASA NTRS1982

Inverting travel times with a triplication

A method based on the use of constrained spline fits is used to overcome the difficulties arising when body-wave data in the form of T-delta are reduced to the tau-p form in the presence of cusps. In comparison with unconstrained spline fits, the method proposed here tends to produce much smoother models which lie approximately in the middle of the bounds produced by the extremal method. The method is noniterative and, therefore, computationally efficient. The method is applied to the lunar seismic data, where at least one triplication is presumed to occur in the P-wave travel-time curve. It is shown, however, that because of an insufficient number of data points for events close to the antipode of the center of the lunar network, the present analysis is not accurate enough to resolve the problem of a possible lunar core.

Jarosch, H. S.↗
NASA NTRS2022

Gaussian Process Regression Method for Costing SmallSat Bus Capabilities

NASA is responding to the growing interest in, andcapabilities of, small satellites for science applications with an increasingnumber and frequency of Announcements of Opportunityfor small satellite space missions. Estimating the probabilitythat these mission concepts will fit within the small cost capsof these opportunities is largely driven by the probability thatone of the burgeoning number of small satellite providers will beable to meet the payload’s accommodation requirements withinthe budget for the spacecraft. JPL has collected a databasecontaining technical specifications and cost of commerciallyavailable Smallsat buses across various vendors. The primarypurpose of the database is for use in JPL’s Team X architecturestudies to inform cost estimates of a spacecraft bus which fitsthe customer’s technical requirements for their payload andmission. Customer needs are often unique and don’t alignperfectly with an off-the-shelf commercial spacecraft bus, whichmotivates the need to develop a cost model across the continuoustechnical parameter space.Al’s Bus Cost Distribution Estimator (ABCDE) uses Gaussianprocess regression (GPR) to predict commercial Smallsat spacecraftbus cost based on a subset of a customer’s technicalrequirements (payload mass, payload power, delta V, pointingcontrol, and downlink rate). GPR is implemented in ABCDE asa Bayesian method which fits an implied multivariate regressionon the technical parameters and uses kriging to intentionally“overfit” the residuals. Overfitting the residuals allows costestimates to collapse in uncertainty closer to the data pointswhile maintaining larger uncertainty intervals in regions of parameterspace with fewer data records. The data used to fit thismodel is sensitive and represents cost estimates for off-the-shelfcommercial buses. GPR simultaneously protects the sensitivityof the database and uses the sparse nature of the database toaccount for uncertainty in cost in a useful way. For a givenset of customer technical requirements, the tool provides a costestimate distribution, the percentiles of which can be interpretedas a confidence level of finding a commercial bus under a specifiedcost cap. ABCDE dramatically pushes the boundaries ofspacecraft cost estimation models due to its Bayesian methodology(accounting for the maximum uncertainty in the underlyingregression), the mathematically advanced kriging methodology,and the novelty of its application in Team X architecture tradestudies.

Austin, Alex↗
NASA NTRS1989

Analysis of leading edge separation using a low order panel method

An examination of the potential flow computer code VSAERO to model leading edge separation over a delta wing is examined. Recent improvements to the code suggest that it may be capable of predicting pressure coefficients on the body. Investigation showed that although that code does predict the vortex roll-up, the pressure coefficients have significant error. The program is currently unsatisfactory, but with some additional development it may become a useful tool for this application.

Sandlin, Doral R.↗
NASA NTRS2003

Real-time three-dimensional color doppler evaluation of the flow convergence zone for quantification of mitral regurgitation: Validation experimental animal study and initial clinical experience

BACKGROUND: Pitfalls of the flow convergence (FC) method, including 2-dimensional imaging of the 3-dimensional (3D) geometry of the FC surface, can lead to erroneous quantification of mitral regurgitation (MR). This limitation may be mitigated by the use of real-time 3D color Doppler echocardiography (CE). Our objective was to validate a real-time 3D navigation method for MR quantification. METHODS: In 12 sheep with surgically induced chronic MR, 37 different hemodynamic conditions were studied with real-time 3DCE. Using real-time 3D navigation, the radius of the largest hemispherical FC zone was located and measured. MR volume was quantified according to the FC method after observing the shape of FC in 3D space. Aortic and mitral electromagnetic flow probes and meters were balanced against each other to determine reference MR volume. As an initial clinical application study, 22 patients with chronic MR were also studied with this real-time 3DCE-FC method. Left ventricular (LV) outflow tract automated cardiac flow measurement (Toshiba Corp, Tokyo, Japan) and real-time 3D LV stroke volume were used to quantify the reference MR volume (MR volume = 3DLV stroke volume - automated cardiac flow measurement). RESULTS: In the sheep model, a good correlation and agreement was seen between MR volume by real-time 3DCE and electromagnetic (y = 0.77x + 1.48, r = 0.87, P <.001, delta = -0.91 +/- 2.65 mL). In patients, real-time 3DCE-derived MR volume also showed a good correlation and agreement with the reference method (y = 0.89x - 0.38, r = 0.93, P <.001, delta = -4.8 +/- 7.6 mL). CONCLUSIONS: real-time 3DCE can capture the entire FC image, permitting geometrical recognition of the FC zone geometry and reliable MR quantification.

Validation Studies↗
NASA NTRS1991

Doppler Global Velocimeter Measurements of the Vortical Flow Above a Thin Delta Wing

A new measurement technique is being developed by NASA to measure off-surface flow fields. This method, Doppler global velocimetry, will allow quantification of complex three-dimensional flow fields at video camera rates. The entire flow field structure within a selected plane is measured simultaneously rather than by scanned, point-by-point measurements using conventional laser velocimetry. Data obtained using this technique will be used to correlate with other data sets for verification, and following verification, provide a quantified, highly detailed definition of the flow field. This will help to improve the understanding of fluid physics, supplement and broaden the database required to validate and refine computational fluid dynamics (CFD) models, and improve aircraft design methodology. To assess the capability of the technique, velocity measurements of the vortical flow field above a thin 75-degree delta wing were made in the NASA - Langley Basic Aerodynamics Research Tunnel. Preliminary comparisons of the results were made with similar measurements obtained using a three component laser velocimeter indicate that this technique is capable of describing the entire three - component velocity flow field simultaneously within a measurement plane in real time.

Usry, Jimmy W.↗
NASA NTRS1987

Velocity selection in the symmetric model of dendritic crystal growth

An analytic solution of the problem of velocity selection in a fully nonlocal model of dendritic crystal growth is presented. The analysis uses a WKB technique to derive and evaluate a solvability condition for the existence of steady-state needle-like solidification fronts in the limit of small under-cooling Delta. For the two-dimensional symmetric model with a capillary anisotropy of strength alpha, it is found that the velocity is proportional to (Delta to the 4th) times (alpha exp 7/4). The application of the method in three dimensions is also described.

Barbieri, Angelo↗
NASA NTRS1990

Application of the LAURA code for slender-vehicle aerothermodynamics

Application of a three-dimensional thin-layer Navier-Stokes code (LAURA) to compute the laminar, perfect gas aerothermodynamics of slender vehicles is demonstrated. Comparison of solutions with experimental data enabled an assessment of the code's aerodynamic heating prediction capabilities. The results show radial grid refinement to a wall cell Reynolds number of 2 to be accurate for predicting aerodynamic heating to a slender cone. Additional comparisons for an 80 deg slab-delta wing and a generic Aero-Space Plane vehicle show the method to be generally accurate using this radial cell spacing. Discrepancies between the predicted and measured heating in a region of crossflow separation on the Aero-Space Plane geometry are noted which indicates the need for further study. While additional applications and comparisons are required to fully test the LAURA program, the results of this study demonstrate the current level of confidence and the engineering utility of this particular code.

Thompson, Richard A.↗
NASA NTRS1993

Computationally efficient algorithms for real-time attitude estimation

For many practical spacecraft applications, algorithms for determining spacecraft attitude must combine inputs from diverse sensors and provide redundancy in the event of sensor failure. A Kalman filter is suitable for this task, however, it may impose a computational burden which may be avoided by sub optimal methods. A suboptimal estimator is presented which was implemented successfully on the Delta Star spacecraft which performed a 9 month SDI flight experiment in 1989. This design sought to minimize algorithm complexity to accommodate the limitations of an 8K guidance computer. The algorithm used is interpreted in the framework of Kalman filtering and a derivation is given for the computation.

Pringle, Steven R.↗
NASA NTRS1993

Parameterization of the radiative properties of cirrus clouds

A new approach is developed for the parameterization of the radiative transfer in the atmosphere involving cirrus clouds. The parameterization scheme integrates in a coherent manner the delta-four-stream approximation for radiative transfer, the correlated k-distribution method for nongray gaseous absorption, and the scattering and absorption properties of hexagonal ice crystal. It was found that the present scheme is well suited for incorporation in numerical models for studies of the climatic effects of cirrus clouds as well as for investigations of interactions and feedbacks between cloud microphysics and radiation.

Fu, Qiang↗
NASA NTRS1996

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

Taylor, Arthur C., III↗
NASA NTRS1997

Gauche Ethyl Alcohol: Laboratory Assignments and Interstellar Identification

Ethyl alcohol (ethanol) is known to possess a pair of closely spaced excited torsional substates (gauche+, gauche-) at an energy of approximately 57 K above the ground (trans) torsional substate. We report an extended analysis of some gauche - gauche+ Q-branch ((Delta)J = 0) transitions with a three-substate fixed frame axis method (FFAM) Hamiltonian. Our approach accounts for complex trans-gauche interactions for the first time. In addition, we are able to obtain intensities for perturbed rotational transitions, and to determine the trans to gauche+ separation to be 1185399.1 MHz. A complete ground state rotational-torsional partition function accounting for the previously neglected gauche substates is presented. Based on our analysis, a total of 14 U lines obtained towards Orion KL can now be assigned to gauche substates of ethanol. Analysis of these lines yields a rotational temperature of 223 K and a total (trans + gauche) column density of 7.0 x 10(exp 15)/sq cm. The column density is in reasonable agreement with the recent value of 2-3 x 10(exp 15)/sq cm based on observations of trans-ethanol by Ohishi et al., although there is some disparity in the rotational temperatures. Eight additional U lines in the literature are assigned to transitions of gauche ethanol.

Pearson, J. C.↗
NASA NTRS2007

Thermal Model Correlation for Mars Reconnaissance Orbiter

The Mars Reconnaissance Orbiter (MRO) launched on August 12, 2005 and began aerobraking at Mars in March 2006. In order to save propellant, MRO used aerobraking to modify the initial orbit at Mars. The spacecraft passed through the atmosphere briefly on each orbit; during each pass the spacecraft was slowed by atmospheric drag, thus lowering the orbit apoapsis. The largest area on the spacecraft, most affected by aeroheating, was the solar arrays. A thermal analysis of the solar arrays was conducted at NASA Langley Research Center to simulate their performance throughout the entire roughly 6-month period of aerobraking. A companion paper describes the development of this thermal model. This model has been correlated against many sets of flight data. Several maneuvers were performed during the cruise to Mars, such as thruster calibrations, which involve large abrupt changes in the spacecraft orientation relative to the sun. The data obtained from these maneuvers allowed the model to be well-correlated with regard to thermal mass, conductive connections, and solar response well before arrival at the planet. Correlation against flight data for both in-cruise maneuvers and drag passes was performed. Adjustments made to the model included orientation during the drag pass, solar flux, Martian surface temperature, through-array resistance, aeroheating gradient due to angle of attack, and aeroheating accommodation coefficient. Methods of correlation included comparing the model to flight temperatures, slopes, temperature deltas between sensors, and solar and planet direction vectors. Correlation and model accuracy over 400 aeroheating drag passes were determined, with overall model accuracy better than 5 C.

Amundsen, Ruth M.↗
NASA NTRS2017

Full-Coverage High-Resolution Daily PM(sub 2.5) Estimation using MAIAC AOD in the Yangtze River Delta of China

Satellite aerosol optical depth (AOD) has been used to assess population exposure to fine particulate matter (PM (sub 2.5)). The emerging high-resolution satellite aerosol product, Multi-Angle Implementation of Atmospheric Correction(MAIAC), provides a valuable opportunity to characterize local-scale PM(sub 2.5) at 1-km resolution. However, non-random missing AOD due to cloud snow cover or high surface reflectance makes this task challenging. Previous studies filled the data gap by spatially interpolating neighboring PM(sub 2.5) measurements or predictions. This strategy ignored the effect of cloud cover on aerosol loadings and has been shown to exhibit poor performance when monitoring stations are sparse or when there is seasonal large-scale missngness. Using the Yangtze River Delta of China as an example, we present a Multiple Imputation (MI) method that combines the MAIAC high-resolution satellite retrievals with chemical transport model (CTM) simulations to fill missing AOD. A two-stage statistical model driven by gap-filled AOD, meteorology and land use information was then fitted to estimate daily ground PM(sub 2.5) concentrations in 2013 and 2014 at 1 km resolution with complete coverage in space and time. The daily MI models have an average R(exp 2) of 0.77, with an inter-quartile range of 0.71 to 0.82 across days. The overall Ml model 10-fold cross-validation R(exp 2) (root mean square error) were 0.81 (25 gm(exp 3)) and 0.73 (18 gm(exp 3)) for year 2013 and 2014, respectively. Predictions with only observational AOD or only imputed AOD showed similar accuracy.Comparing with previous gap-filling methods, our MI method presented in this study performed bette rwith higher coverage, higher accuracy, and the ability to fill missing PM(sub 2.5) predictions without ground PM(sub 2.5) measurements. This method can provide reliable PM(sub 2.5)predictions with complete coverage that can reduce biasin exposure assessment in air pollution and health studies.

PM2.5↗
NASA NTRS1974

Extension of leading-edge-suction analogy to wings with separated flow around the side edges at subsonic speeds

A method for determining the lift, drag, and pitching moment for wings which have separated flow at the leading and side edges with subsequently reattached flow downstream and inboard is presented. Limiting values of the contribution to lift of the side-edge reattached flow are determined for rectangular wings. The general behavior of this contribution is computed for rectangular, cropped-delta, cropped-diamond, and cropped-arrow wings. Comparisons of the results of the method and experiment indicate reasonably good correlation of the lift, drag, and pitching moment for a wide planform range. The agreement of the method with experiment was as good as, or better than, that obtained by other methods. The procedure is computerized and is available from COSMIC as NASA Langley computer program A0313.

Lamar, J. E.↗
NASA NTRS1981

Investigation of aerodynamic characteristics of wings having vortex flow using different numerical codes

The aerodynamic characteristics of highly sweptback wings having separation-induced vortex flow were investigated by employing different numerical codes with a view to determining some of the capabilities and limitations of these codes. Flat wings of various configurations-strake wing models, cropped, diamond, arrow and double delta wings, were studied. Cambered and cranked planforms have also been tested. The theoretical results predicted by the codes were compared with the experimental data, wherever possible, and found to agree favorably for most of the configurations investigated. However, large cambered wings could not be successfully modeled by the codes. It appears that the final solution in the free vortex sheet method is affected by the selection of the initial solution. Accumulated span loadings estimated for delta and diamond wings were found to be unusual in comparison with attached flow results in that the slopes of these load curves near the leading edge do not tend to infinity as they do in the case of attached flow.

Reddy, C. S.↗